
Videnskabsfagsprojekt, 1. modul, Vinter 2012, id:441  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
English abstract
With this project, we try to map the development of the various mathematical definitions of computability and how they converged to the definition we use today. We treat this development as exemplary of the development of new mathematical theories, and attempt to understand which mechanisms are in play, when new mathematics are developed. We do this by giving a historical overview of developments in the theoretical mathematics from Hilbert's problems in 1900 and up to the Church and Turing articles of 1936 and 37. In this overview we try to extract recurring trends, which can help to elucidate the overall issues. As a tool for this we analyse the authors' motivation, distinguishing between intrinsic and extrinsic motivations in relation to mathematics. We conclude that the overall trend in this development was driven by an inner mathematical motivation that had its roots in Hilbert's quest to formalise mathematics at the beginning of the 1900s. The definition of computability arose as part of efforts to resolve the mathematical challenges in this period. However, Turing also considered it vital to analyse how people perform computations and uses this analysis as a basis for the development of the Turingmachine. This approach to computability also contributes to his definition having the greatest impact in subsequent history. In summary, the internal mathematical motivation has interacted with external factors, which has gone on to become important later on. This is not a unique example in mathematics, and shows how the concept of computability can be considered as exemplary for the development of mathematics more generally.
Videnskabsfagsprojekt, 1. modul, Vinter 2012, id:442  
Vejleder:  Mogens A. Niss 
Findes på RUb:  Ja 
Videnskabsfagprojekt, 1. modul, Vinter 2012, id:443  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
English abstract
This project gives an account of the crisis of the foundation of mathematics as it prevailed around 1900. After a brief description of the background for Russell's Paradox we describe selected elements of formal logic in general and propositional logic in particular, of predicative logic, and of naive set theory with a view to understanding in what sense one could speak of a crisis at all. We delineate the basics of the formalisation of axiomatic systems, and in particular we show how Zermelo and later Fraenkel succeeded in formulating set theory in such a way that it was able to serve as a foundation of mathematics. Russell's type theory, which was another attempt at providing a sound basis for mathematics, is described as far as it relates to the handling of the paradox. Finally, we argue that it is only reasonable to describe the situation as a crisis for that branch of mathematics which purports to establishing a foundation of mathematics solely based on logic, without any reference to intuition and without the arbitrariness of axioms.
Integreret speciale  modelbyggervariant, 2. modul, Vinter 2012, id:444  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
Altered levels of the steroid hormone cortisol has been observed in some melancholic depressed patients. The reason for this is not fully understood. The level of cortisol in the blood is regulated by the neuroendocrine system called the hypothalamicpituitaryadrenal(HPA)axis. By proposing mathematical models for cortisol's synthesis and transport in the blood parts of this system are being investigated. For the ACTHinduced cortisolsynthesis is established a comprehensive mechanismbased model. This model can be parted into submodels to investigate specific parts of the cortisolsynthesis. MatLab simulations of a submodel of the activation of protein kinase A (PKA) indicates the occurrence of a maximum activation of PKA, at the total concentration of cyclic adenosine monophosphate being four times the total concentration of the PKA tetrameric. Simulations of a submodel for the system from the concentration of cytosolic cholesterol (CC) to the secretion of cortisol shows that the concentration of cholesterol in the mitochondrial inner membrane and the synthesis of steroids is strongly influenced by the concentration of the cholesterol transport protein StAR and the degree of phosphorylation. Variations of CC are of importance only at concentrations being less than 1000 nM, which is half of the standard concentration estimated in the literature. Furthermore are set up models of activation of melanocortin 2 receptor and cortisol mobilization in the cell cytostol on the basis of the curent knowledge. Simulations of these models, however do not yet show operational results. The model developed in this project for cortisol transport in the blood describes the binding of the hormone to the carrier protein, corticosteroid binding globulin (CBG). Simulations of the model shows that CBG increases the total concentration of cortisol in the blood, while the concentration of cortisol on the free form remains the same. The output of the concentration of free cortisol, however, is at a high level compared with the literature. Changes in the rates of production and of elimination can approximate this picture, but maybe the reason for the high concentrations are to be found in the model's simplified construction, which as an example does not include an exchange of cortisol in the body's tissues.
Modelprojekt, Bachelor. modul, Vinter 2012, id:445  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
The present work is a mathematical investigation of the insulin granule motility and the role of actin filaments in pancreatic (formel)cells. It is supported by numerical analysis based on computer simulations. It appears that one dimensional motion of insulin granules, along micro tubuli and actin filaments, does not favor rapid transportation, which may indicate a mean of exocytosis regulation. Unrestricted random walks in three dimensions due to thermal fluctuations of the cytoplasmic molecules are, mathematically, more likely to transport the granules to the periphery of the cell. These findings are based on a simplified (formel)cell model with neglected chemical, electric and electrostatic forces and are not decisive for the interaction between granules and actin filaments. Lastly, the actin filament network close to the cell membrane is hypothesised to cause a smallscale mass diffusion of insulin granules.
Modelprojekt, Bachelor. modul, Vinter 2012, id:446  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
This project report explores the Slingshot Effect. The Slingshot Effect is an expression of the phenomenon that an object in space can be accelerated by the gravity of a given planet. The study is conducted by setting up a differential equation that describes the movement of a space probe within a solar system encompassing the sun, the Earth, and the space probe itself. The purpose of setting up a differential equation describing this movement is to find explanations that may clarify the ways in which the space probe moves when positioned far away from Earth. The explanations found are functions that describe speed and position over time. Since it is not possible to analytically determine the reciprocal movement of three objects in the future, the mass of the space probe must be considered in relation to the mass of the sun and the mass of the Earth. Upon considering this relation, it becomes evident that the mass of the space probe is very small when compared to the mass of the sun and the mass of Earth, and thus, it can be presumed that the space probe will not affect the sun or the Earth with any given force. As a result, the system encompassing the sun, the Earth and the space probe will not conserve its energy. To provide a critical view on this study of the Slingshot Effect, a system consisting of the space probe and the Earth is defined. From within this system, the Slingshot Effect can be examined, provided that one is at a distance between the sun and the Earth at which the Earth's field of gravity is affecting the trajectory of the space probe. By solving the differential equation explaining the movement of the space probe, and by comparing the results to the theoretical study of the Slingshot Effect, it is examined how exact a study of the Slingshot Effect one can perform. The project report concludes that it is possible to satisfactorily study the Slingshot Effect by setting up a differential equation explaining the movement in a system without energy conservation. The results of the study show that the effect on the Slingshot Effect is less significant than the theoretical effect, and that the desired effect can only be achieved at an unrealistic distance from the centre of the Earth.
Professionsprojekt, 2. modul, Vinter 2012, id:447  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
This report deals with the modelling and simulation of variation in production of natamycin in a bioreactor by the method of mathematical modelling. The report was made in collaboration with the company DuPont who delivered a large amount of data from their 2010 and 2011 batches. The data of each batch was segregated into useful and unuseful data and the useful data was analysed with the purpose of extracting information, revealing patterns and characteristics on which grounds a mathematical model could be built. The mathematical model was constructed not only on these grounds but also on the grounds of the behavioural aspects of the bacterium Streptomyces Natalensis. To account for the observations made in the data analyses multiple models was constructed and tested but only one of them exhibited reasonable behaviour namely the twospecies model (The twophase model also did all right to some extent). The model was validated by checking if there were any discrepancies between the data analysis and the predictions made by the model. The two species model assumed, as the name suggested, that the bioreactor contained two cultures a non producing and producing one. The model contained a set of parameters which was to be determined. By searching in the vicinity of a guess of these parameters the best numerical solution to all batches was found where each batch was allowed to have different starting values. The values of the parameters suggested that the non producing culture was having a significantly bad influence on the producing one as expected. Other than not being able to reproduce some small oscillations in the natamycin concentration the model seemed to do quite well. The concentration of natamycin in the tank was solely determined by the starting conditions of the two cultures. By inspecting the starting values of the two cultures compared to the data for the maximum natamycin production, it was clear that one would like to start with as pure a sample as possible meaning a very low population of the non producers and a high concentration of the producers. The non producing culture was eliminated to see what would theoretically happen to the production. The results showed that the production would reach the same maximum production in less than half the time. The maximum concentration of natamycin was ten times higher than when the nonproducing culture was present. We did not believe that this was realistic because new phenomena which our model could not take into account could start occurring when the natamycin concentration got too high. Multiple suggestions of how to continue this investigation were brought forward in the perspective.
Videnskabsfagsprojekt, 1. modul, Vinter 2011, id:421  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
In our mathematical science project: "Problems vs. Theorems" we try to find the answer to the following question: Is the driving force in mathematics i.e. what shapes mathematics, mathematical problems or mathematical theorems ? We try to answer the above posed question by looking at three cases: Two mathematical problems; a) the quadrature of the circle and b) the trisection of an angle and a mathematical theorem; Bolzano's theorem, where we furthermore in the latter include the Intermediate Value Theorem. In our three cases we consult some mathematicians work on the cases and our time horizon spans from the ancient Greek mathematicians to the 19th century. To decide whether it is mathematical problems or mathematical theorems that are the driving force in mathematics, it is crucial that in trying to solve the case of either: a) the quadrature of the circle and b) the trisection of an angle or c) formulating Bolzano's Theorem and the Intermediate Value Theorem that new mathematics has been produced. The quadrature of the circle has produced the method of exhaustion (a method that later led to our modern day integration in mathematics), a more precise way of calculating (formel) (by the use of the method of exhaustion) and proof that (formel) is transcendent. The trisection of an angle has helped in finding the solution to third degree equations. Bolzano's Theorem and the Intermediate Value Theorem have after they were formalized become pillars in classical mathematical analysis. On the basis of our project section we conclude, that mathematical problems and mathematical theorems both are driving forces in mathematics.
Speciale  formidlervariant, 2. modul, Vinter 2011, id:422  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
English abstract
This project investigates how differential calculus is applied in the subject of mathematics in upper secondary education in Denmark. This includes an investigation of what serves as the deciding factor for teachers when planning the instruction of differential calculus. The report identifies the concepts and competences, as well as interactions between them, as they appear in the curriculum and instructive documents from the ministry. A selection of textbooks undergoes a similar analysis. The results of the analysis are compared with six interviews with teachers (two at each of the three different study programmes offered in upper secondary education). The interviews were carried out using a semistructured method that allows an insight into the interviewee's world. The interviews show that there is a clear consensus that the teaching of calculus requires a focus on reasoning competences, problem solving competences and symbol and formalism competences. On this background it is concluded that the determining factor in relation to the teaching of calculus is the academic level of the students, but it is also influenced by the description of the curriculum, the textbooks in use, the interdisciplinary context and the teacher. There is a contradiction between the teacher's ambition to impart understanding to the students and the teacher's wish for a satisfactory examination result. In the project it is identified that a computer algebra system is not used as a tool to give the students a deeper understanding of differential calculus. This is considered as a potential tool to solve the apparent contradiction between ambition and wish.
Videnskabsfagsprojekt, 1. modul, Vinter 2011, id:423  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
This project deals with the development of the set theory established by the German mathematician Georg Cantor in the late 19th century and particularly focuses on the continuum hypothesis. This conjecture has been puzzling minds since the first publications and expecially since David Hilbert's inclusion of the hypothesis in the list of the most important and potentially influential mathematical problems of the time. This paper covers the evolution of the set theory starting from the origins of Cantor's first works in the set theory up to Ernst Zermelo and his axiomatics, building a base and afterwards trying to establish the role of the continuum hypothesis, it's origin, recognition and influence on the set theory. The existence of the hypothesis apparently has been more important for research in this field than the solution itself. The latter actually has not arrived until 1960s and didn't bring any new insights on the nature of continuum, infinity or the concept of the set. Hilbert's attention to the continuum hypothesis was chosen as a reference point for the project's main question of the continuum hypothesis importance and influence.
Videnskabsfagsprojekt, 1. modul, Vinter 2011, id:424  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
Mathematics is an enormous field with over five thousand different subcategories and with approximately two hundred thousand theorems published each year. Surely the mechanisems behind the development of mathematics must be both complex and diverse. However it is the goal of the report to shed some light on the matter. As a means to reach this goal mathematical problem solving is chosen as area of special interest. In order to evaluate mathematical problems influence on the development of mathematics a precise definition of a "mathematical problem" must first be presented. With the presented definition two problems are chosen as case study, the problems are "the quadrate of the circle" and "the parallel postulate". The problems are then solved and an evaluation of the impact of the problems is sought through an investigation of the works in which the solution to the problem is presented. The results of the investigation is discussed and the problems are found to have an influence on the development of mathematics through motivation and in mathematics, as in many other fields, motivation is of upmost importance.
Professionsprojekt, 2. modul, Vinter 2011, id:425  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
In this project the HPAaxis is modelled, and thus the feedback and feedforward mechanisms between CRH, ACTH, and cortisol, where cortisol provides negative feedback on ACTH and CRH via the glucocorticoid receptors respectively in the pituitari and in the hypothalamus. The purpose of this model is to investigate ultradian pulsatility in the hormone concentrations. This model is based on the model in Gupta et al. (2007), which models the interaction between CRH, ACTH, cortisol, and the glucocorticoid receptors in the pituitary. Walker et al. (2010) have made an extension of this model, in which they justify that the time delay from cortisol is stimulated to it is being released, may be the cause of the ultradian pulsatility. Delay differential equations may have oscillatory behavior, why it is interesting to examine whether other mechanisms than time delay can result in oscillations. Therefore, this projects purpose is to investigate whether other extensions of the model from Gupta et al (2007), can result in oscillations. In this project a model is developed, which models the interaction between CRH, ACTH, cortisol, and the glucocorticoid receptors in the hypothalamus and in the pituitary. The novelty of this model is to include the inhibition of CRH via the glucocorticoid receptors in the hypothalamus. It is assumed, that the inhibition of CRH in the hypothalamus via the glucocorticoid receptors, is in the same way, that the inhibition of ACTH via the glucocorticoid receptors in the pituitary. An analytical and a numerical analysis of the model is made in order to investigate whether the model can result in oscillations. Based on the numerical analysis it is concluded that the model can result in oscillations for certain parameter values. It also shows that the frequency of the oscillations is physiologically relevant. Thus it is concluded that the mechanisms of the project model may be the cause of the ultradian pulsatility.
Videnskabsfagsprojekt, 1. modul, Vinter 2011, id:426  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
In this project we examine the Henstock integral. The integral was first defined by Jaroslav Kurzweil in 1957 and further developed by Ralf Henstock from 1961. The Henstock integral solves some classical integration problems, but has never achieved any greater usage. The Henstock integral expands the definition of the Riemann integral with a gauge funktion. With this little extra you get a theory of integration with obvious advantages. The Henstock integral has no improper integrals, it is able to integrate unlimited functions where Lebesgue fails, and the convergence properties of the Henstock integral are similar to those of the Lebesgue integral. In this project we have defined the Henstock integral on the real line, and compared it to the Riemann integral and the Lebesgue integral. We have also speculated on the lack of usage of the Henstock integral. The conclusion reached: The gauge function is an important improvement over the Riemann integral. Because of the gauge funktion, the Henstock integral obeys one part of the fundamental theorem of calculus without conditions. There are several reasons for the lack of usage of the Henstock integral; but primarily it is due to the fact, that the Henstock integral does not solve any interesting problems, that other integrals theories have not solved already.
Professionsprojekt, 2. modul, Vinter 2011, id:427  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Truncated Singular Value Decomposition (TSVD) regularization method have been used by Zhao et al. {"Kronecker product approximations for image restoration with new mean boundary conditions" (2011), Applied Mathematical Modelling, Vol. 36, pp. 225237}. In this report, I propose an alternative regularization the Tikhonov method. The new regularization method gives better relative error when applied to Kronecker product approximation solutions with mean boundary condition.
Speciale  formidlervariant, 2. modul, Vinter 2011, id:428  
Vejleder:  
Findes på RUb:  Ja 
Videnskabsfagsprojekt, Modul 1. modul, Vinter 2011, id:429  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
This report investigates what motivates Thomas Stieltjes, Henri Lebesgue and Johann Radon to construct their theories of integration. There has both been investigations of the original articles but also of more modern interpretations of these integrals. Not only are the integrals investigated but also theories surrounding the integrals, to place the three discoveries in a historical context and at the same time explains how the three theories are constructed. We find that Stieltjes is greatly motivated by the divergent series. Stieltjes constructs his integral as a generalized form of the Riemann integral to analyse continued fractions in an attempt to shed light on the divergent series. Lebesgue and Radon on the other hand are inspired by the theory of integration itself. They construct their integrals based upon already well established theories. Lebesgue starts by requiring his integral to possess some specific properties and later builds his integral on the bases of his measure theory. Radon generalizes the Stieltjes and the Lebesgue integral with respect to his construction of a (formel)field and measure. We have made a discussion about the different aspect of how mathematics evolve in chapter 8.
Speciale  modelbyggervariant, 2. modul, Vinter 2011, id:430  
Vejleder:  
Findes på RUb:  Ja 
This master thesis researches probabilistic description logics with the aim of showing how the different probability interpretations are reflected in the existing formalisms. As an integrated thesis in Mathematics and Computer Science, this project focuses on the mathematical as well as the conceptual differences between the different probability interpretations first generally, then specifically in probabilistic description logics. Some decidability issues are addressed as well. The thesis centers on one particular article by Tao et al. (2007) as the only one that uses the belieftype probability for terminological axioms such as concept inclusions. Most other research is focused on the frequency interpretation, which is perceived to be more useful, since there is a simple method for acquiring the probability values. The approach of Tao et al. is less popular for practical reasons, however, it can help us fully understand the behaviour of probabilistic description logics. It is my aim to critically investigate this article in detail, fill in the gaps of their explanations and make it accessible for students of Mathematics and Computer Science who are unfamiliar with this topic.
Speciale  modelbyggervariant, 2. modul, Vinter 2011, id:431  
Vejleder:  Stig Andur Pedersen og Anders J. Hede Madsen 
Findes på RUb:  Ja 
In the present thesis, a theory of semantic competence is modeled using tools from epistemic logic. The resulting formal model is used to analyze a problem from the philosophy of language, namely Frege's Dilemma. There are two aims of the thesis: to construct a formal theory of semantic competence, and to show that the formal theory can be used as an useful analytical tool in uncovering the informational structure behind problems from the philosophy of language. The first aim is achieved by, first, deciding for which theory of meaning a theory of semantic competence is wanted. Due to its simplicity, Millianism is chosen. Then various nonformal theories of semantic competence are evaluated with respect to finding one which allows for an objective, intersubjective comparison of competence levels. It is argued that the conceptual theory of (Marconi, 1997) is the best choice: the theory has a clearly defined structure making modeling possible, and is based on empirical studies from cognitive neuropsychology. Following these initial choises, the modeling framework and its philosophical interpretation is presented. The framework used is epistemic logic, and both the propositional and quantified versions are introduced. As a more expressible logical language is required, manysorted quantified epistemic logic is presented, and a novel, general completeness result is shown for manysorted extensions of quantified modal logic. Having thus set the stage of achieving the first aim, a slightly simplified version of the theory of (Marconi, 1997) is modeled. A suitable modelclass is defined and a meaning function is added to capture Millian meaning. Based on the shown completeness result, a sound and complete axiom system is presented, and a logic representing the formal theory is thereby found. The model is then validated. It is shown that both the essential ontological properties as well as the competence types from Marconi's theory are present. It is further shown that the formal counterparts of the competence types from Marconi's theory adhere to the principles dictated by empirical studies. Thereby, the first aim is achieved. To accomplish the second aim, proof of concept is shown. This is done by analyzing an objection to the correctness of the Millian theory of meaning, namely Frege's Dilemma (Frege, 1892). The formal theory is used to analyze both disjuncts of the dilemma, while focusing on the epistemic situation of the agent, i.e. the agent's level of semantic competence. The formal theory of semantic competence allows for multiple notions of semantic competence, each resulting in a unique rendering of the dilemma. Based on these analyses, it it is concluded that once the underlying informational structure of the discussed situations is revealed, neither disjunct proves to be a problem for the Millian theory of meaning. Hereby, the second aim is accomplished. However, I raise an intuitive objection to one of the analyses. It is argued that the objection introduces an unaccounted for parameter, namely contexts. In order to show that this objection is not fatal for the proposed analysis, a chapter is devoted to the construction of a contextual theory of semantic competence. The notion of contexts is incorporated into the models for semantic competence, and the possibilities for finding a complete axiomatic system is discussed, but no completeness result is shown. Therefore, a formal theory, i.e. a logic, for contextual semantic competence is not presented. However, the modeltheoretic machinery is used to reanalyze the problematic case. It is shown that when the situation is modeled in a contextual model, the epistemic analysis of the disjunct again showed the Puzzle about Identity is unproblematic for the Millian view. Overall, the constructed formal theory of semantic competence is shown to elucidate informational aspects of the problems posed to the philosophy of language by Frege's Dilemma. In particular, once the informational structure of the problems is clear, it is shown that each argument is far from being as decisive against Millianism as has been the mainstream view in 20th century philosophy of language.
Videnskabsfagsprojekt, 2. modul, Vinter 2010, id:409  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
The purpose of this project is to investigate how the development of holomorphic dynamics can be viewed in a history of science perspective. The starting point for our investigation is that production of knowlodge in mathematics cannot be explained outside its context. We apply the epistemic configurations developed by the German historian for mathematics and science Moritz Epple to the development of holomorphic dynamics. To produce knowledge one needs to pose questions and questions need to be answered. The term epistemic object is the entity of interest. The mathematician investigates the epistemic object to expand his or her knowledge. The epistemic techniques is the tools he og she applies to provide answers to the questions posed. An epistemic configuration is a constellation of epistemic objects and techniques. We have selected a number of results from the development of holomorphic dynamics. The first period lasts from the end of the 19th century until the mid1920's. Here we have described Koenig's work with local behavoiur around fixed points, the normal families developed by Montel as well as the construction of the sets later on known as the Fatou and Julia sets. The next historic period lasts from the mid1970's to the mid 1980's. We describe Mandelbrot's fractals and a couple of results by Douady, Hubbard and Sullivan. We touch upon the application of quasiconformal maps to holomorphic dynamics. There is at least three different epistemic configurations in the selected research episodes: The local behaviour of dynamic systems, the global behaviour as studied by Fatou and Julia and the global behaviour studied from the end of the 1970's. We discuss the role of the computer in the development of holomorphic dynamics. Our conclusion is that the use of computers cannot be directly regarded as an epistemic technique. The computer has however played an important role as a tool for visualisation. It has also been applied to considering objects of interest and foster further understanding.
Modelprojekt, 2. modul, Vinter 2010, id:410  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
We look at social force models as a way to model the behaviour of human crowds, in order to evaluate how well these types of models simulate crowd behaviour, and what the models' strengths and weaknesses are. In order to do this evaluation, we implement a computer simulation of an exemplary social force model. In order to create this simulation, we pick an exemplary model that is well described in the article that presents it, and analyse it in detail, filling in details from other articles when necessary. Based on this analysis of the model, we go from the abstract model formulation to a concrete numerical simulation by filling in required details, sucs as how to approximate the movement of pedestrians, how to set initial conditions and values, and how to implement the interaction between pedestrians and walls in practice. From our results, it is clear that our simulation (with the right parameters) exhibits reasonable pedestrian behaviour upon visual inspection. While we successfully replicate some results from the litterature, other effects do nok manifest themselves. We discuss several resons for this discrepancy, including features that are missing from the model, parameter values, effects of using random numbers to generate the initial conditions and possible errors in our implementation of the model. Based on the results of our own simulations and our review of the social force modelling field, we assess social force models and their strengths and weaknesses. We conclude that social force models are not based on any theories for the behaviour of crowds, but are created to replicate a set of observations. As such, any confidence in their productions must come from a record of producing results fitting observations; and since the field is relatively new, they have not yet reached this state. Social force models do, however, provide a practical way to simulate something that would otherwise be impossible to simulate. As such, they are the best available way to provide e.g. guidance when designing facilities that must accommodate many pedestrians, and given time the accuracy of their predictions will probably increase.
Videnskabsfagsprojekt, 2. modul, Vinter 2010, id:412  
Vejleder:  
Findes på RUb:  Ja 
English abstract
The project provides with Wessels and Argands mathematical treatises a vision of how geometric representation is used as leverage for the existence of the complex plane and whether the complex numbers can be said to be in a sense a Kuhn's revolutionary discovery. Initially there will be a review of the modern definition of complex numbers. Taken in answering the problem formulation based on a comparative analysis of Wessels and Argands geometric works with the complex plane. It is concluded that the objectlevel manages the complex plane to dissolve the anomaly as the complex numbers has hitherto been, but at the metalevel requires acceptance of the complex numbers a change in the understanding of mathematics subject area, which implies a paradigm shift from platonic to formalist understanding of mathematics.
Modelprojekt, 1. modul, v2009/10, id:397  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
This project is based around the analysis of a mathematical description of V. cholerae epidemics in cities connected by a river system. The stability analysis is descriped step by step to give the reader a thourough understanding of the material. A Matlab package has been coded and is included in full in the appendix. The program is explained superficially in the project. The usefulness of the modelis discussed in regards to the parameters needed, and the results reaced by an artificial scenario calculated by the program. It becomes evident that there are some problems withe the current model, due to several parameters that needs to be calibrated to specific outbreaks after they occur. This is mainly caused by a lack of understanding of the bacteria. Some problems concerning the calculations in Matlab are uncovered, which will result in an error that grows over longer timespans.
Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:448  
Vejleder:  Anders J. Hede Madsen 
Findes på RUb:  Ja 
English abstract
In the present report we investigate the extent to which primary school and high school math teaching follows the idea of the genetic method and the advantages and disadvantages of this method. We do this by focusing on what we believe is a representative example, the notion of function. In the study we are therefore explaining the historical development of the concept of functions through historical literature, then we through educational materials explain how the learning development in relation to the notion of function is in primary and high school. We analyze the learning process based on Sfards (1991) model of mathematical concept formation, and analyze the use of mathematics history as a means generally from Jankvists (2007) framework of methods and objectives of mathematics history in the classroom. We conclude that educational curricula in primary and high school in part follows the idea of the genetic method, but not consciously. We also conclude that there is some learning benefits of teaching by the genetic method, but that it should not stand alone, as the method does not include an explicit requirement for mathematics history as a goal, which we consider necessary.
Speciale  formidlervariant, 2. modul, Sommer 2013, id:449  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:450  
Vejleder:  Anders J. Hede Madsen 
Findes på RUb:  Ja 
English abstract
The objective of this project is to investigate influences from people and historical events which had an impact on Riemann's work and mathematical results. Also the importance of the Riemann hypothesis in the world of mathematics in the years after 1859 and up to date has been subject of research here. Leonhard Euler was the first mathematician to eventually conquer the Baselproblem. This achievement was followed by the formula to determine (formel). But the most valued contribution was probably his ingenious rewriting of the series expression of the Zeta function as an infinite product containing the primes. Riemann's 1859paper is a sketchy presentation of seminal ideas and applications in the area of analytic number theory and complex analysis. Results are submitted without rigor and without formal proos. The article was not prepared for publication, in the same manner as earlier published articles. In the project we describe the first results, mentioned in the article. As a consequence of the Riemann araticle the first major result was the proof for the prime number theorem in 1896. In historical perspective a large part of the work solving the Riemann hypothesis is concentrated on calculating zeros of the zeta function. With the invention of the computer the calculation of zeros were improved considerably. These calculations has not determined the status of the hypothesis, but much of the progress has been prosperous in other fields of mathematics. We conclude that even though the Riemann hypothesis remains unsolved, it has been greatly influential on mathematics in many fields.
Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:451  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:452  
Vejleder:  
Findes på RUb:  Ja 
English abstract
Based on the scientific theories developed by Popper and Kuhn, we analyze and discuss the creative steps in mathematical proofs seen from the point of view of Lakatos "Proofs and refutations" using two cases, one by Gauss and one by Huygens. In both cases there are clearly creative steps present. We conclude that using RUCs competence "flower" and "The Creative/Reproductive cycle of Mathematics" we will beneficially be able to use experimental and creative steps in proofs as a way of developing mathematical skills as an integrated part of teaching mathematics.
Modelprojekt, Bachelor. modul, Sommer 2013, id:453  
Vejleder:  Mogens Allan Niss 
Findes på RUb:  Ja Ja 
English abstract
This paper details a study of the distinction between prescriptive and descriptive elements in mathematical modelling. Through preliminary definitions of prescription and description we thoroughly analyse the modelling process in four specific cases: Optimization of a can, the Gini coefficient, mandate allocation methods and perspective drawing. We identify where in these processes prescriptions and descriptions, respectively, are made and examine how they shape the particular model and its use. Finally we argue that our preliminary definitions are reasonable and conclude that it is definitely prudent to distinguish between prescriptive elements and descriptive elements in both the modelling process and in the use of models of a mathematical nature.
Professionsprojekt, 2. modul, Sommer 2012, id:432  
Vejleder:  
Findes på RUb:  Ja 
The paper discusses the possibility of improving the teaching of mathematics in the Danish high school by changing the educational practice from a monologuebased dominated communication towards a higher degree of dialoguebased communication in the class room. The paper therefore examines the understanding of dialogue and the increase of user involvement in the class room. The discussions in the paper are based on a case study of a teaching in descriptive statistics in level c in a Danish high school class. The paper builds on a dialogical perspective in the analysis of the interaction between students and teacher based on the theory and methods developed by the Norwegian teacher Olga Dysthe, and it tries to identify attitudes and learning strategies that can be used to improve the learning and teaching of mathematics.
Professionsprojekt, 2. modul, Sommer 2012, id:433  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
In this project, we investigate geodesic motion on high dimensional manifolds, in an attempt at creating a caricature model which may help in the understanding of fluid dynamics. For such systems of (formel) particles in (formel), it is possible to interpret this as a manifold (formel), defined such that the potential energy will be constant at every point, which gives rise to the (formel)dynamics. By using an algorithm from (7), which allows only geodesic motion, it is possible to move around on a manifold (formel). Because of energy barriers the system will waggle in the neighbourhood of an especially stable point (formel) for a long time, before it changes position very fast to another stable point (formel). Because of our interest in the geometric structure of (formel), we are construction a family of manifolds (formel), in an attempt to capture the characteristics movements on (formel). To understand the structure of (formel), we investigate different relations between (formel) and (formel) analytically, and by use of the geodesic algorithm. We investigate a hypothesis saying that, a simply connected surface can possess the physical characteristics, that are observed on the manifold (formel) alone by adjusting the number of dimensions, (formel). By doing a series of computersimulations we show that this is not the case. When adjusting the parameter (formel) after (formel), it is showned, that it is possible to change the topology for (formel). By making this topology change we get the behavior we were looking for. This indicates that (formel) can work as a caricatur model for fluid dynamics, and in that way help getting a better understanding of configurational properties of fluid behavior.
Speciale  formidlervariant, 2. modul, Sommer 2012, id:434  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
In the year of 2005, a new reform of the upper secondary school in Denmark was introduced. The purpose of the reform was, among other things, to implement new interdisciplinary subjects and to introduce new interdisciplinary requirements. The master thesis at hand examines how interdisciplinarity between mathematics and social studies has been practiced during the latest years as a result of the new reform. The first part of the thesis looks back upon earlier reforms to search for interdisciplinary options and later compares these options to the structure of the new 2005reform, where new study areas and interdisciplinary constructions have been introduced. Afterwards, the thesis makes a theoretical description of how interdisciplinarity is viewed and the meaning of closely related concepts. For the study it has been necessary to establish a theoretical framework for the use of analysis of the collected empirical data. The second part of the thesis starts out with an analysis of 23 specialized study projects in mathematics and social studies. Subsequently, a collection of 18 math and social study teachers coming from four different schools have been interviewed. Both analyses show a relatively small amount of interdisciplinary courses between the two subjects, and that the cooperation from the beginning has run into some difficulties that still call for improvements. A common directedness of both subject groups towards more and better cooperation, and a search for exemplary topics and issues, that are being tested regularly, and finally, a good policy for professional development is absolutely necessary, if the major goal is to get the students to see possibilities in interdisciplinary work between math and social studies. If all of it or at least some of it is successful, the chance that more students choose the combination of the two subjects for their specialized study project will improve.
Videnskabsfagsprojekt, 1. modul, Sommer 2012, id:435  
Vejleder:  
Findes på RUb:  Ja 
English abstract
The aim of this report is to investigate which role mathematic experiments  "experimental mathematics" has played in the development of mathematic theories in selected cases from the first half of the "Modern Mathematic" period. This is done through a literature survey of the following two cases:  Euler's solution of "The Basel Problem"  Gauss's work on the ArithmeticGeometric Average At first there is given a review of the two cases. Afterwards the cases are analyzed and discussed from a "experimental mathematic" point of view using the analysis method Epistemic configurations. Based on the results from the analysis and discussions of the two cases it seems clear that the conjectures proposed by Euler and Gauss based on their mathematic experiments, was the germ and clue for the development of their mathematic theory in the two cases. It is concluded that "experimental mathematic" has played a key role and hereby had crucial significance for the development of the mathematic theories in the two cases.
Speciale  formidlervariant, 2. modul, Sommer 2012, id:436  
Vejleder:  Uffe Thomas Jankvist 
Findes på RUb:  Ja 
English abstract
Videnskabsfagsprojekt, 1. modul, Sommer 2012, id:437  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
This project is based on the article "Natural immune boosting in pertussis dynamics and the potential for longterm vaccine failure", which puts the modeling of whooping cough (Pertussis) and the associated obstacles in focus. The motivation of the project is based on the problems that arise from the model presented. The purpose is to depict the differences that occur in variations of mathematical systems. This is done by analyzing and interpreting this model, as well as a simpler model, and then comparing the solutions for the two. From the analysis, an insight to the theoretical and mathematical description of spread and contamination patterns has been obtained. The two models are then compared to each other. The intention is to reveal the consequence of expanding upon a compartment model, and thus the system of differential equations. The two models display a different level of detail which is reflected in the associated analysis. The simple model is a Measles model, and the pertussis model has the higher degree of detail. The analytic methods applied when describing the systems of differential equations appear to have a limited use in the expanded system. This leads to mathematical complications. In order to approach these problems, other mathematical tools are applied, such as change of basis and decrease in dimensions. Thus standard solution models can be reapplied.
Videnskabsfagsprojekt, 1. modul, Sommer 2012, id:438  
Vejleder:  
Findes på RUb:  Ja 
English abstract
In this project we investigate whether or not there excist correlations for a beadspring model of a polymer melt. This project used computer simulation to investigate whether there were correlations between the virial and the potential energy. We conclude that there are no correlation for this type of molecular pair potential and the corresponding molecular virial. We conclude the project by presenting a model system, which presumably would have such correlations.
Speciale  formidlervariant, 2. modul, Sommer 2012, id:439  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
This project is about how students handle assignments in modelling. The project is based on three different junior classes in STX and HF. Each class gets four different assignments in random order. The assignments are designed in such a way, that the students, at least get through the systematization and mathematization of the mathematical modelling cycle, that the students should be able to solve the assignment in less than an hour, and that the students should use different mathematical competences and modelling competence in solving the assignments. During the assignments the students will be observed relative to how they solve the assignments. The observations will be analysed relative to the modelling cycle, implemented anticipation, the didactial contract of Brousseau and the sociomathematical norms of Yackel and Cobb. This project concludes, that the students have the most difficulties with the systematization, mathematization and the validation of the modelling cycle. Specifically the students have problems with making assumptions, representations of data, making the model and the validation of the model. The project also concludes, that the students have many difficulties with implemented anticipation in the systematization and mathematization. When the students come to a problem in the assignments of modelling, it can be concluded, that the students search for a specific answer from the teacher or they choose an easier solution to the assignment.
Professionsprojekt  formidlervariant, 2. modul, Sommer 2012, id:440  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, Sommer 2011, id:413  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
This report presents the idea for neurophysiologic functional similarity between algebra and geometry. I begin with a short historical overview on the subject accomplished by three mathematical proofs illustrating my hypothesis. Next, I discuss the neurophysiologic aspect of the problem emphasizing on clinical cases which demonstrate the functional link (between algebra and geometry) in the human brain.
Modelprojekt, Bachelor. modul, Sommer 2011, id:414  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
This project is about mathematical models and the spread of cervical cancer. Cervical cancer develops from the human papillomavirus (HPV), which is a collection of nearly 200 different viruses that causes everything from warts on the feet to cervical cancer. There has in recent years been much focus on cervical cancer, partly because it's one of those cancers, which it is actually possible to limit the spread off in several ways. From a mathematical point of view, it is of particularly strong interest to develop mathematical models that can predict the development of cervical cancer, and assist in a more focused development of screening and vaccination programs. Although it is possible to get the vaccine against HPV 16 and 18, which causes most of the cases of cervical cancer, modeling results shows that there is still a need, for screening programs to catch those cases the vaccine fails to prevent. I have in this project looked at one article RUC project from 2010 both of which have mathematical models for the spread of cervical cancer, as well as looked at the effect of a vaccination program. Our main conclusion is that, it does have a small benefit to vaccinate men, however it is rather marginal, and it would be preferable to instead use the cost of this on other kinds of treatment.
Modelprojekt, Bachelor. modul, Sommer 2011, id:415  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
Speciale  formidlervariant, 2. modul, Sommer 2011, id:416  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
English abstract
The aim of this thesis is to investigate the potential benefits of including history of mathematics in the teaching of mathematics in the Danish upper secondary school. More specifically the research has been focused on, whether history of mathematics can be used (1) to support students' understanding of mathematical concepts; (2) to develop students' mathematical competencies and overview and judgement regarding mathematics; (3) to uncover metadiscursive rules in order to have students reflect upon them. The heart of this work has been the design and implementation of a teaching unit in the history of mathematics in a second year class in a Danish upper secondary school coupled with the analysis of the data material collected during the implementation of the teaching unit. Both the design of the teaching unit and the analysis of the data material are founded on general theories of the didactics of mathematics as well as theories specifically focused on the use of history of mathematics in the teaching of mathematics. The conclusion of the research is that history of mathematics can be used as a means to detect problems in students' understanding of functions. Regarding the students' understanding of mathematical concepts, mathematical compentencies and overview and judgement regarding mathematics the research shows, that history og mathematics can be used to challenge these aspects of the students' understanding of mathematics. Regarding the metadiscursive roles history of mathematics can be used to facilitate the students' explicit reflections upon such rules and to get an insight into some of the students' own metadiscursive rules.
Speciale  formidlervariant, 2. modul, Sommer 2011, id:417  
Vejleder:  
Findes på RUb:  Ja 
English abstract
This master thesis is motivated by the fact that examples often are used to ease the teaching and learning of mathematics. On this basis it is investigated what the functions and importance of examples when teaching and learning mathematics is, and whether it is possible based on didactics of mathematics to design examples which supports student's learning of mathematical concepts. The thesis has found that there has not been conducted research on this topic within didactics of mathematics. On the other hand, within the field of psychology of learning there has been conducted research on "learning by induction" and "learning by examples". These research have been uncluded in this thesis to illustrate to what extent "learning by examples" has been researched before. Furthermore, it has also been necessary to define when something can be defined as an example. The thesis has included a wide range of theories from the didactics of mathematics. The purpose of these theories is to provide a basis for designing a course, and particularly for designing mathematical examples. There are a total of four different courses designed for four different high school classes, respectively, an Alevel class and three Blevel classes. Each of the courses spans for two days with a total of 4 lessons, and each course deals with a different mathematical topic. The courses have been implemented and executed, and it is the collected data that serves as the underlying for the analysis and discussion. The thesis concludes that it is possible to design examples that supports the student's learning of mathematical concepts based on theories from the didactics of mathematics. At the same time, it is not possible to design examples without also designing the context in which they occur, and in this context the learning objective becomes particularly important. It can also be concluded that it is not possible to design examples that support reification, but that it instead is possible to design examples that have a reification potential. Furthermore, it can be concluded that examples are essential for the teaching and learning of mathematics. Regardless of how the examples are designed, they will always shape the student's learning, by for example managing the learning focus among other things. Examples quickly become the subject of a teacher's teaching, and it is possible with examples to promote specific learning goals. As such, it becomes important for the teacher to be able to design and analyze examples in a way that ensures the use of examples that promote the appropriate learning objectives. Failing to use the "right" example for a specific learning objective, may result in a derailment of the intended learning process.
Videnskabsfagsprojekt, 1. modul, Sommer 2011, id:418  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
The history of the vectors in the Danish gymnasium from 1900 to 2005 has been elucidated through this project. The rapport gives an introduction to three mathematical philosophies: Logicism, Formalism and Structuralism, and to the historical development of vector and vector space. Furthermore, the historical development of vectors will contain a review of the three different ways vectors can be considered: a geometrical, a physical and a mathematical structure. A short introduction to didactics and the gymnasium reforms in the 1900's will be made too. The central point of the project is the analysis of the vectors in the gymnasium mathematical educations through the 1900 century. The period will be devided into 4 smaller time frames: 19001935, 19351959, 19601990 and 19912005. In these periodes characteristics of the time will be reviewed, the relevant law changes will be clarified and mathematical books and exam questions will be exemplified. The rapport illustrates the difficulties when vectors were implemented in the gymnasium. From the start, in the physic education; followed by the introduction into the mathematical education first with physical examples, later as a mathematical structure and today as some kind of geometrical unit. The introductions of vectors were partly driven by society and the technological development, partly by prominent people who recognized the importance of vector mathematics.
Speciale  modelbyggervariant, 2. modul, Sommer 2011, id:419  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
In this thesis a model of the baroreflex as presented in Ottesen and Olufsen 2010 is modified and later optimized against experimental data. It is investigated if the model can describe the experimental data, the answer is inconclusive. The model takes the change in pressure as an input and provides a heart rate as output. In the thesis the model is made dimensionless and the original models discrete time delay funktion is replaced by a distributed delay function. The experimental data originates from a series of HUTexperiment sessions on a group of test persons, young healthy men in their mid twenties. The HUTsessions exposed the test subjects to a consecutive series of five HUT's. The first of the five HUT's took place after an injection with saltwater (placebo), and the following four HUT's each took place after an atropine injection. The mathematical model is optimized on data from a series of HUTexperiments on the test subject referred to as Jens. The model is solved using the CVODES solver, which applies a variable order and variable step size implementation of the backwards Difference method. The sensitivity analysis performed to lock parameters of the model is a direct method that runs parallel with the BDF method. The parameter estimation method is a Metropolis Markov Chain Monte Carlo method (MCMC). The model fits reasonably well on data from Jens held in supine position after the saltwater injection, and the parameters found by MCMC are not physiologically unreasonable. The parameter values are used as an initial guess for a model describing Jens during a tilt. This procedure of sensitivity analysis followed by MCMC optimization and then applying the most likely parameters as initial guess for the following experiment are repeated for all 5 tilts. None of the heart rate data in the tilts are captured well by the optimized parameters which attain physiologically unrealistic values. Another model optimization is done on a HUTexperiment on the test person Danny. The optimization attempts to fit parameters to a pre tilt supine phase, a tilt up phase and an upright phase. The optimization produces poor fits. Due to physiologically confusing behavior in pulse data of the test persons compared to measured pressure data. And the fact that the model at several of these points produces qualitatively more meaningful ouputt, it is concluded that more investigations on other HUT data must be undertaken in order to give a conclusive answer to the problem statement.
Videnskabsfagsprojekt, 1. modul, Sommer 2011, id:420  
Vejleder:  Carsten Lunde Pedersen 
Findes på RUb:  Ja 
English abstract
The report deals with the historic development of two mathematical concepts, distributions and currents, which were formalised in the period 19301955 by respectively Laurent Schwartz and George de Rham. The basis for this is that the two theories have faced different faiths. The theory of distribution has become a well known mathematical concept, whereas currents is almost unknown. This happened in spite of the fact that currents acts as a generalization of distributions. The main aim of this report is to clarify the reasons why distributions is a well known part of mathematics today, and likewise to study why current, in spite of it beeing a generalization, is almost unknown. To create an overview of the historic development, the work of Moritz Epple, called epistemic configurations, is used. It basicly gives a good way to clarify what mathematical issues layed the basis for the reason to develop a mathematical theory and likewise which already known parts of mathematics were used to develop it. In the review of the historical development there are different indications why distributions became a known theory. Amongst some of these things is that the theory of distribution acted as the main object for Schwartz to work with and also he was able, in a very short span of time, to formulate a great part of the theory. Also his ability to be very determined of answering relevant questions were some of the reasons. Beside this it is argumented that the level of complexity of the theory is low, combined with the fact that the theory gives a rigorous use of the (formel)distributions, makes it suitable and interesting for people who are not working with mathematics as their principal interest. In the review of the historic development of theory of currents there are indications to why the theory never became popular. The theory of currents was not the main subject of de Rhams work. Also a period of fifteen years pas by from de Rham first introduction of currents, which had some defects, and to his final formalization, which acted as a generalization of distributions. It is argued that this time span had an influence on the spread of currents. Besides that, it is assessed that the foundations of currents and distributions are to different, to let the fact that current generalizes distributions be of any real importance.
Integreret speciale, modelbyggervariant, 3. modul, Sommer 2010, id:407  
Vejleder:  
Findes på RUb:  Ja 
English abstract
Bachelorprojekt, 1. modul, Sommer 2010, id:408  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
The protein code has an enormous storage capacity which, cannot be entirely covered by even the most complex living organism known to mankind. This report focuses on generative stochastic models for protein synthesis that can be tested mathematically. I analyze the sparseness of the protein code, generated by these stochastic models, using three different methods: histograms, analysis of not present patterns, and eigenanalysis also known as spectral analysis. I test eight stochastic models, every one having different level of complexity, in order to determine which one approximates most the biological data. I found solid evidences that one of these models outperforms the rest by having the best approximation among them. Unfortunately the complexity of this model prevents it from eigenanalysis and because of this no conclusive answers can be provided.
Speciale modelbyggervarianten, 2. modul, 2014, id:411  
Vejleder:  
Findes på RUb:  Ja 
English abstract
The purpose of this thesis is to investigate how the spectral signal from an agricultural field is influenced by the vertical distribution of chlorophyll through the canopy. In particular it is examined whether a uniform vertical distribution of chlorophyll improves the results of two types of models using satellitebased remote sensing data. Analysis of variance and simple linear regression is used to characterise the vertical chlorophyll profile in a canopy for field plots in five different European countries with a variety of crops. Out of a total of 68 fields, 28 fields are found to be characterised by a uniform vertical chlorophyll distribution while 16 fields have either a decreasing or increasing vertical distribution of chlorophyll. The vertical chlorophyll profile for 6 fields cannot be characterised by either of these models. 18 fields are not classified as observations lack homogeneity of variances. Biophysical conditions can be estimated by an empiricalstatistical model where spectral vegetation indices are related to field measurements of biophysical variables such as leaf area index (LAI) or leaf chlorophyll content. The empirical relation cannot be generalised as it depends on crop species, context and time. A physicallybased model such as PROSAIL can be used to estimate biophysical variables. PROSAIL uses input regarding the geometry and architecture of the canopy as well as leaf pigment content to simulate the spectral signal. The Matlab code for PROSAIL was adjusted to compensate for an error in the implentation of the ellipsoidal leaf angle distribution. Simulated reflectance data is used to evaluate the sensitivity of the vegetation indices. They are shown to be responsive of changes in leaf angle and LAI and the chlorophyll index in particular is shown to be sensitive of the leaf chlorophyll content. The empirical relation between the vegetation indices and LAI as well as (formel) is improved for fields with a uniform vertical chlorophyll profile but remains highly contextdependent. PROSAIL is used to simulate the reflectance from a number of Danish wheat and barley fields from 2008 and 2009. The deviation between measured and simulated reflectance is evaluated in relation to LAI, plant type, landscape and vertical distribution of chlorophyll. It is shown that the deviation regarding red reflectance is influenced by the vertical chlorophyll profile, however, the simulation of reflectance of visible light is generally improved at low LAI. The simulation of near infrared reflectance is improved at higher LAI levels.
Professionsprojekt formidlervariant, 3. modul, 2014, id:456  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
The purpose of this report is to examine how to mathematically describe probability and how to qualitatively interpret the concept of probability in relation to such a mathematical theory. The mathematical part of the study is carried out on the basis of Kolmogorov's "Grundbegriffe der Wahrscheinlichkeitsrechnung" (1933), as it is the most recognized and applied mathematical theory in the field. Since there still exists widely disagreement about how probability can be understood qualitatively, the interpretive part of the study is based on a variety of interpretations: the classical interpretation, the frequency interpretation, the propensity interpretation, the logical interpretation and the subjective interpretation. The report will firstly examine the historical development of the concept of probability from antiquity to present day. Afterwards the axioms of "Grundbegriffe" as well as some of the key theorems will be presented. Finally, the different interpretations and their relation to the mathematics will be presented and analyzed. It is concluded that the Kolmogorov axioms are succesful because of their simple structure and their usefulness in specific situations, while they simultaneously avoid dealing with the interpretation of probability. At the same time, it is estimated that there are no perfect interpretation models of probability, but the frequency interpretation provides a viable tool for scientific use.
Modelprojekt, 1. modul, 2014, id:468  
Vejleder:  
Findes på RUb:  Ja 
English abstract
The main focus of this article is to observe and describe how a population will change in time as a function determined by another population. More accurately there has been constructed a simple and a modified dynamical system used to describe the change in the number of users on facebook on both PC and Mac as a function of time. The simple model (formel) simply says that either you already have facebook  or you do not. If you do not, you are in a population where everyone without facebook has the same probability of creating an account on facebook  the only difference is whether you own a PC or a Maccomputer. If you already have facebookaccount, you have the same probability of deleting your account as the other users on your given system. This results in a state of equilibrium. When analyzing the parameters it became obvious that the rate of people deleting facebook will determine the number of constant users, while the rate of people signing up will determine how fast you reach the equilibrium. The modified model (formel) is essentially the same. It, however, has one small factor changed: Once you have deleted your facebook account, you will not be interested in signing up again. This small change alters the entire result as there no longer will be a state of equilibrium. The amount of facebook users will climb to a global maximum before declining slowly  but steadily. There will still be new people creating accounts, but it cannot match the amount of profiles being deleted. It has been impossible to get accurate parameters  which is why they have been determined as good as was possible. This, however, means that the graphs and predictions might not be accurate, but they should still give a good indication of how the amount of facebook users should climb and fall as time goes by. Essentially facebook will eventually lose popularity if this model has a shed of truth in its prediction. The only question remaining is how long facebook can remain the monarch of social media and who will eventually take over.
Fagmodulprojekt, 1. modul, 2014, id:469  
Vejleder:  Kenneth Hagde Mandrup Nielsen og Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
The basis of the project is in a mathematical model made by Behn et al. (2001). The model describes differentiation of the immune systems Thelper cells. The model can be used to predict the development of allergic reactions. The purpose of the project is to determine the conditions for other immunological processes, named backgroundcytokines. In the analysis the assumption that background cytokines has only a little effect on the Thelper cells differentiation is viewed critically. This is done by making a stability analysis of the model for varying concentrations of background cytokines. The stability analysis showed a change in the stability of the equilibrium points for high concentrations of background cytokines. The model in Behn et al. (2001) can be used to describe the differentiation of Thelper cells and the development of allergic reactions for concentrations of backgroundcytokines under 10.
Speciale, 3. modul, 2013, id:454  
Vejleder:  
Findes på RUb: 
English abstract
Queueing delays are a potentially significant source of latency in modern computer networks, especially when links come under load. This phenomenon has been coined bufferbloat; and controlling queueing in intermediate gateway devices plays an important role in mitigating it. This thesis seeks to gain further insight into the behaviour of queueing in networks, using the Linux kernel as a realistic example of a realworld system and modelling it using mathematical queueing theory. Three queueing theory models have been formulated to model the queueing mechanisms of a Linuxbased gateway, and the numerical model predictions have been compared to the observed values. The goal of the experiments has been to ascertain how well the models predict the observed queue length distributions, how well they predict the queue waiting times, and to what extent the fairness queueing implementation in the Linux kernel can be considered to have completely independent queues. For the M/M/1/K and M/D/1/K models, traffic was generated specifically to match the model assumptions (with exponentially distributed arrival intervals and exponential or deterministic service times). The results of this show some correlation between model predictions and observations for these models, even though it does not hold up to a rigorous statistical test. For TCP traffic (being modelled using the MMPP/D/1/K queue, based on the Markovmodulated Poisson process) this correlation is almost completely absent; although this is most likely due to the fact that the numerical calculations for the MMPP model produce dubious results that are almost entirely independent of the choice of parameterisation: remedying this has not been possible. The observations of the system indicate that for traffic that matches the assumptions of the models, the queueing theory model predictions can be used as a reasonble qualitative indicator of the system behaviour. Furthermore, the experiments show the efficiency of packet transmission in the Linux kernel, which causes the queues to be more likely to be emty than predicted. Also apparent in the results data is the difference in behaviour between traffic with exponential and deterministic service times and between different traffic rates, which is to some extent matched by the model predictions and which validates the measurement and traffic generation methodology. Lastly, the interaction of the TCP control loop with the queue is apparent in the observations, corresponding well to what is expected from the theory of TCP operations. Finally, the results show that fairness queueing can to a large extent be thought of as a set of completely separate queues. However, in the Linux kernel implementation, the queueing space is shared beween individual queues, making the queue lengths be distributed differently from what a separate queue interpretation would suggest.
Speciale, 3. modul, 2013, id:455  
Vejleder:  
Findes på RUb:  Ja 
English abstract
This thesis deals with danish secondary school students' conceptual understanding of functions. The function concept is chosen as a case study because of its importance to mathematics as a discipline, and because of its central role in the danish educational system. The aim of the thesis is to characterise students' conceptual understanding of functions through a combination of theoretical work and empirical studies. The theoretical framework serves as a guidance for the decelopment of the methodology, as well as an analytical tool for describing, understanding, and communication observations. The main theory is Anna Sfard's theory of reification  a theory that describes fundamental aspects of the development of mathematical concepts, which can be found within the historical development of concepts in mathematics as a discipline, as well as within the learning process of individuals. Based on theoretical arguments and observations from the literature, the theory is revised and extended. The essence of the extension is that during the learnings process, an individual's conceptual understanding can develop differently across different representations of the same concept. The extension is referred to as disjointreificationofrepresentations hypothesis. The hypothesis has significant consequences for the characterisation of students' conceptual understanding and therefore potentially for how teachers can support and challenge students' conceptual understanding. Three empirical studies, containing a total of 17 pairs of students, spread across two danish secondary schools, are conducted. The studies consist of video/audio recordings of pairs of students who are solving a set of mathematical problems, which were designed according to the theory of reification, with the aim of characterising the students' understanding of the function concept. The data analysis consists of a close scrutiny of the video recording and the students' written answers to the problems. Observations are presented in the form of transcribed dialogues between the students. These dialogues are then analyzed within the theoretical framework of the thesis. Based on the analysis a characterisation of the students' understanding of the function concept is given. The overall conclusion of the thesis is, that important aspects of secondary students' conceptual understanding can be probed through video recording of problem solving sessions, and that it can be characterised by stating the level of reification which the student has attained of the concept in its different representations.
Fagmodelprojekt, 1. modul, 2013, id:464  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 2013, id:465  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
In this science project, we examine the concept of the limit as it appears in the works of Newton, Bolzano and Cauchy, and relate these to their differing motivations and purposes with mathematics. First of all, the project examines each of these mathematicians' background  historically, culturally and mathematically. Afterwards, we examine each of their individual mathematics, focusing especially on quotes and excerpts from the texts Principia by Newton, Rein analytischer Beweis by Bolzano, and Cours d'Analyse by Cauchy. The excerpts are chosen with the purpose of exemplifying each of the three mathematicians' concepts of the limit as much as available, but their respective motivations and purposes are also partially deducted from these texts. The project finds that Newton, as a physician, uses the limit primarily on the grounds of how it might be applicable to certain problems, and geometry plays a central role in his proofs. Conversely, we see that Bolzano much prefers the rigor of purely analytical mathematics to geometry, and his concept of the limit reflects this. The project also finds that Cauchy views geometry as having a greater sense of rigor than analysis, and that this rigor is important to him not only in his concept of the limit, but his mathematics in general. Finally, we compare the three mathematicians' concepts of the limit, and conclude that each of their motivations and purposes have had a profound impact on their formulation of the limit.
Modelprojekt, 1. modul, 2013, id:466  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
Colony Collapse Disorder (CCD) is a syndrome affecting the European honeybee (Apis mellifera). Affected hives lose their worker bees, but very few dead workers can be found in and around the hive. The syndrome has many suspected causes. Notable suspects are Varroa destructor, Nosema ceranae, American foulbrood and neonicotinoids. Earlier analyses have given no final conclusion about the main cause of CCD. Therefore, this study proposes a novel method for examining the main cause that is, by analyzing the spreading of the syndrome in space and time, rather than symptoms in the individual hive. We demonstrate that this is an applicable method of assessing whether the syndrome is transmitted through direct contact, spread via airborne spores, or distributed randomly. As a concrete example of this, we examine the spreading pattern of a disease transmitted via contact, both through mathematical analysis and through a simulation in GNU Octave. From this examination it is apparent that patterns can be easily told apart if a pathogen is transmitted from a point source in an area and the wind has a prevalent direction. For pathogens endemic in an area, our method has a more limited application. This report is a pilot study on inverse problem solving, directed at both human and veterinary epidemiology, aiming to identify diseases from their pattern of spreading.
Videnskabsfagsprojekt, 1. modul, 2013, id:467  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
This project examines the contributions in the history, in the development, of the modern mathematical definition of infinity, as well as problems that may have occurred in the use of it. The problem is formulated as following; "What challenges has arised in the association with the acceptance of infinity, and how have the chosen cases contributed to the development of the modern concept of infinity ?". The Study that is made to answer this will be through three main cases, Den infinitesimale begyndelse, Den stringente definition, Cantors aktuelle uendelighed, where the examination is based on a more modern notation which is defined in the project. These cases take you on a travel through the history of infinity, where the accept in infinity, both potential and actual, is happening. Through the report it is shown how geometric considerations, made in the 1700, leads to the infinitely small quantities, which are not rigor defined at that time. This definition was first presented in the 1800's, and is defined from a general point of view. Not long after, the use of infinitely small quantities becomes unnecessary "through the (formel)notation which also implies a rigor definition of the concept of potential infinity. It will be no earlier than the 1800's that a more rigor definition of the existence of actual infinity is made, and this definition will be accepted.
Professionsprojekt formidlervariant, 2. modul, 2013, id:471  
Vejleder:  Uffe Thomas Jankvist og Mogens Allan Niss 
Findes på RUb:  Ja 
Professionsprojekt formidlervariant, 2. modul, 2013, id:470  
Vejleder:  Mogens Allan Niss & Uffe Thomas Jankvist 
Findes på RUb:  Ja 
Professionsprojekt formidlervariant, 2. modul, 2013, id:472  
Vejleder:  Mogens Niss og Uffe Jankvist 
Findes på RUb:  Ja 
Professionsprojekt formidlervariant, 2. modul, 2013, id:473  
Vejleder:  Uffe Jankvist og Mogens Niss 
Findes på RUb:  Ja 
Professionsprojekt formidlervariant, 2. modul, 2013, id:474  
Vejleder:  Mogens Niss og Uffe Thomas Jankvist 
Findes på RUb:  Ja 
Professionsprojekt formidlervariant, 2. modul, 2013, id:475  
Vejleder:  Mogens Niss og Uffe jankvist 
Findes på RUb:  Ja 
English abstract
This report concludes the programme in mathematics counselling at Roskilde University. Through three projects, each with a different mathematical focus, the report illustrates and examines the three stages of counselling: identification, diagnosis and intervention. In each project, we use a specially designed test by Mogens Niss and Uffe Jankvist to help identify students with learning problems. The test results also work as the starting point for diagnosing each student. Hereafter different paths are chosen to help the students overcome their learning problems. The topic for the first project is "concepts and their creation", and the mathematical focus is algebra. An analysis of the test results show that problems with equationsolving serves as a marker for general problems in algebra, and therefore the empirical emphasis has been placed in this area. In order to diagnose the specifik learning problems of the students, more tests and interviews are needed. After several discussions with the identified students about mathematical problems, developed on basis of the diagnosis, an evaluating test indicates that dialogue as a way of counselling can lead to buildingup or activating the concept images of the students that improves their understanding and use of methods in algebra. The test results do nok provide evidence to conclude that students without problems in algebra mainly choose mathematics at an Alevel (the higher level), while students with major problems in this area choose it at a Blevel. Therefore, there is no basis for organizing the teaching differently due to this aspect. On the other hand, the test results show the tendency that girls do less well than boys in algebra at the beginning of the HTXprogram. In the second project we investigate different aspects about "mathematical reasoning and proof". In order not to let algebra overshadow the learning difficulties in this field, we use mainly geometrical arguments. It is shown that the identified students have proof schemes on the two lowest taxonomical levels, i.e. external conviction proof schemes and empirical proof schemes. We cannot show any connection between the students' beliefs and their learning problems. However, we use the beliefs of the entire class to decide that group work is a possible way of intervention. Through creation of didactical situations and internalisation we conclude that the sociomathematical norms and learning opportunities arising from the classbased intervention helps the identified students overcome several of their learning problems. Finally, we examine students' difficulties in "modelling" in the third project. Instead of projecting our own ways of explaining how to model, some excellent students are interviewed and their strategies are successfully passed on to the students identified with learning problems. The intervention is again a combination of counselling dialogue and a classbased intervention with focus on premathematizing and mathematizing. On basis of our research in the three projects we conclude that a test (in combination with teacher observations) is a good way of identifying students with learning problems. To diagnose the origin of those problems, interviews and possibly extra tests are needed. Counselling conversations about problems designed to suit the student's specific needs work well as an intervention, and this can be even more successful if combined with classbased intervention creating sociomathematical norms among the students. This, however, is not always possible, and then the counselling can be complemented with Internet resources as exercises and videos and specially developed materials.
Professionsprojekt formidlervariant, 2. modul, 2013, id:476  
Vejleder:  Mogens Allan Niss og Uffe Thomas Jankvist 
Findes på RUb:  Ja 
English abstract
This report documents our work with identifying, diagnosing, and intervening towards students at htx with difficulties within mathematics. The work has been carried out as part of the Mathematics Supervisor Education at Roskilde University. The work consists of three mini projects each with a different theme: concepts and development of concepts, reasoning and proving, and models and modeling. Students with difficulties within mathematics have been identified on the basis of detection tests, and selected students' difficulties have been diagnosed using general and specific literature, leading to analysis of focused tests and interviews where the student in dialogue solves specially designed problems. Problems with algebra and proportionality, and beliefs about mathematics, have shown to be of significance to a selected student's ability to reason and model mathematically. We have developed a method of intervention aimed at this student, based on ideas from, among others, Modeling Eliciting Activities. The method is based on: scaffolding of problems with focus on processes and pattern recognition; creation of cognitive conflicts; dialogue; a variety of representational media, including physical embodiments. With a targeted intervention, based upon this method, we have found improvements in this student's ability to work with proportionality and mathematical modeling.
Professionsprojekt formidlervariant, 2. modul, 2013, id:477  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
In this project, we have explored the challenges high school students in mathematics at level B may have when solving simple algebraic equations. We investigated whether an intervention of limited duration can help a student from an instrumental understanding of equation solution to a relational understanding. We consider a selected student from a mathematics B class. We investigate whether it is possible to plan an intervention program. The planning and analysis of the intervention builds upon Duval's theory of shift in register and Sfards three phases to achieve a structural understanding of a concept like equations. We learn that a longer intervention is needed if all aspects of the equation solution for simple equation in one unknown must be included. But it should be feasible  especially if it is taken into account which kind of registers the students benefits the most from.
Videnskabsfag, 2. modul, 2010, id:399  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
The present work regards the validation of mathematical model of biological systems with perspectives from the philosophy of science. Validation of two mathematical models of HypothalamoPituitaryAdrenal (HPA) axis are used to exemplify a validation process. Initially, a review of literature on validation is presented and fundamental concepts is defined. The biological system of the HPA axis is exhibited and used as a conceptual model. Following is the construction of two closely related mathematical models of the biological system. Methods for parameter identifiably, estimation and sensitivity are introduced and followed by a section on methods for quantitative operational validation. Parameter estimation and sensitivity analysis is performed along with crossvalidation and a qualitative analysis of model fit and results are summarized and discussed. It is concluded that neither model could be validated partly due to lack of data, but that further research would be beneficial.
Modelprojekt, 1. modul, 2010, id:400  
Vejleder:  Eksaminator Anders Madsen 
Findes på RUb:  Ja 
English abstract
In the present paper syntax, constant domain semantics with nonriged constants and an axiom system for nagent systems with identity for a termmodal logic is presented. This allows operator indices to be terms of the firstorder language resulting in poerators doubling as predicates. Quantification over agents is possible and the agents are reflected in the semantic structure. It is shown how classic epistemic axioms af S5 can be added to the core system. Examples of expressibility are given, and venues of further research addressed.
Model, 1. modul, 2010, id:401  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
This project is about mathematical models and the spread of cervical cancer. Cervical cancer develops from the human papillomavirus (HPV), which is a collection of nearly 200 different viruses that causes everything from warts on the feet to cervical cancer. There has in recent years been much focus on cervical cancer, partly because it's the cancer which in the developing world kills more women than any other, and partly because it's one of those cancers, which it is actually possible to limit the spread off in several ways. From a mathematical point of view, it is of particularly strong interest to develop mathematical models that can predict the development of cervical cancer, and assist in a more focused development of screening and vaccination programs. Although it is possible to get the vaccine against HPV 16 and 18, which causes most of the cases of cervical cancer, modeling results shows that there is still a need, for screening programs to catch those cases the vaccine fails to prevent. We have in this project looked at two articles, both of which have mathematical models for the spread of cervical cancer, as well as looked at the effect of a vaccination program. Since one of the articles already have been the subject of a thorough study of a former RUC project from 2009, we have in this project, chosen to focus more on the model developed in the Finnish article. In light of both a general description of HPV and a review of the Finnish model, we have formulated and discussed our own model, which have been adapted to Danish conditions, with a special emphasis on whether the conclusions in the article by Barnabas et.al. can be applied to Denmark. Our main conclusion is that, it does have a small benefit to vaccinate men, however it is rather marginal, and it would be preferable to instead use the cost of this on other kinds of treatment.
Videnskabsfag, 2. modul, 2010, id:402  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
In this project I would like to examine the role of mathematics inthe scientific discipline of artificial intelligence. Firstly I will briefly discuss how the terms intelligence and learning can be defined. The results will be used to motivate the abandonment of the traditional binary logic and introduction of fuzzy logic. This theory will give us the power to express fuzzy terms like "frequently" or "almost ever" in more or less mathematical terms. (The last sentence itself contains due to the term "more or less" a fuzzy statement.) Finally the benefit gained from this change in logic will be examined when showing the change from expert systems to neural networks. The report ends with introducing an idea how fuzzy logic and neural networks could be marged to take advantages of both system. The books "Artificial Intelligence  A Guide to Intelligent Systems" written by Michael Negnevitsky and "A first course in Fuzzy Logic" by Hung T. Nguyen and Elbert A. Walker will be used as references.
Videnskabsfag, 2. modul, 2010, id:403  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
Model, 1. modul, 2010, id:404  
Vejleder:  
Findes på RUb:  Ja 
Speciale, forskervariant, 3. modul, 2010, id:405  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
This thesis studies dynamical systems given by Zd on a subset of the unit circle. We describe rotation numbers and present a series of known results about rotation subsets of the circle. To new theorems that provide ways of generalising results from d 0 2 to higher degree are proved. Perspectives are drawn to polynomial dynamics, since the main theorem of the thesis can be used to describe the structure of connectedness locus of cubic polynomials.
Speciale, modelbyggervariant, 3. modul, 2010, id:406  
Vejleder:  Johnny Ottesen og Mette S. Olufsen 
Findes på RUb:  Ja 
In this thesis we examined the phenomena caused by initial gravitational effects and short term neural control when the human body is subjected to a headuptilt (hut) test. This was done by constructing a simple mathematical model, which describes the systemic circulation of the cardiovascular system. The human body is divided into two parts; the lower and the upper body, which are further divided into venous and arterial compartments. The left heart isdescribed as a pump with timevarying elastance, thus making the model pulsatile. The system is modeled as an electrical analogue in which pressure is analogous to voltage. Flow to current, compliance to capacitance, and resistance is the same in both settings. The circuit can be represented by five nonlinear ordinary differential equations. To predict dynamics during hut, the neural control is included by defining timevarying peripheral resistance, venous compliance, and heart contractility. These regulating mechanisms were modeled by setpoint fuctions and sigmoidal functions, which resemble the behavior seen in experiments. We also developed an idealized cardiovascular model of the human body, where teh body is considered an elastic cylinder. We found the hydrostatic invariance point, and related this to the hut. The model was validated using data from a healthy 25 year old subject who underwent hut, and parameter estimation techniques were employed to estimate a set of parameters that minimized the least squares error between the model and the data. By identifying correlated parameter pairs and fixing insensitive parameters we were able to obtain reliable estimates for five model parameters during hut, and nine parameters in steady state. In steady state, we used three data sequences to obtain more reliable estimates. The constructed model was able to predict dynamics observed in the data both during steady state and during hut. There are fluctuations in the data which cannot be explained by the model, but we believe these originate from the respiration of the patient, something that is not included in the model. All model variables produce physiologicaly reasonable results during the hut: cardiac output drops the same amount as seen in the lterature, lower venous pressure is increased in agreement with other studies, and upper arteral pressure resembles the data obtained. These results show that the simple model can be used to predict responses from larger groups of subjects. Subsequent analysis of parameter estimates have potential to be used to predict differences within and between these groups of subjects. However, before using the model in a larger study, we suggest to include the following model improvements: 1) Include a simple model for the respiration of the patient. 2) The control of the lower venous compliance should be a strictly mechanical feature, and not part of the baroreflex system. 3) The upper peripheral resistance should also be controlled.
Model, 1. modul, 2009/10, id:392  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
This project originates from the question of how come Mathematics is so effective, and hence is being used in so many other areas of the world, other than that of mathematics. Our question regards how come mathematics works in other discplines than mathematics itself. Our approach to the question was through three different cases, where mathematics could be assigned a great deal of the reasonfor the success. We tried to spread out in our choices af cases, both when it came to the way mathematics is interacting, but also when it came to what scientific fields, we were looking at. The three cases were the HardyWeinberg law on genetic populations, the JPEG algorithm used for compressing digital images, and a cardboard model of the Planetarium in Copenhagen. Through our analysis of these three cases, we found, firstly, that it is not possible to give a common description of what it means that the mathematics "works" in the case. The mathematics works in different ways in the different cases. Secondly, we found that the reason that mathematics can be used, is also different among the cases. Our assumption is that these results are general, that one cannot find one common reason that mathematics work.
Profession, formidlervariant, 3. modul, 2009/10, id:393  
Vejleder:  
Findes på RUb:  Ja 
English abstract
Model, 1. modul, 2009/10, id:390  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
Mathematical modelling of isomorphs in IPLliquids The purpose of this project is to investigate, in part whether group theory, can be used as a model for isomorphic curves in IPLliquids, and in part whether the explanation of isomorphic behaviour can be found as symmetry in solutions to the, for this project unknown, differential equations that controls the dynamics in simulations of vicous liquids By analysing the IPLmodel with group theory a transformation group GIPL was suggested as a way of describing the equivalence relation r1n/3 /T1 = r2n/3/T2. From this it was shown, that isomorphic curves can be described as orbits in the (T, r)plane, where each of the orbits can be identified as elements in the quotient space by means of isochors and isotherms. From this it is concluded, that orbits can be used as a model for isomorphs, since these capture some of the isomorphic characteristics. As a frame of reference to the unknown differential equations, the heat equation is used as a simple example of a system of differential equations. Based on Olver [1993] a symmetry group Gi is established, for which the solution T(x, t) = je?(x?Kt) is group invariant. From the parameters (k, c, r), which define the contant K, an equivalence relation is created along with a group, Geq, that describes this relation. From this it is shown, that solutions to the heat equation are invariant to transformation by Geq. From the analysis of the heat equaiton in respect to symmetry groups, group invariant solutions and invariance towards transformations of the parameters in the heat equation it is postulatet, that the existence of isomorphs imply the presence of solutions that are invariant to the transformation of the underlying system of differential equations. Such an invariance should thus be pressent in all liquids that exhibit isomorphic behaviour. For IPLliquids it is surmised that the equivalence relation given by a constant ratio between r n/3 and T along isomophic curves has a relation to this invariance.
Videnskabsfag, 2. modul, 2009/10, id:391  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 2. modul, 2009/10, id:394  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
The effect of computers on pure mathematics is investigated. First, some of the most celebrated proofs between 1940 and present are listed with the role of the computer detailed for each case. In the second part, the philosophical implicatons of the computers in mathematics are investigated by recounting the controversy following the proof of the FourColour Theorem, then the famous JaffeQuinn discussions, and finally the discipline called experimental mathematics is examined. As a conclusion the empirical element of the computers in mathematics is analyzed, together with the formalizability of the mathematical knowledge, and eventually the values of mathematical proofs are discussed.
Speciale, Modelbyggervariant, 3. modul, 2009/10, id:395  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Speciale, modelbyggervariant, 3. modul, 2009/10, id:396  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
We investigate a ODE model and appertaining claims from [PDG06]. A paradigmatic and fundamental discussion about continuity/discontinuity of the phenomena in question was undertaken. It was concluded that the standpoint taken in [PDG06], where they argue for discontinuity, is not entirely justified. In addition, it was shown that if discontinuity turns ourt to be true, a much more applicable methodology in the form af Kalman filtering, could be utilized instead of using stochastic differential equations as proposed in [PDG06]. Under the assumption of continuity of the phenomena in question, investigations was in turn undertaken. First of all, alternative parameter estimation techniques was tried out but with limeited results. It was hypothesized that glucagon had to be taken into account, and models extending the ODE model form [PDG06], was proposed. One of these actually attined enhanced physiologically reasonable model behaviour, but essential model deficiency is till present. Obvious problematic parts of the extended model, that could be responsible for the poor fitting results, was hypothesized for future work. This hypothesis also have physiological implications w.r.t. an increased understanding of the human glucose regulatory system.
Videnskabsfag, 2. modul, 2009/10, id:398  
Vejleder:  
Findes på RUb:  Ja 
English abstract
In this paper we investigate probability theories on the basis of acceptance, reception and setup. The investigation is based on the two theories respectively Kolmogorov's measuretheoretic approach from 1933 and on Shafer and Vovk's gametheoretic approach from 2001. The system of axioms made by Kolmogorov represents the common approach to probability theory, and the framework made by Shafer and Vovk represent the new approach to probability theory. We taking into account the historic development of probability theory and to how the different approaches to probability theory should be understood. In addition we examine the two theories, and the elements in the two theories are compared to each other. In the presentation of both theories we present the Central Limit Theorem, and we also include some examples of the theorem. We are concluding that the historic context has great in fluence on the reception and the acceptance of probability theories. This is clearly shown in relation to the demand of a new axiomatic system. Besides that it is concluded that it is possible to make different axiomatic approaches to probability theory depending on one's approach to probability. The elements in different axiomatic systems and frameworks do either way have some similarities.
speciale, 3. modul, 2009, id:383  
Vejleder:  
Findes på RUb:  Ja 
English abstract
videnskabsfag, 2. modul, 2009, id:384  
Vejleder:  Anders Madsen 
Findes på RUb: 
English abstract
Model, 1. modul, 2009, id:385  
Vejleder:  Viggo Andreasen 
Findes på RUb: 
English abstract
The present project propose a deterministic model for the replication of the bacterial chromosome based on the work by Mahaffy & Zyskind (1989). The main aim of this project is to examine how external factors influence on the stability of the model. In order to do this, we examine how the production of DnaA and the doubling rate of the cell mass, affects the models stability. This is done in an analytical analysis of the model near equilibrium, and further by a mumerical analysis of output values near equilibrium. Furthermore we propose and discuss extensions of the model. These extensions include modelling of RIDA, datA, Sequestration of the dnaAgene by SeqA and remodelling of oriC to contain multiple DnaAboxes. We conclude that there is a possibility for the existence of a transcritical bifucation, which resolves in a shift of stability.
Model, 2. modul, 2009, id:386  
Vejleder:  
Findes på RUb: 
Model, 1. modul, 2009, id:387  
Vejleder:  Johnny Ottesen 
Findes på RUb: 
Speciale, modelbyggervariant, 3. modul, 2009, id:388  
Vejleder:  Michael Pedersen 
IMFUFAtekst:  469 
Findes på RUb: 
Speciale, modelbyggervariant, 3. modul, 2009, id:389  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  469 
Findes på RUb:  ja 
English abstract
In this thesis two mathematical models of the hypothalamicpituitaryadrenalaxis (HPAaxis) are build using well known physiological mechanisms. The HPAaxis controls the secretion of the hormones CRH, ACTH and cortisol. The regulation of these hormones are important to human health. These hormones are the variables in two systems of coupled nonlinear differential equations that constitute the models. The models includes a negative feedback of cortisol on ACTH. The first model has a negative feedback from cortisol on CRH corresponding to the "standard biology textsbook" description of the HPAaxis. The second model allows a feedback from cortisol on CRH to be positive og negative depending on the cortisol concentration by including mechanisms from hippocampus. For parameter values in a physiologically relevant range it is investigated if the models are capable of guaranteeing solutions with reasonable levels in hormone concentration. It is investigated if the models are capable of producing the ultradian oscillations that are observed in data of hormone concentrations. It is investigated if an external imposed function on the differential equation governing the CRH concentration can cause the circadian rhythm that is seen in the concentrations of ACTH and cortisol. Previous papers of the HPAaxis [1] and [2] claim to make models showing ultradian oscillations. We analyze the two models and find significant drawbacks that must be elaborated for a successful model taking care of the physiological mechanisms of the HPAaxis. Results of analytical investigation of our models For both models the results of the investigation is that all solutions end in a trapping region in the positive octant of (R3), thus guaranteeing reasonable levels in hormone concentration. Within this trapping region there exists at least on fixed point. The first model has a unique fixed point. The unique fixed point is locally stable for all physiological choices of parameters. Therefore no Hopf bifurcation is possible as an explanation for the ultradian oscillations in data. For the second model more than one fixed point is possible. The stability of a fixed point is categorized depending on the sign of the feedback on CRH at the fixed point. A sufficient, easily applicable criteria for a unique, globally stable fixed point is formulated for a more general model. This can be applied on the two specific models. Results of numerical investigation of our models In the case of a unique fixed point this is asymptotically stable for all reasonable parameter values and initial conditions. Perturbating the parameters in the second model makes the system undergo a bifurcation where two new fixed points emerge. In the case of three fixed points there is one unstable fixed point and two asymptotically stable fixed points. For all reasonable values of parameters and initial conditions the solutions converge towards one of the two stable fixed points. Thus for reasonable parameter values neither of the models are capable of producing the ultradian oscillations. The analytical criteria for a globally stable fixed point is fulfilled for some set of parameters within physiologically relevant ranges for both models. An external input in the differential equation governing CRH is capable of showing circadian oscillations in ACTH and cortisol concentration.
Profession  forskning, 3. modul, 2008/09, id:377  
Vejleder:  
Findes på RUb:  ja 
English abstract
bachelorprojekt, 1. modul, 2008/09, id:379  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
bachelorprojekt, 1. modul, 2008/09, id:380  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
Bachelorprojekt, 1. modul, 2008/09, id:381  
Vejleder:  Viggo Andreasen 
Findes på RUb: 
This paper is dealing with epidemics on scalefree networks. We are investigating whether an epidemic in a scalefree network can be approximated by models that were made for simpler random networks. We are fitting the KermackMcKendrick SIR model to epidemic data which was generated by a computer simulation. We show how the continuous model and the discrete simulation are related by transferring the parameters of the two models via the discrete ReedFrost epidemic model. We conclude that although the data points of the scalefree epidemic can be fitted with the SIR model with a good precision, there is a difference in the parameters of the two epidemic curves, which means the simulation and the model take place on different time scales. We investigate other factors as well that are specific for scalefree networks such as the assortativity of the network (i.e. when similar nodes are connected to each other) and the inhomogeneity of the scalefree networks. The assortativeness has a minor effect on the epidemic, namely diseases spread more slowly in disassortative networks. The inhomogeneous structure of the network can have an effect on the spread of diseases and we examine the effect that the degree of the starting node has on the course of the virus. Finally we demonstrate that immunizing those nodes that have the most links is an effective way to control the virus1.
Videnskabsfag, 2. modul, 2008, id:368  
Vejleder:  
Findes på RUb:  Nej 
English abstract
Profession  formidlervariant, 3. modul, 2008, id:369  
Vejleder:  Tinne HoffKjeldsen 
Findes på RUb:  Ja 
English abstract
This project is concerning interdisciplinarity in the upper secondary school in Denmark. It has a theoretical component where the content of the concept of "interdisciplinarity" is studied. Different foreign and domestric theories are analyzed regarding the general notion of the "interdisciplinarity". In addition an analysis is made of the concept in domestic theories related specifically to the upper secondary school in Denmark. The second part of the project is an empirical study of papers made in the year 20072008 by students of the upper secondary school in the 3rd grade. It inolves a qualitative study concerning the appearance of different types of interdisciplinarity within the papers and the integration of the two subjects in the papers  history and mathematics. Several different types of interdisciplinarity and a high level of integration of the two subjects are found in the papers.
Videnskabsfag, 2. modul, 2008, id:370  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
In this paper we unravel som abstract mathematical ideas and theorems that are used to handle the cortical surface matching problem. A problem that is linked to structural MRI. Gu and Yau addresses this issue in a number of articles. They propose an algorithm for approximating conformal parametrization of brain surfaces. We find that the algorithm is based on the conceptual framework of Riemannian geometry.
Model, 2. modul, 2008, id:371  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
The project is about the status of Social Choice theory as mathematical model. The theory treats aggregations of individual preferences over a set of choices to a collective preference of the same choices. This is often used in economics and decision theory. The project presents the main notions of the theory, as they are formulated by Kenneth Arrow and Amartya Sen. As an example of results within the model, Arrows Impossibility Theorem is presented and proofed. To show the range of the model, som examples from the use in economics and decision theory is presented. There is also presented a discussion about the foundation of the theory, represented of a liberalist and Marxist inspired critique. The conslusion says among other things, that the impossibility theorem and the model is often used in situations not included by these.
Model, 1. modul, 2008, id:372  
Vejleder:  
Findes på RUb:  Nej 
English abstract
The starting point for the project is a mathematical model made by McBryde et al. (2007). The model simulates the hospital acquired spread of patient infection with Methicillinresistant Staphyloccocus aureus (MRSA) in an intensive care unit. We clarify the predictions and results of the model. The purpose of this is to infer on how to make recommendations for interventions against hospital acquired MRSA. We analyse and take a critical standpoint regarding the construction of the model and our results. Many assumptions regarding to the spread of MRSA lie in the foundation of the model which can also be recognized in the parameters it includes. We discuss the importance of the two versions of the model which is both stochastic and deterministic. Furthermore we find it important to put the model into a broader perspective by discussing the assumptions behind, measurements for the output of the results and overall applicability. The purpose of this discussion is to be able to place McBryde et al. (2007) in a wider context of research projects with a mathematical approach to hospital acquired infections by antibiotic resistant bacteria.
Model, 1. modul, 2008, id:373  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
This report investigates a matemathical model for the severe blood poisoning sepsis. The model is developed by Zuev et al. (2006) as a patient specific model with one patient specific, dimensionless parameter, H, which is dependent of the patients BMI. In the paper by Zuev et al. (2006) it is not shown how the model is actually made patient specific by means of only one parameter, which is why the argument is made in the report. We perform an investigation consisting of stability analysis and sensitivity analysis. The stability analysis consists of a primarily algebraic analysis, where steady states and eigenvalues of the Jacobian matrix are investigated, and a numerical analysis where we focus on the general dynamics of the model. We find 3 different dynamics for the model where the patient recovers if H >0.86, while the patients at (XXX) will experience a periodic course of disease without either recovery nor death as an outcome. Finally patients with H < 0.52 will certainly die if treatment is not initiated. By including the sensitivity analysis, we furthermore find, that the model is somewhat accurate for H < 1, but at larger values of H, the output of the model are related with great incertainty. In total we conclude that the model by Zuev et al. (2006) is sufficient to describe sepsis. It will, however, demand further work before it can be implemented. We recommend significantly more empiric evidence and a more biological ivestigation. Our analyses recommend a discussion about whether it is suitable to make a model with only one patient specific parameter. This discussion gain further relevance since this parameter is also a bifurcation parameter, and the parameter which the variables ahs the highest sensitivity too. In the paper by Zuev et al. (2006), H is proposed to be dependent of variuos things; age, lung capacity etc. By means we find criticizable. We also suggest an expansion of the model, to incorporate antibiotic treatments. Finally we give a suggestion to implementation  which will need to wait for further validation of the model to take place.
Speciale, forskervariant, 3. modul, 2008, id:382  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb: 
English abstract
This report examines which kinds of interdisiplinarity a mathematics teacher in the Danisk hig school ("gymnasieskolen") can use, when he or she teaches. The report makes a theoretical description of the general meaning of the concept of interdisciplinarity, and how this concept can be interpreted into a context of mathematics and a context of high school. The report develops special notions to describe cooperation between mathematics and history. In the reports empirical part, apporx 30 specialized thesis from the high school, written with basis in the disciplines of mathematics and history, is analyzed. The analysis shows, that the cooperation between the tow disciplines is dominated by monodisciplinary works, with variation in the ability to be joined in the end of the thesis. It also shows that a larger degree of integration between the two disciplines is possible. The report recommends that mathematics and history teachers together develops subjects better fitted for thesis, that they orientate towards problems instead of topics and an increased forcus on training special competencies in the cooperation between mathematics and history. The report is exemplary. Its method can be transferred to cooperation between other disciplines.
Videnskabsfag, 2. modul, 2007/2008, id:362  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
This project is concerned with deduction in ancient Greece. It is based upon studies of two sentences by Euclid and Archimedes respecitively and the theories of Aristotle. The analysis will evolve around the matter of the rigorism of the sentences and whether it is possible to apply a pedagogic aspect to some of the actions, concepts and definitions used by the tree Greeks. I conclude that the rigorism of the sentences meet the modern standards of today quite well. In addition I conclude that it is possible to apply a pedagogic aspect to their work.
Model, 1 og 2. modul, 2007/2008, id:363  
Vejleder:  Johnny Ottesen og Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 2. modul, 2007/2008, id:364  
Vejleder:  
Findes på RUb:  Ja 
Profession  formidlervariant, 3. modul, 2007/2008, id:365  
Vejleder:  
Findes på RUb:  Ja 
In 2005 a new law concerning the Danish High Schools was legislated by the Danish Parliament. This new law gives rise to changes in the ways in which teaching in mathematics is to be organized. The content of the project is the preparation of a short course in mathematics at the lowest Danish High School level (Matematik C) which is obeying these new ideas.
Profession  modelbygger, 3. modul, 2007/2008, id:366  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
In this project I study the advantages and the disadvantage by the use of Spectralmethods for the solution of the NavierStokesequations. My case will be the formation and dynamics of rings of smoke. I conclude that the Spectralmethods are too dependent on good conditions. And therefore my model is not particularly suitable for the simulation of rings of smoke
Model, 2. modul, 2007/2008, id:367  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Model, 1 og 2. modul, 2007, id:352  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 1 og 2. modul, 2007, id:353  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Model, 1. modul, 2007, id:354  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
The purpose of this project is to examine what influence the regulation of blood vessel compliance has on syncope during tilt experiments. This is accomplished by introducing a compartmentmodel of the circulation and introducing models of the effect of gravity, regulation of blood vessel compliance and seepage af fluid from the blood to the surrounding tissues. Teh equations of the model are solved numerically with ODE15s in MatLab. It is concluded that the limitation of regulation of vein compliance may be the cause of syncope during tilt experiments.
Videnskabsfag, 2. modul, 2007, id:355  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 3. modul, 2007, id:356  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
Modelbyggervariant, 3. modul, 2007, id:357  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Model, 1 og 2. modul, 2007, id:358  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Videnskabsfag, 1. modul, 2007, id:359  
Vejleder:  Mogens Niss 
Findes på RUb: 
Speciale  modelbyggervariant, 3. modul, 2007, id:360  
Vejleder:  
Findes på RUb:  Ja 
English abstract
In this thesis we present a population forecast for women in Denmark 50 years from now. We use mathematical modeling to produce the forecast. The mathematical model consists of an accounting model and separate submodels for fertility, death frequency, emigration frequency and number of immigrants. In the setup of each submodel we use statistical methods, and we focus on locating and describing possible soures of uncertainty. The resulting forecast shows both the uncertainty of the size of the total population and the uncertainty of oneyear age classes 50 years from now. The uncertainty grows quickly during the perod. We therefore conclude that the value of the forecast as a basis for making decisions is limited after 30 yeras and almost nonexistent after 50 years. The most certain mechanism of the population forecast is death, and the greatest source of uncertainty is linked to fertility. The strongest weakness of the forecast is the description of migration, which is based on ad hocassumptions. However, the forecast of the oldest agegroups makes sense throughout the entire time horizon, whereas the forecast of the youngest agegruoups loses its applicability after 30 years. The results of the forecast are compared with corresponding population projections from DREAM and Statistics Denmark. Their expected projections are in accordance with the median curves of our forecast. Since the forecast shows that the uncertainty grows rapidly throughout the period, we conclude that the uncertainty grows rapidly throughout the period, we conclude that population projections are of limited value on time durations more than 5 to 10 years, without considerations of uncertainty.
speciale  Modelbyggervariant, 3. modul, 2007, id:361  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
Speciale, 3. modul, 2007, id:378  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
The basic problem of this thesis was suggested by John Hubbard in Hubbard (2006). Here he provided an example of a discrete group 3x3 matrices that preserve the hyperboloid: (formel) in the case K = 7. The question becomes: what if we choose a different values than 7? Hence the purose of this thesis is to invesigate certain groups of discrete isometries that preserves these hyperboloids for different (formel). Geometrically the hyperboloids are indistinguishable, yet the groups of discrete isometries are nonisomorphic. However, to see this we must describe the groups and this can be done by finding a group presentation of each group. This is not as simple as it might seem. The first obstacle is to find members of the groups. This poses some difficulties depending on the value of K. The second obstacle is to find a fundamental domain for the group and the last obstacle is to use this domain to write up the presentation and describe the quotient. The first many chapters of this thesis is follow the above scheme as abstractly as possible. Throughout the case K = 3 will presented as an eksempel. Tin the last chapter the group presentations and quotients in the cases K = 3, K = 7 and K = 11 are derived. When readingthis thesis the reader might notice the absence of covering spaces and in fact most notions from the interesting field of algebraic topology. The absence of covering space is simply a matter of not introducing anything more than is used in the thesis. On a formal note this thesis fulfills the requirements of a research type thesis (forskervarianten). The subject matter has only been found to be treated briefly in Hubbard (2006), which has meant that a lot of independent work has gone into describing the case K = 3 and K = 11.
Videnskabsfag, 2. modul, 2006/2007, id:347  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
English abstract
Under the collection of litterature about game theory the authors attention has been drawn to a statement by Urs Relstab that game theory has had an impact on economic theory which is much greater than normally stated in economic textbooks. Following that line the following project seeks to give an answer to the question: Which role has game theory played in the evolution of the model of competitive equilibrium?
, 1. modul, 2006/2007, id:348  
Vejleder:  Anders Madsen 
Findes på RUb: 
Cryptography has a long and fascinating history. Neoteric cryptography was used as a tool to protect national secrets and strategies. The proliferation of computers and communications systems in the 1960s brought with it a demand from the private sector for means to protect information in digital form and to provide security services. In this project we will introduce the history of cryptography, the concept of cryptography and two cryptography algorithms named symmetric key cryptography algorithm and public key cryptography algorithm and some examples which are using these two algorithms. Actualloy, we will focus on understanding the mathematic knowledge which is used in the cryptography algorithms in order to discover which role mathematic knowledge act in the development of cryptography.
1, Model. modul, 2006/2007, id:349  
Vejleder:  
Findes på RUb:  Ja 
Modelbygger, 3. modul, 2006/2007, id:350  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  ja 
English abstract
Model, 1. modul, 2006/2007, id:351  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
This paper describes an experimental study in control of a forced damped pendulum. We add a linear control parameter to the equation of the pendulum and by creating and using a pendulum simulation program ("pendulspillet"), we gain knowledge about how this parameter affects the motion o the pendulum. Experimentally we obtain a control algorithm that stabilizes a set of orbits, into a small neighborhood of a saddle. We propose an analytical investigation of the reulting direction and magnitude of the control, by analysis of the stablre and unstable manifolds, since we believe this would contribute to improvements of stabilization speed and energy comsumption of the control. Furthermore we conclude that, although this is a linear control problem, The OGYmethod does not work for this particular kind of control.
, . modul, 2006, id:335  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
Model, 1 + 2. modul, 2006, id:337  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
English abstract
Interfaces and interfacial tension are interesting in many ways, one of the more peculiar things, which is unlike other things in science, is the thermodynamical dependence on the shape af the interface. When we consider a thermodynamical system of two or more phases the thermodynamical equilibrium is determined by the shape of the interface between the phases. The study of this interfacial shape is a perfect application for differential geometry since the interfaces can always be described with smooth curves with only countably many (often zero) points of discontinuity. The differentiability of these curves is very important to the study of interfaces and has the interesting application that the pressure difference across the interface is proportional to the normal curvature of the interface. In this respect, interfacial phenomena is a study which can be read about in a math book, it is a direct application of differential geometry. This makes interfacial phenomena interesting and special compared to other scientific fields of study. The idea in this project is to map out the characteristics of interfaces, interfacial tension, and their applications. The project is driven by the interest in these strange phenomena and seek to uncover how they should be described. Finally one should note that the authors of this report are at different stages of their education and consequently the status of this report differ among the authors. For Anatol this report is writen as part of the second module, and as such it is supposed to be a mathematical modelling project. For Jesper and Jon on the other hand, this project is their final mathematical project.
Model, 1. modul, 2006, id:340  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
Model, 1. modul, 2006, id:343  
Vejleder:  Bernhelm Booss Bavnbek 
Findes på RUb:  Ja 
English abstract
Model, 2. modul, 2006, id:344  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Profession  modelbygger, 3. modul, 2006, id:345  
Vejleder:  
Findes på RUb:  Ja 
English abstract
Developing epidemiological models extend an important scientitic field of research within mathematical populations biology. Some of the most highly applied models are the classical SIR and SEIRmodels that descripe the dynamical pattern in a population exposed to a given disease. This paper contains an expansion of the SIRmodel to a TSIRmodel that incorporates timeseries, and the model is used on a set of data consisting of births and easles infected individuals in the years 19001967 in Copenhagen county. The group of susceptibles is reconstructed from the number of births by statistical regression modelling, and the amount of measles infected individuals is reproduced from the reconstructed susceptibles. Due to lack of stationarity in the susceptible group it turns out that the model is not adequate in its way of reproducing measles infected individuals in the original timeperiod. Meanwhile it is to som extend possible to gain a reproduction of the measles infected individuals when the model is applied to an appropriate time interval where the susceptibles exposes a relatively great stationarity. Thereby it is concluded that the useability of the model presumes that it is employed on a set of data that exposes a great deal of stationarity in the susceptible group in the entire modelled period.
Model, 1. modul, 2006, id:346  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
In this report a mathematical model describing a physical system consisting of a rubber tube placed in a fluidfilled tank is formulated and analysed. This experiment is not subjected to empirical inquiry, but our experiment has clear analogy to previous works. A pump is compressing the tube periodically at a place of asymmetry. The report has two main purposes: To formulate a model that investigates if a mean flow is existent, and to find out which mechanisms are responsible for creating a mean flow. The model is formulated in accordance to the compartment principle and consists of 11 1st order interdependent differential equations. The equations are formulated according to conservation of mass and Newtons 2. law. When the size of each compartment approaches zero the differential equations approksimates the equation of continuity and the linearized Euler equation in one dimension with a frictional term. In the final model inertans, resistance and compliance varies with the radius of the tube. These three terms are thought to contribute to the mean flow and we wish to find out which of the three contributes the most. The equations in the model are solved numerically in MatLab to establish a mean flow. Afterwards the inertans, resistance and compliance are kept constant in pairs. The report concludes that it is possible to create a frequency dependent mean flow, and that the inertans contributes primarily to the frequency dependent mean flow.
Videnskabsfag, 1 + 2. modul, 2006, id:374  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb: 
English abstract
Speciale, 3. modul, 2006, id:375  
Vejleder:  Bernhelm BoossBavnbek, matematik John Gallagher, datalogi 
Findes på RUb: 
English abstract
In present thesis a scheduling problem i s modelled first as a linear integer programming problem, then this type of modeling is compared to modelling of scheduling problems as Answer Set Programming (ASP) programmes. Next a graphical user interface (GUI) for modelleling scheduling problems in the ASP implementation SMODELS, is implemented. Through the GUI, four scheduling problems from the health sector in Denmark are implemented and tested and the effectiveness of the SMODELSalgorithm is evaluated against other methods for solving combinatorial optimisation problems. It is concluded that modelling of scheduling problems as linear integer programming problems, is equivalent to modelling them as ASP programmes. Further it is concluded that the sensitivity of a model of a scheduling problems is high. On the results of experimentation, it is concluded that certain types of rules in ASP programme, and that diminuitive changes of the parameters of a scheduling programme in SMODELS may have unforseeable consequenses on the running time. Finally the argument is advanced that algorithms prioritising finding nonoptimal but good solutions fast, is preferrable.
Speciale, 3. modul, 2006, id:376  
Vejleder:  Jesper Larsen 
Findes på RUb: 
English abstract
Diseases with a complex genetic background of low SNP pentrances, high genetic heterogeneity, and epistasis pose severe challenges for traditional statistical methods of association mapping. The objectives of this thesis is to develop a method that can detect associations when several SNPs have an effect on a trait, to evaluate the method on both simulated data and on the population cohort Inter99, and to test the influence of different genetic models on the statistical power of the test. In this thesis the MAMSE method, Mixture model for Association studies of Multiple SNP Effects, based on the mixture model theory has been constructed. It is based on calculating the probability of observing the phenotupic data under a specific genetic model, which should account for the combined effect of multiple SNPs. The method sums over all possible SNP combinations that could be pathogenic to form a likelihood ratio test of the hypothesis of no genetic contribution. A great advantage of the method is due to the way it jointly tests for association for all possible combinations of risk alleles. Note that even though highorder interactions are being investigated, the number of parameters is very small because the methd sums over the possible effects. Based on both simulation studies and selected data analysis of the populationbased cohort Inter99 it can be concluded that the method is able to detect associations when several SNPs affect a trait. The results of this work suggests that especially for epistatic as well as for genetically heterogenic data does the method exhibit substantial statistical power to reveal the effects. Furthermore, this work concludes based on simulation studies, that the choice of genetic model under which the hypothesis test is based has great impact on the statistical power of the test. Choosing the correct model gives the test substantial power, and since the application of the MAMSE method reduces the number of tests dne tremendously it is recommended to test under both a dominant, recessive, and an additive model when there is no prior knowledge of a certain genetic model. This is weighed as the best tradeoff between loss of power by doing multiple tests and gain of power by using the correct model.
Modelprojekt, 1. modul, 2006, id:458  
Vejleder:   
Findes på RUb:  Nej 
Profession, 3. modul, 2005, id:320  
Vejleder:  Anders Madsen 
Findes på RUb:  Nej 
, . modul, 2005, id:321  
Vejleder:  Mogens Niss 
Findes på RUb:  ja 
English abstract
HTM is one of the traffic models used to model how different changes in the traffic structure will effect the whole traffic in the area in and around Copenhagen. As an ordinary citizen whitout any deeper knowledge of how traffic models function it is difficult to estimate whether or not the resluts of the model is realistic. To make such a judgement you would have to know which assumptions the developers had made during the construction of the model and at the same time you need to know about the math used. This report uses HTM as starting point for a discription of what a traffic model consists of and how it works. Furthermore, there is a analysis of whether or not HTM is able to foretell any realistic future traffic situation.
, 2. Modul. modul, 2005, id:324  
Vejleder:  Johnny Ottesen 
Findes på RUb: 
English abstract
We have nexamined the tffects of respiration on blood flow velocity in the brain during postural change from sitting to standing. A system of differential equations is used to describe the cardiovascular system. The differential equations are solved using Euler's Method of numerical approximation and MATLAB 6.1. The parameters of the model are optimized using the NedlerMead algorithm. We have examined four different kinds of respiration. Hyperventilation has nogligble effect on blod flow velocity. Normal respiration has a small effect on the blood flow velocity in the brain. Deeper respiration and breath holdnig has a small, but noticeable effect on blood flow velocity in the brain.
, . modul, 2005, id:325  
Vejleder:  Anders Madsen 
Findes på RUb: 
English abstract
This report is a presentation of the history of expansion of series, with respect to orthogonal system. The most important aspects from Fourier to Haar are sketched, wih focus on Haar, whose work contributes to the foundation of the modern development in this field. The issues conserning the mathematicall motivation of his work, and how they are characterized compared to Fourier's work, is sketched. It elaborates on the internal processes in science development, ie. The mathematical motives and results. The external processes, ie. Issues that aren't specifically mathematical by nature, are less weighted.
Videnskabsprojekt, . modul, 2005, id:326  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
, . modul, 2005, id:328  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Nej 
Videnskabsfagsprojekt, . modul, 2005, id:329  
Vejleder:  Moges Niss 
Findes på RUb: 
Model projekt, . modul, 2005, id:330  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
In the report at hand the twocomponent flow af a lavalamp is simulated. The level set approach is being used to handle the free surface and to compute the surface tension to be used in NavierStokes equation. The implementation of the level set function in the modules of Femlab, a finite elemts based program, is described. We conclude that the level set approach os well fit to iterate the position of the dynamic surface and to compute its curvature. In the present imolemantation the level set function distributes the surface forces over a broad band in both sides of the free surface. However, the dynamics if the level set function does not secure constant width of the band, which give rise to nonphysical surface forces in i regions where the level set function is being seriously deformed.
, . modul, 2005, id:331  
Vejleder:  Anders Madsen (matematik) Bo HolstChristensen (datalogi) 
Findes på RUb: 
English abstract
speciale, . modul, 2005, id:332  
Vejleder:  Dorthe Posselt og Jesper Larsen 
Findes på RUb: 
English abstract
The dissertation contains an experimental study and a mathematical modeling and simulations study of the lightinduced structural flexibility of the photosynthetic thylakoid membrane system in higher plants. This system is uniquely organized into appressed grana stacks with helically wound stroma lamellae surrounding them. A significant functional feature of thr system is to separate two aqueous compartments, the outer stroma and the inner lumen. Tge system is thought to respond reversibly to moderate illumination manifested structually by a shrinkage of the grana stacks.
Modelprojekt, . modul, 2005, id:333  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
, bachelormodul. modul, 2005, id:334  
Vejleder:  Anders Madsen 
Findes på RUb:  Nej 
English abstract
The purpose of this project os to investigate and evaluate the results, which were determined in the scientific report MBH98. In that report the last seven hundred years global mean temperatures were compared, and it was concluded that the temperature from 1400 to 1900 has been constant but from 1900 until today the temperature has risen dramatically. This entire problem is namedthe hockey stick model. On the basis of the data input and the omplementation af these, the mathematical methods, the overall model description, and the evaluation and description of some of the areas of criticism it is concluded that out of the 22 climate indicator time series only 2 arehockey stick shaped. The way PCA has been used it is plausible that these 2 series are identical e.g. thry are in fact the same. Climatologists point out that the acceleration of this serie's growth is due to other factors than climate factors why it is not a climate indicator. As a part of PCA on another type of climate indicators, a network of wood rings, a statistically method is used, Preisendorfer's rule N, but the MBH98 has not been consistent on the use of this rule. This leads to the question if the rule has been used in the MBH98. Lastly, MBH98 uses a nontypical way to normalise its data so it is questionable af the procedure shown in the report is conventional. The conclution os that one should be careful being to sure of the conclutions found in MBH98 is probably necessary in order to be able to determine the temperature for the last 700 hundred years.
videnskabsprojekt, . modul, 2005, id:336  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb: 
English abstract
Speciale, 3. modul, 2005, id:338  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb: 
English abstract
, . modul, 2005, id:339  
Vejleder:  Anders Madsen og Bernhelm BoossBavnbek 
Findes på RUb: 
English abstract
Profession  formidling, 3. modul, 2005, id:341  
Vejleder:  Poul Winther Andersen 
Findes på RUb: 
Videnskabsfag, 1. modul, 2004/2005, id:313  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 1 + 2. modul, 2004/05, id:312  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
English abstract
In 1965 Paul Benacerraf published his article "Whar Numbers Could not Be". In this article he stated that this is not acceptable for the understanding of mathematics. In this essay we redraw the lines of the philosophical view on ontology of Mathematics, called mathematical structuralism, primarily represented by the philosopher of mathematics Stewart Shapiro. He thinks that the objects of mathematics are structures and places in structures, and that structures are really existing objects. Since both numbers and sets are positions in structures, he thinks that such a view on the ontology of mathematics may include alle wanted objects. Since we find some weak points concerning the axiom of existecne in Shapiors theory of structures, we look upuon other theories of structuralism. More specifically the category theory and som philosophical views about it. Our conclusion is, that the mathematical structuralism as it is formulated by specially Shapiro is giving a new view on the ontology of mathematics, so problems like "numbers is not objects" can be avoided. But the theory formulated by Shapiro, as well as the theory of categories, still nedde to explain how we know that such thin as structures exist. Before the philosophical discussions, the reader are introduced to naiv and axiomatic set theory, the common view on mathematical structures and the overall view on structures formulated by the group of mathematicians known as Bourbaki. The essay can be read by all interested in mathematics and the philosophy of mathematics. It though may be necessary to have som skills in logic.
Videnskabsfag, 1. modul, 2004/05, id:314  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
Videnskabsfag, 2. modul, 2004/05, id:315  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
Model, 2. modul, 2004/05, id:316  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb: 
Model, 1. modul, 2004/05, id:317  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Model, 1. modul, 2004/05, id:318  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Profession, 3. modul. modul, 2004/05, id:322  
Vejleder:  Mogens Niss 
Findes på RUb:  ja 
, . modul, 2004/05, id:327  
Vejleder:  Tinne Hoff Kjeldsen og Stig Andur Pedersen 
Findes på RUb: 
videnskabsfag, 1. modul, 2004, id:288  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 1. modul, 2004, id:289  
Vejleder:  Bernhelm BossBavnbek 
Findes på RUb:  Nej 
English abstract
Formidlervariant, 3. modul, 2004, id:290  
Vejleder:  Jacob Jacobsen 
Findes på RUb:  Ja 
Forskervariant, 3. modul, 2004, id:291  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2004, id:292  
Vejleder:  Michael Danielsen 
Findes på RUb:  Ja 
Videnskabsfag, 1. modul, 2004, id:293  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 1. modul, 2004, id:294  
Vejleder:  
Findes på RUb:  Nej 
Speciale, 3. modul, 2004, id:295  
Vejleder:  Jesper Larsen, matematik Niels Boye Olsen, fysik 
Findes på RUb:  Ja 
English abstract
Modelprojekt, 1. modul, 2004, id:297  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 2004, id:298  
Vejleder:  Jacob Jacobsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 2004, id:299  
Vejleder:  
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 2004, id:300  
Vejleder:  Per Gregersen 
Findes på RUb:  Ja 
English abstract
In the project a mathematical analysis is made of GTAP  an economic model for quantitative analyses of policy issues on a global basis. The equations of GTAP are presented, together with the economical and mathematical assumptions necessary. A numerical solution to the initial value problem of GTAP is presented. A combined analysis based on the mathematical modelling process, which is described in the beginning of the project. In the analysis it is concluded that the economical and mathematical assumptions and their consequences are hidden from the modeluser. A theoretical validation of the models is therfore impossible. Furthermore, the model assumptions demand that the database is fitted to equilibrium, which together with the models economical assumptions also makes an empirical validation of the model impossible. It is therefore impossible to either theoretically or empirically validate the model, yet it is still used in policy decisionmaking. We ask for a debate on the consequences and uncertainties involved with quantitative use of the model.
Modelprojekt, 1. modul, 2004, id:301  
Vejleder:  Michael Danielsen 
Findes på RUb:  Nej 
Modelprojekt, 2. modul, 2004, id:302  
Vejleder:  Jesper Larsen 
Findes på RUb:  Nej 
English abstract
Modelprojekt, 1 + 2. modul, 2004, id:303  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
English abstract
We wish to find the answer to the following question "How is the vascular system affected by the breating process?". We have created a model of the vascular system, by using energy band formalism and wish to determine how the change in pressure will affect the blood flow. We have used mechnical and electrical laws to create the model, and estimated the parameters of the model so that we would receive values of the pressure, flow and volume close to those of experimental data. Our model consists of (among other) two arteryvein branches, wich represent the chest and liver. The model contains two branches because the chest and the liver are affected in different ways by the breathing process. The breathing process itself is accounted for in a change in pressure in the elements of the model, and we have examined how big an effect the depth of the breath, the length of the breath and the ground pressure have on the vascular system. The ground pressure is the minimum pressure in the chest, which keeps the lungs from collapsing. Byh variation of the parameters that control the depth of the breath, the length of the breath and the ground pressure, we can examine their effects on the vascular system. We have found that the length of the breath has got no effect on the blood flow, while both the depth of the breath and the ground pressure has. Deep breathing and high ground pressure result in a bigger flow.
Videnskabsfagsprojekt, 1. modul, 2004, id:304  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 2. modul, 2004, id:305  
Vejleder:  Poul Winther Andersen 
Findes på RUb:  Nej 
Modelbygger, 3.. modul, 2004, id:306  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
Modelprojekt, 1. modul, 2004, id:307  
Vejleder:  Poul Winther Andersen og Jesper Larsen 
Findes på RUb:  Ja 
Speciale, 3. modul, 2004, id:308  
Vejleder:  Tinne Hoff Kjeldsen (matematik) Stig Andur Pedersen (filosofi) 
Findes på RUb:  Ja 
English abstract
Speciale  Forskervariant, 3. modul, 2004, id:309  
Vejleder:  Johnny Ottesen (matematik) Jeppe Dyre (fysik) 
Findes på RUb:  Ja 
English abstract
The purpose of the work reported in this thesis is to test the central assumption of the Shoving Model for the temperature dependence of the viscosity of supercooled liquids, developed at the Institute for Mathematics and Physics at Roskilde University, by performing numerical calculation on a model liquid. The central assumption of the Shoving Model is that the activation energy necessary to make a flow event in supercooled liquids is due to a compression of the surroundings of the rearranging molecules. Therefore the activation energy is only associated with the molecules in the surroundings defined as those which moves less than a certain threshold value during a flow event. The major part of the work done has been the development of an algorithm capable of finding the molecular configurations responsible for the activation energy. These configurations are equivalent to first order saddle points of the energy function of the entire system. Similar a flow event can be described as a transition from one minimum of this function to another. The system used in this work is a bulk binary LennardJones model liquid consisting of 500 molecules in which the energy is given purely by pair interactions. The basic idea behind the algorithm, called Meta Line Drag (Meta LiD), is that a saddle point between the minima in a flow event can be found by making consecutive plane minimisations along the vector connecting the minima on hyperplanes which are perpendicular to this vector. The Meta LiD algorithm is able to find saddle points in 50% of the investigated flow events. The failure of the remaining is mainly due to a disability to handle directions of negative curvature within the minimisation hyperplanes or areas where the eigenvector of the smallest eigenvalue and the vector connecting the two minima in the flow event diverges. By performing energy calculations on the molecular configurations of the saddle points it is found that the majority (75%) of the activation energy is in the surroundings. This supports the central assumption of the Shoving Model, although only partly because the Shoving Model assumes that all of the activation energy is in the surroundings.
Speciale  forskervariant, 3. modul, 2004, id:310  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
English abstract
The object of study in this thesis is a family of quadratic rational maps (formel) parametrized by the multipliers of the fixpoints at the origin and infinity. We consider Lambdaparameter planes for fixed (formel), or more precisely the connectedness loci in these planes, i.e. the sets of parameter values, which give connected Julia sets for the corresponding quadratic rational maps. The connectedness loci are for fixed (formel) denoted (formel). We prove that these connectedness loci move holomorphically with Lambda, by construction of a dynamical holomorphic motion of (formel), parametrized by the unit disk. This means that we construct a map (formel), which is holomorphic in Lambda for all (formel). Furthermore it is shown that for any (formel) it holds that (formel), which implies that (formel) is a homeomorphism onto (formel) for any (formel). The necessary concepts and statements from the theory of Riemann surfaces, quasiconformal mappings and comples dynamics are introduced and we present and/or use properties for the hyperbolic metric, polynomiallike mappings, quasiconformal surgery and the BrannerHubbard holomorphic motion. This is done in order to give, as far as possible, a selfcontained construction and proof of the holomorphic motion.
Speciale  modelbygger, 3. modul, 2004, id:311  
Vejleder:  Johnny T. Ottesen 
Findes på RUb:  Ja 
English abstract
Modelprojekt, 1 og 2. modul, 2003, id:281  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Professionsprojekt, modelbygger, 3. modul, 2003, id:282  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Nej 
Speciale, forskervariant, 3. modul, 2003, id:283  
Vejleder:  Tine Wedege 
Findes på RUb:  Ja 
English abstract
Videnskabsfagsprojekt, 2. modul, 2003, id:284  
Vejleder:  
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2003, id:285  
Vejleder:  Bernhelm Booss Bavnbek 
Findes på RUb:  Ja 
English abstract
The focal point of this project is routing in mobile adhoc networks. The original purpose was, to make possible an analytic comparison of reallife routing algorithms. This turned out to be difficult, and we have therefore worked with a broader question: What can mathematical models express, concerning routing in mobile adhoc networks, and what deficiencies does these models have with regard to an assessment of reallife routing algorithms ? We treat models based on stochastic graph theory. In particular we treat in depth two models. One which describes the probability that a finite network is connected, and another which describes how utilization of multiple routes, can decrease routing overhead by delaying the time, at which point new routes must be searched for. The conclusion is, that it is limited what we at present moment can say about routing, with the aid of mathematical models. However, as a start, we can give a few limited partial results. The studied models have several deficiencies, among others, the lack of a time aspect, and lack of named nodes. Furthermore it is questionable whether some of the assumptions, used in the models, are too restrictive.
Videnskabsfagsprojekt, 1. modul, 2003, id:286  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
English abstract
Videnskabsfagsprojekt, 2. modul, 2003, id:287  
Vejleder:  
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2003, id:296  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  420 
Findes på RUb:  Ja 
Speciale, 3. modul, 2003, id:319  
Vejleder:  Jeppe Dyre, fysik Jesper Larsen, matematik 
Findes på RUb:  Ja 
English abstract
Videnskabsfagsprojekt, 2. modul, 2002, id:267  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Modelbyggervarianten, 3. modul, 2002, id:268  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
speciale, 3. modul, 2002, id:269  
Vejleder:  Jesper Larsen Niels Boye Olsen Clive Ellegaard (NBI) Ken Haste Andersen (DTU) 
Findes på RUb:  Ja 
Videnskabsfag, 1. modul, 2002, id:270  
Vejleder:  
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 2002, id:271  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
English abstract
When a vertical jet hits a leveled surface, an equilibrium will arise. Within a radius r of the jet, the level of the liquid will be low. At a distance r from the jet this level will increase abruptly. This ring discontinuity is called the hydraulic jump. While preparing a thesis at the University og Copenhagen [4] in 1995, two students observed that the hydraulic jump could assume a polygonal form. In 1997, this peculiar discovery gave rise to a model, which had the purpose of describing which physical mechanisms are the governing of the existence of the polygonshaped jump. The basis of the model is an asserted linetension combined with a balance of forces extered on the exterior of the jump. The development of this model is not documented in detail in any publication. In this report the existing model is deployed and analysed. This is done to clarify if the mechanisms of the model gives sufficient conditions to verify the existence of the polygonal jumps. The report concludes that the model is capable of reflecting a numberof qualitative characteristics of the jump. The linetension, however, is not substantiated in any physical principle. Because of this a new model, which is better theoretically founded, is desirable. In this report the controlling equations of a new model is deduced from the physical principle of mass preservation (among others). The two models will be briefly compared and discussed.
Videnskabsfag, 2. modul, 2002, id:272  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Forskervariant, 3. modul, 2002, id:273  
Vejleder:  
Findes på RUb:  Ja 
Modelprojekt, 1. Modul + 2. Modul. modul, 2002, id:274  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Nej 
Videnskabsfagsprojekt, modul 2. modul, 2002, id:275  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Speciale, modelbyggervariant, 3. modul, 2002, id:276  
Vejleder:  Carsten Lunde Pedersen (Matematik) Keld Helsgaun (Datalogi) 
Findes på RUb:  Ja 
This Master Thesis deals with Fractal Image Compression, a lossy method for compressing digital images. Fractal Image Compression is based on image modelling with fractal structures known as iterated function systems (IFS). Compression of an image is done by constructing a iterated function system having the image as its fixed point. The system is composed of contractive affine mappings between self similar regions of the image. The parameters describing the function system serves as the compressed representation of the image. Decompression is done by iterating the function system from a random image, thus generating the fixed point of the system i.e. the original image. This thesis deals with three aspects of fractal compression, including mathematical foundation, implementation and useability of the method. The underlying mathematics is explored, covering traditional IFS, IFS with Probabilities and Recurrent IFS. Based on the mathematical theory, a prototype for fractal compression is implemented and then compared to both JPEG and an existing fractal compression application. We conclude that the most important mathematical results that makes fractal compression possible are the collage theorem for compression and the fixed point theorem for decompression. For the implementation of fractal compression methods, partitioned iterated function systems (PIFS) are used. These systems are not as mathematically well founded as the traditional IFS, but solves a number of problems that hinder implementation of traditional IFS in applications for image compression. Even though the prototype proves fractal compression to be a working method for lossy image compression, our tests show the quality vs. Compression ratio to be poor and not comparable to standard JPEG compression. Thus, fractal compression as implemented in the prototype is a poor substitute for common lossy image compression methods.
Modelprojekt, 1. modul, 2002, id:277  
Vejleder:  
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 2. modul, 2002, id:278  
Vejleder:  
Findes på RUb:  Ja 
Videnskabsfag, 1 og 2. modul, 2002, id:279  
Vejleder:  Erik von Essen 
IMFUFAtekst:  416 
Findes på RUb:  Ja 
Speciale, modelbyggervariant, 3. modul, 2002, id:280  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
English abstract
In this master thesis we present an agestructured school oriented epidemic model. The model is in two parts; one part describes a single epidemic season using a standard epidemic model, while the other part is a descrete seasontoseason map which describes the loss of susceptibles due to the epidemic. The analysis of the model focus on periodic solutions of the model. If a threshold value exceeds unity the map has an endemic stationary state. Without the introduction of an agedependent reduction in the susceptibility or infectiousness, the endemic stationary state is stable and possible oscilations of infected are of a size that does not correspond with data. With the introduction of an agedependent reduction in the infectibility, the model shows both stablre and unstable oscilations. For a limited choice of parameter values and stating points the existens of an attractor is established.
Forskervariant, 3. modul, 2001, id:258  
Vejleder:  Ulrich Kohlenbach Stig Andur Pedersen Anders Madsen 
IMFUFAtekst:  401 
Findes på RUb:  Ja 
English abstract
, 3. modul, 2001, id:259  
Vejleder:  
Findes på RUb:  Nej 
Videnskabsfag, 1. modul, 2001, id:260  
Vejleder:  Erik Von Essen 
Findes på RUb:  Ja 
Model, 1. modul, 2001, id:261  
Vejleder:  Erik von Essen 
Findes på RUb:  Nej 
Model, 2. modul, 2001, id:262  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Model, 1 og 2. modul, 2001, id:263  
Vejleder:  
Findes på RUb:  Ja 
Forskervariant, 3. modul, 2001, id:264  
Vejleder:  Carsten Lunde Pedersen 
Findes på RUb:  Ja 
English abstract
This paper deals with the subject of Fractal Image Compression. The paper gives a overview of the mathematical foundation for Fractal Image Compression of grayscale reallife images. Aim of this paper is to answer the followin question What is the mathematical foundation for fractal compression and decompression of images? The paper touches the areas of Generel Topology, Measure Theory and the Theory of Dynamical Systems. It is concluded that the theory of Iterated Function Systems, more specificaly the fixed point theorem and the collage theorem, are the most important building blocks of Fractal Image Compression.
Videnskabsfag, 2. modul, 2001, id:265  
Vejleder:  Tinne Hoff Kjeldsen Bernhelm BoossBavnbek 
IMFUFAtekst:  403 
Findes på RUb:  Ja 
Forskervariant, 3. modul, 2001, id:266  
Vejleder:  John Villumsen Carsten Lunde Poulsen 
Findes på RUb:  Ja 
English abstract
Professionsprojekt, Forskningsvarianten, 3. modul, 2000, id:237  
Vejleder:  John Villumsen og Viggo Andreasen 
IMFUFAtekst:  382 
Findes på RUb:  Ja 
Videnskabsfags og prof.projekt, Formidlervariant, 1 + 3. modul, 2000, id:239  
Vejleder:  Mogens Niss 
IMFUFAtekst:  383 
Findes på RUb:  Ja 
Professionsprojekt, Modelbyggervarianten, 3. modul, 2000, id:240  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  380 
Findes på RUb:  Nej 
English abstract
In this report we present an extension of a mathematical model of pressure as a function of time and volume in the left ventricle of the heart. It is useful both at isovolumetric contraction and at ejection to the cardiovascular system. The model is an extension of a model originally proposed by J. P. Mulier. The goal of this extension is a possible scaling of the model so as to validate it at different heart rates. Additionally, this new model is implemented into a cardiovascular model.
Professionsprojekt, Formidlervarianten, 3. modul, 2000, id:244  
Vejleder:  
Findes på RUb:  Ja 
In this report a high dimensional model of glycolysis is described by the StuartLandau equation. Describing the glycolysis in this way reduces the number of dimensions considerably. However, it is also an approximation, and the main objective is to compare the StuartLandau approximation with the original model. This is possible because a way to transform the StuartLandau coordinates back to the physical space exists. In the last chapter a table lists the results when the amplitudes, the periods, and the mean values for the StuartLandau approximation and the original model are compared.
Modelprojekt, 2. modul, 2000, id:245  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  388 
Findes på RUb:  Ja 
English abstract
In the following paper we present the main results of a one term graduate student project. The entire work is presented, in Danish, in Jakobsen & Niss. We analyse the form of the fluiddynamical equation of motion, in a two dimensional model with distributed sources and periodic boundary conditions. We conclude that the form of the equation of motion depends on the assumptions about the fluid entering and leaving the model. Futher we look at the total kinetic energy in the model, and how it depends on the assumptions.
Professionsprojekt, Modelbyggervarianten, 3. modul, 2000, id:247  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 2. modul, 2000, id:248  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1 og 2. modul, 2000, id:249  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 2000, id:250  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Professionsprojekt, formidlervarianten, 3. modul, 2000, id:251  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
videnskabsfagsprojekt, 1. modul, 2000, id:252  
Vejleder:  John Villumsen 
Findes på RUb:  Ja 
Professionsprojekt, formidlervariant, 3. modul, 2000, id:253  
Vejleder:  Oluf Danielsen og Mogens Niss 
Findes på RUb:  Ja 
Professionsprojekt, formidlervariant, 3. modul, 2000, id:254  
Vejleder:  Stig Andur Pedersen 
IMFUFAtekst:  393 
Findes på RUb:  Ja 
Professionsprojekt, Formidlervariant, 3. modul, 2000, id:255  
Vejleder:  Tine Wedege 
IMFUFAtekst:  395 og 396 
Findes på RUb:  Ja 
English abstract
Formidlervariant, 3. modul, 2000, id:256  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
English abstract
Videnskabsfag, 1. modul, 2000, id:257  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
Professionsprojekt, Formidlervarianten, 3. modul, 19992000, id:243  
Vejleder:  Erik von Essen 
Findes på RUb:  Nej 
English abstract
Modelprojekt, 2. modul, 19992000, id:246  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
English abstract
Videnskabsfagsprojekt, 1. modul, 1999, id:218  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
Professionsprojekt, formidlervarianten, 3. modul, 1999, id:219  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1999, id:220  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1 + 2. modul, 1999, id:221  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Nej 
Modelprojekt, . modul, 1999, id:222  
Vejleder:  
Findes på RUb: 
Ingen projektrapport afleveret til MATSN.
Modelprojekt, 2. modul, 1999, id:224  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Professionsprojekt, modelbyggervarianten, 3. modul, 1999, id:225  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Professionsprojekt, 3. modul, 1999, id:226  
Vejleder:  Mogens Niss 
IMFUFAtekst:  371 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1999, id:227  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1999, id:228  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  386 
Findes på RUb:  Nej 
Projektet behandler problemet om hvorvidt man v.h.a. formelle matematiske metoder kan sammenligne og kvalitetsvurdere forskellige mandatfordelingsmetoder, og derigennem evt. bestemme den mest neutrale.
Professionsprojekt, formidlervarianten, 3. modul, 1999, id:229  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1999, id:230  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 1 + 2. modul, 1999, id:231  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1999, id:232  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Professionsprojekt, 3. modul, 1999, id:233  
Vejleder:  Stig Andur Pedersen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1999, id:234  
Vejleder:  John Villumsen 
Findes på RUb:  Ja 
Projektrapporten omhandler matematiske modeller anvendt i kombinatorisk kemi.
Professionsprojekt, Forskervarianten, 3. modul, 1999, id:235  
Vejleder:  Carsten Lunde Petersen 
IMFUFAtekst:  369 
Findes på RUb:  Ja 
English abstract
This thesis summarizes som important results from the theories of Riemann surface geometry and complex dynamics in order to apply them in the analysis of quadratic correspondences. The example of the arithmeticgeometric mean value is used as a starting point to expose som properties of quadratic correspondences. Attempts to define Fatou and Julia sets as well as regular and limit sets for correspondences are presented.
Professionsprojekt, Modelbyggervarianten, 3. modul, 1999, id:236  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
English abstract
Professionsprojekt, Modelbyggervarianten, 3. modul, 1999, id:238  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1 + 2. modul, 1999, id:241  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Modelprojekt, 1 + 2. modul, 1999, id:242  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Professionsprojekt, 3. modul, 1999, id:459  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Speciale, 3. modul, 1999, id:460  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
, 2. modul, 1998, id:197  
Vejleder:  Jesper Larsen 
Findes på RUb:  Ja 
speciale, 3. modul, 1998, id:208  
Vejleder:  
IMFUFAtekst:  353 
Findes på RUb:  Ja 
Professionsprojekt  formidlervarianten, 3. modul, 1998, id:209  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 1998, id:210  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  357 
Findes på RUb:  Ja 
, 1. modul, 1998, id:211  
Vejleder:  Mogens Niss 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 2. modul, 1998, id:212  
Vejleder:  
Findes på RUb:  Nej 
Modelprojekt, 2. modul, 1998, id:213  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  356 
Findes på RUb:  Ja 
Model og videnskabsfagsprojekt, 2. modul, 1998, id:214  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 2. modul, 1998, id:215  
Vejleder:  
IMFUFAtekst:  362 
Findes på RUb:  Ja 
Professionsprojekt  speciale, 3. modul, 1998, id:216  
Vejleder:  Stig Andur Pedersen 
Findes på RUb:  Ja 
Professionsprojekt, modelbyggervarianten, 3. modul, 1998, id:217  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1 + 2. modul, 1998, id:223  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 199798, id:207  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:198  
Vejleder:  
Findes på RUb:  Ja 
In the following I have examined the use of a stochastic decision function in Bayesian sampling planning. More precisely I examined the problem of accepting or rejecting a batch of articles described by a normally distributed average weight. Such a decision can be made by using a polynomial loss function. If we let the loss function be linearly dependent on the size of the samlpe, we can find the optimal size of the sample. In this report I have examined the appliance of a stochastic decision function proposed by /Ho, 1995). The purpose of this decision function is to allow for the buyer to bargain after the sample have been tested. I have written a program in Mathematica that can find the optimal size of the sample and loss function. Results from this program show that the stochastic decision function does not have a great influcence on the minimizing sample size.
Modelprojekt, . modul, 1997, id:196  
Vejleder:  Johnny Ottesen og Jacob Jacobsen 
Findes på RUb:  Ja 
Model, 2. modul, 1997, id:193  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  nej 
Professionsprojekt, formidlervariant, 3. modul, 1997, id:194  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 2. modul, 1997, id:195  
Vejleder:  Jacob Jacobsen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1997, id:188  
Vejleder:  
IMFUFAtekst:  337 
Findes på RUb:  Ja 
Modelbyggervariant, 3. Modul. modul, 1997, id:190  
Vejleder:  Mogens N. Olesen 
Findes på RUb:  Ja 
Professionsprojekt formidlervariant, 3. modul, 1997, id:199  
Vejleder:  
Findes på RUb:  Ja 
Professionsprojekt, formidlervariant, 3. modul, 1997, id:200  
Vejleder:  
Findes på RUb:  Nej 
Proffession, formidlervariant., 3. modul, 1997, id:201  
Vejleder:  Erik von Essen 
Findes på RUb:  Nej 
Modelprojekt, 1. modul, 1997, id:202  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  347 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:203  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:204  
Vejleder:  Jesper Larsen 
Findes på RUb:  Nej 
Modelprojekt, 2. modul, 1997, id:205  
Vejleder:  Stig Andur Pedersen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 1997, id:206  
Vejleder:  Stig Andur Pedersen 
Findes på RUb:  Ja 
Introduktionsprojekt, 1. modul, 1997, id:461  
Vejleder:  
Findes på RUb:  Ja 
Introduktionsprojekt, 1. modul, 1997, id:462  
Vejleder:  
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1997, id:463  
Vejleder:  Stig Andur Pedersen 
Findes på RUb: 
Professionsprojekt  modelbyggervariant, 3. modul, 1996/97, id:186  
Vejleder:  Jacob M. Jacobsen og Jesper Larsen 
IMFUFAtekst:  331 
Findes på RUb:  Ja 
, 2. modul, 1996/97, id:187  
Vejleder:  Jacob Jacobsen 
Findes på RUb:  Nej 
Model, 1. modul, 1996, id:192  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 2. modul, 1996, id:175  
Vejleder:  Mogens Brun Heefelt 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1996, id:176  
Vejleder:  Mogens Brun Heefelt 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1996, id:177  
Vejleder:  Jacob M. Jacobsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 1996, id:178  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 1996, id:179  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 1996, id:180  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, . modul, 1996, id:181  
Vejleder:  
Findes på RUb:  Ja 
Modelprojekt, . modul, 1996, id:182  
Vejleder:  Carsten Lunde Petersen 
Findes på RUb:  Ja 
Professionsprojekt , 3. modul, 1996, id:183  
Vejleder:  Viggo Andreasen og Michael Danielsen 
IMFUFAtekst:  318 
Findes på RUb:  Ja 
The thesis deals with modelling of the human respiratory system. A model of the human respiratory system is developed for use in the anaesthesia simulator SIMA. The model contains lung mechanics, airway dynamics, the blood transport system, the dissociation of gasses in blood and tissue, the metabolism and the pH value of blood. The models are basically compartment models extended with vector compartment variables and a technique that allows the distribution in inhomogeneous compartsments to be found by use of the derived of the dissociation function. This supports interactions between several transported substances well.
Professionsprojekt , 3. modul, 1996, id:184  
Vejleder:  
IMFUFAtekst:  321 
Findes på RUb:  Ja 
Professionsprojekt  formidlervariant, 3. modul, 1996, id:185  
Vejleder:  Mogens Niss 
IMFUFAtekst:  325 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, modul 1. modul, 1996, id:189  
Vejleder:  
Findes på RUb:  Ja 
Model, 2. modul, 1996, id:191  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Professionsprojekt  formidlervarianten, 3. modul, 1996, id:174  
Vejleder:  
Findes på RUb:  nej 
Videnskabsfagsprojekt, 3. modul, 1996, id:161  
Vejleder:  Anders Madsen 
IMFUFAtekst:  317 
Findes på RUb: 
, . modul, 1996, id:164  
Vejleder:  Bernhelm BoossBavnbek og Stig Andur Pedersen 
IMFUFAtekst:  326 
Findes på RUb:  Ja 
English abstract
Modelprojekt, 2. modul, 1996, id:165  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Modelprojekt, 2. modul, 1996, id:166  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Ja 
Praksisprojekt formidlingstype, 3. modul, 1996, id:168  
Vejleder:  Erik von Essen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, . modul, 1996, id:169  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, 1. modul, 1996, id:171  
Vejleder:  Anders Hede Madsen 
Findes på RUb:  Ja 
Praksisprojekt modelbygning, . modul, 1996, id:172  
Vejleder:  Anders Hede Madsen 
Findes på RUb: 
Specialerapport, 3. modul, 1996, id:173  
Vejleder:  Stig Andur Pedersen 
Findes på RUb:  Ja 
A: Projekt B: Videnskabsfagsmodul, A: Modul 1. modul, 1995, id:143  
Vejleder:  A: Bernelm BoossBavnbek. B: Jacob Jacobsen. 
Findes på RUb:  B: Nej 
, 3. modul, 1995, id:144  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  290 
Findes på RUb: 
Projektrapport, 3. modul, 1995, id:145  
Vejleder:  
IMFUFAtekst:  303 
Findes på RUb:  Nej 
Speciale, . modul, 1995, id:150  
Vejleder:  Mogens Niss 
Findes på RUb: 
Videnskabsprojekt, Bachelor. modul, 1995, id:151  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Nej 
Projekt, . modul, 1995, id:152  
Vejleder:  Viggo Andreasen 
IMFUFAtekst:  302 
Findes på RUb: 
Praksisprojekt, 3. modul, 1995, id:153  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
Projektrapport, Bachelor. modul, 1995, id:154  
Vejleder:  Jacob Jacobsen 
Findes på RUb:  Nej 
Historisk projekt, . modul, 1995, id:155  
Vejleder:  Jacob Jacobsen 
Findes på RUb: 
Videnskabsprojekt, 2. modul, 1995, id:156  
Vejleder:  Lars Kadison 
Findes på RUb:  Nej 
Praktisk modelbyggerprojekt, 3. modul, 1995, id:158  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  301 
Findes på RUb: 
Modelprojekt, . modul, 1995, id:159  
Vejleder:  
IMFUFAtekst:  299 
Findes på RUb: 
Videnskabsprojekt, Bachelormodul. modul, 1995, id:160  
Vejleder:  Anders Madsen 
Findes på RUb:  Nej 
, Bachelormodul. modul, 1995, id:162  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
, Breddemodul. modul, 1995, id:163  
Vejleder:  Johnny Ottesen 
Findes på RUb:  Ja 
Modelprojekt, 1. modul, 1995, id:167  
Vejleder:  Erik von Essen 
Findes på RUb: 
Videnskabsfagsprojekt, . modul, 1995, id:170  
Vejleder:  
Findes på RUb:  Ja 
, 2. modul, 199495, id:157  
Vejleder:  Jesper Larsen 
Findes på RUb:  Nej 
Speciale, . modul, 1994, id:125  
Vejleder:  Johnny Ottesen 
Findes på RUb: 
Projektrapport, 3. modul, 1994, id:126  
Vejleder:  Viggo Andreasen 
IMFUFAtekst:  281 
Findes på RUb:  Ja 
, . modul, 1994, id:127  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb:  Nej 
With the focus on ideas rather than chronololy, this text deals with the fundamental problem of knot theory: to decide when two knotted curves are distinct. We develop invariants, first simple ones, and then more complicated as the Alexander polynomial, and ends up with proving that the Jones polynomial is an invariant, using two different approaches. In the conclusion, we outline the promising connections between knot theory and other fields, and finally use our knowledge about knot theory to comment on what seems to be general mathematical "phenomena".
Modelprojekt, 2. modul, 1994, id:130  
Vejleder:  Jesper Larsen 
Findes på RUb: 
Videnskabsfagsprojekt, 1. modul, 1994, id:131  
Vejleder:  Anders Madsen 
Findes på RUb:  Ja 
, 1. modul, 1994, id:133  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  309 
Findes på RUb: 
, 1. modul, 1994, id:134  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  276 
Findes på RUb:  Ja 
, . modul, 1994, id:135  
Vejleder:  Lars Kadison 
Findes på RUb:  Ja 
, . modul, 1994, id:136  
Vejleder:  Lars Kadison 
Findes på RUb: 
, 3. modul, 1994, id:137  
Vejleder:  Viggo Andreasen og Jesper Larsen 
IMFUFAtekst:  274 
Findes på RUb: 
Videnskabsfagsprojekt, 2. modul, 1994, id:138  
Vejleder:  Viggo Andreasen og Jesper Larsen 
Findes på RUb:  Ja 
Projektrapport, 2. modul, 1994, id:139  
Vejleder:  Mette Olufsen 
IMFUFAtekst:  273 
Findes på RUb:  Ja 
Videnskabsfagsprojekt, . modul, 1994, id:140  
Vejleder:  Johnny Ottesen 
Findes på RUb: 
Speciale, . modul, 1994, id:141  
Vejleder:  Stig Andur Pedersen 
Findes på RUb: 
Speciale, . modul, 1994, id:142  
Vejleder:  Mogens Niss 
IMFUFAtekst:  294 
Findes på RUb: 
Videnskabsfagsprojekt, . modul, 1994, id:146  
Vejleder:  Anders Madsen 
Findes på RUb: 
Formidlingsprojekt, 3. modul, 1994, id:147  
Vejleder:  Anders Madsen 
IMFUFAtekst:  293 
Findes på RUb:  Ja 
Projektrapport, 2. modul, 1994, id:148  
Vejleder:  Johnny Ottesen 
Findes på RUb: 
Ingen rapport
, . modul, 1994, id:149  
Vejleder:  Johnny Ottesen 
Findes på RUb: 
, 2. modul, 1993, id:113  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  242 
Findes på RUb: 
, . modul, 1993, id:120  
Vejleder:  Jesper Larsen 
Findes på RUb: 
Projektrapport, 3. modul, 1993, id:121  
Vejleder:  Mogens Niss 
IMFUFAtekst:  253 
Findes på RUb: 
, 2. modul, 1993, id:122  
Vejleder:  Mogens Niss 
Findes på RUb: 
, 2. modul, 1993, id:123  
Vejleder:  Stig Andur Pedersen 
Findes på RUb: 
Projektrapport, 1. modul, 1993, id:124  
Vejleder:  Stig Andur Pedersen 
IMFUFAtekst:  250 
Findes på RUb: 
, 3. modul, 1993, id:128  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
, 2+3. modul, 1993, id:129  
Vejleder:  Jesper Larsen 
Findes på RUb: 
Videnskabsfagsprojekt, 1. modul, 1993, id:132  
Vejleder:  Anders Hede Madsen 
Findes på RUb:  Ja 
Kombineret fysik/matematikprojekt, 2/3. modul, 1992/93, id:112  
Vejleder:  Dorthe Posselt og Lars Kadison 
Findes på RUb:  Ja 
, . modul, 1992/93, id:118  
Vejleder:  
Findes på RUb: 
, . modul, 1992, id:101  
Vejleder:  Jesper Larsen 
Findes på RUb: 
, 1. modul, 1992, id:102  
Vejleder:  
Findes på RUb: 
Projektopgave, . modul, 1992, id:103  
Vejleder:  Mogens Niss 
Findes på RUb: 
, 2. modul, 1992, id:105  
Vejleder:  Stig Andur Pedersen 
IMFUFAtekst:  220 
Findes på RUb: 
, 1.. modul, 1992, id:107  
Vejleder:  Gerd Brandell 
Findes på RUb: 
, 2. modul, 1992, id:108  
Vejleder:  Gerd Brandell 
Findes på RUb: 
, . modul, 1992, id:109  
Vejleder:  Jesper Larsen 
Findes på RUb: 
, 1. modul, 1992, id:110  
Vejleder:  Johnny Ottesen 
IMFUFAtekst:  230 
Findes på RUb: 
Projektrapport, 1. modul, 1992, id:111  
Vejleder:  Stig Andur Pedersen, Gestur Olafsson, Peder Voetmann Christiansen 
Findes på RUb:  Ja 
Projektrapport, 2. modul, 1992, id:114  
Vejleder:  Gestur Olafsson og Jesper Larsen 
Findes på RUb: 
, 1. modul, 1992, id:115  
Vejleder:  Anders Hede Madsen 
Findes på RUb: 
Projektrapport, 2. modul, 1992, id:116  
Vejleder:  Mogens Niss 
Findes på RUb: 
, . modul, 1992, id:117  
Vejleder:  Mogens Niss 
Findes på RUb: 
, 2. modul, 1992, id:119  
Vejleder:  
Findes på RUb: 
Modelprojekt, . modul, 1991/92, id:104  
Vejleder:  Gestur Olafsson 
Findes på RUb: 
, . modul, 1991, id:90  
Vejleder:  Viggo Andreasen 
Findes på RUb:  Nej 
Projekt, 2. modul, 1991, id:91  
Vejleder:  Viggo Andreasen og Marc Andersen 
Findes på RUb:  Nej 
, . modul, 1991, id:92  
Vejleder:  viggo Andreasen 
Findes på RUb: 
, 2 og 3. modul, 1991, id:93  
Vejleder:  
Findes på RUb:  Ja 
, 2. modul, 1991, id:94  
Vejleder:  
Findes på RUb: 
, . modul, 1991, id:95  
Vejleder:  
Findes på RUb: 
, 1. modul, 1991, id:96  
Vejleder:  Jesper Larsen og Bernhelm BoossBavnbek 
IMFUFAtekst:  211 
Findes på RUb: 
, 3 + 1. modul, 1991, id:97  
Vejleder:  Johnny Ottesen og H.B. Hansen 
IMFUFAtekst:  231A+B 
Findes på RUb: 
, . modul, 1991, id:98  
Vejleder:  
IMFUFAtekst:  283 
Findes på RUb: 
, 1. modul, 1991, id:99  
Vejleder:  
Findes på RUb: 
, 1. modul, 1991, id:100  
Vejleder:  Lars Kadison, Mogens Brun Heefelt og Stig Skelboe 
Findes på RUb: 
, . modul, 1991, id:106  
Vejleder:  
Findes på RUb: 
, . modul, 1990/91, id:88  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
, 1. modul, 1990, id:85  
Vejleder:  Jacob Jacobsen 
Findes på RUb: 
, . modul, 1990, id:86  
Vejleder:  Jesper Larsen 
Findes på RUb: 
, . modul, 1990, id:87  
Vejleder:  
Findes på RUb: 
, . modul, 1990, id:89  
Vejleder:  Jesper Larsen 
Findes på RUb: 
, . modul, 1989/90, id:83  
Vejleder:  Michael Pedersen og Finn Munch 
Findes på RUb: 
, . modul, 1989, id:72  
Vejleder:  
Findes på RUb: 
, . modul, 1989, id:76  
Vejleder:  
Findes på RUb: 
, . modul, 1989, id:77  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  178 
Findes på RUb: 
, 3. modul, 1989, id:78  
Vejleder:  
Findes på RUb: 
, 2. modul, 1989, id:79  
Vejleder:  Dorthe Olesen 
Findes på RUb: 
, . modul, 1989, id:80  
Vejleder:  
Findes på RUb: 
, . modul, 1989, id:81  
Vejleder:  
Findes på RUb: 
, . modul, 1989, id:82  
Vejleder:  Jesper Larsen 
Findes på RUb: 
, . modul, 1989, id:84  
Vejleder:  Michael Pedersen 
Findes på RUb: 
, 2.. modul, 1988/89, id:75  
Vejleder:  Michael Pedersen 
Findes på RUb: 
, . modul, 1988, id:68  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  163 
Findes på RUb: 
, . modul, 1988, id:70  
Vejleder:  
Findes på RUb: 
, . modul, 1988, id:71  
Vejleder:  
Findes på RUb: 
, . modul, 1988, id:73  
Vejleder:  Dorte Olesen 
Findes på RUb: 
, . modul, 1988, id:74  
Vejleder:  
Findes på RUb: 
, . modul, 1987/88, id:69  
Vejleder:  
Findes på RUb: 
, . modul, 1987, id:63  
Vejleder:  Mogens Niss 
IMFUFAtekst:  151 
Findes på RUb: 
, . modul, 1987, id:66  
Vejleder:  
Findes på RUb: 
, . modul, 1987, id:67  
Vejleder:  
Findes på RUb: 
Speciale, 3. modul, 1987, id:457  
Vejleder:  Anton Jensen, Stig Andur Pedersen 
IMFUFAtekst:  135 
Findes på RUb: 
, . modul, 1986/87, id:64  
Vejleder:  
Findes på RUb: 
, 2. modul, 1986/87, id:65  
Vejleder:  Anders J.H. Madsen 
Findes på RUb:  Ja 
Goddag !
, . modul, 1986, id:55  
Vejleder:  Mogens Niss 
IMFUFAtekst:  119 
Findes på RUb: 
, . modul, 1986, id:57  
Vejleder:  Mogens Brun Heefelt ??? 
Findes på RUb: 
, . modul, 1986, id:58  
Vejleder:  Jesper Larsen 
Findes på RUb: 
, . modul, 1986, id:59  
Vejleder:  Mogens Niss 
IMFUFAtekst:  127 
Findes på RUb: 
, . modul, 1986, id:60  
Vejleder:  
Findes på RUb: 
, . modul, 1986, id:62  
Vejleder:  Jeppe Dyre 
IMFUFAtekst:  128 
Findes på RUb: 
, . modul, 1985/86, id:56  
Vejleder:  
Findes på RUb: 
, . modul, 1985/86, id:61  
Vejleder:  
Findes på RUb: 
, . modul, 1985, id:48  
Vejleder:  Mogens Brun Heefelt 
Findes på RUb: 
, . modul, 1985, id:49  
Vejleder:  Jesper Larsen 
IMFUFAtekst:  107 
Findes på RUb: 
, 2. modul, 1985, id:50  
Vejleder:  
IMFUFAtekst:  109 
Findes på RUb: 
, . modul, 1985, id:51  
Vejleder:  Jesper Larsen 
Findes på RUb: 
, . modul, 1985, id:52  
Vejleder:  Mogens Niss 
IMFUFAtekst:  111 
Findes på RUb: 
, . modul, 1985, id:53  
Vejleder:  
Findes på RUb: 
, . modul, 1985, id:54  
Vejleder:  
IMFUFAtekst:  114 
Findes på RUb: 
, . modul, 1984/85, id:44  
Vejleder:  
Findes på RUb: 
, . modul, 1984/85, id:45  
Vejleder:  
Findes på RUb: 
, . modul, 1984/85, id:46  
Vejleder:  
IMFUFAtekst:  94 
Findes på RUb: 
, 1. modul, 1984/85, id:47  
Vejleder:  
Findes på RUb: 
, . modul, 1984, id:37  
Vejleder:  
IMFUFAtekst:  75 
Findes på RUb: 
, . modul, 1984, id:38  
Vejleder:  
IMFUFAtekst:  99 
Findes på RUb: 
, . modul, 1984, id:39  
Vejleder:  
IMFUFAtekst:  102 
Findes på RUb: 
, 3. modul, 1984, id:40  
Vejleder:  
Findes på RUb: 
, . modul, 1984, id:41  
Vejleder:  
IMFUFAtekst:  85 
Findes på RUb: 
, . modul, 1984, id:42  
Vejleder:  ??? 
Findes på RUb: 
, . modul, 1984, id:43  
Vejleder:  
IMFUFAtekst:  79 
Findes på RUb: 
, . modul, 1983/84, id:36  
Vejleder:  Bernhelm BoossBavnbek 
Findes på RUb: 
, . modul, 1983, id:31  
Vejleder:  
IMFUFAtekst:  67 
Findes på RUb: 
, . modul, 1983, id:32  
Vejleder:  
IMFUFAtekst:  77 
Findes på RUb: 
, . modul, 1983, id:33  
Vejleder:  
IMFUFAtekst:  77 
Findes på RUb: 
, . modul, 1983, id:34  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  65 
Findes på RUb: 
, . modul, 1983, id:35  
Vejleder:  
IMFUFAtekst:  66 
Findes på RUb: 
, . modul, 1982/83, id:29  
Vejleder:  
IMFUFAtekst:  58 
Findes på RUb: 
, . modul, 1982/83, id:30  
Vejleder:  
IMFUFAtekst:  60 
Findes på RUb: 
, . modul, 1982, id:24  
Vejleder:  
IMFUFAtekst:  70 
Findes på RUb: 
, . modul, 1982, id:25  
Vejleder:  
Findes på RUb: 
, . modul, 1982, id:26  
Vejleder:  
Findes på RUb: 
, . modul, 1982, id:27  
Vejleder:  Ingen 
IMFUFAtekst:  51 
Findes på RUb: 
, . modul, 1982, id:28  
Vejleder:  
IMFUFAtekst:  56 
Findes på RUb: 
, . modul, 1981/82, id:23  
Vejleder:  
IMFUFAtekst:  49 
Findes på RUb: 
, . modul, 1981, id:21  
Vejleder:  
IMFUFAtekst:  48 
Findes på RUb: 
, . modul, 1981, id:22  
Vejleder:  
Findes på RUb: 
, . modul, 1980/81, id:19  
Vejleder:  
IMFUFAtekst:  38 
Findes på RUb: 
, . modul, 1980, id:15  
Vejleder:  
IMFUFAtekst:  24a+b 
Findes på RUb: 
, . modul, 1980, id:16  
Vejleder:  
Findes på RUb: 
, . modul, 1980, id:17  
Vejleder:  Mogens Brun Heefelt 
IMFUFAtekst:  29 
Findes på RUb: 
, . modul, 1980, id:18  
Vejleder:  
IMFUFAtekst:  31 
Findes på RUb: 
, . modul, 1980, id:20  
Vejleder:  
IMFUFAtekst:  39 
Findes på RUb: 
, . modul, 1979/80, id:14  
Vejleder:  
Findes på RUb: 
, . modul, 1979, id:12  
Vejleder:  
IMFUFAtekst:  19 
Findes på RUb: 
, . modul, 1979, id:13  
Vejleder:  
IMFUFAtekst:  20 
Findes på RUb: 
, . modul, 1978, id:8  
Vejleder:  
IMFUFAtekst:  16 
Findes på RUb: 
, . modul, 1978, id:9  
Vejleder:  Anders Madsen 
IMFUFAtekst:  1 
Findes på RUb: 
, . modul, 1978, id:10  
Vejleder:  Bernhelm BoossBavnbek 
IMFUFAtekst:  2 
Findes på RUb: 
, . modul, 1978, id:11  
Vejleder:  Anders Madsen 
IMFUFAtekst:  9 
Findes på RUb: 
, . modul, 1977, id:4  
Vejleder:  
Findes på RUb: 
, . modul, 1977, id:5  
Vejleder:  Bernhelm Booss, Mogens Niss 
Findes på RUb: 
, . modul, 1977, id:6  
Vejleder:  
Findes på RUb: 
, . modul, 1977, id:7  
Vejleder:  
Findes på RUb: 
, 2. modul, 1976, id:3  
Vejleder:  Allan Tarp, Mogens Brun Heefelt 
Findes på RUb: 
, . modul, 1975, id:1  
Vejleder:  Mogens Niss 
Findes på RUb: 
, . modul, 1975, id:2  
Vejleder:  
Findes på RUb: 
Videnskabsfag, 1. modul, 2006, id:342  
Vejleder:  Tinne Hoff Kjeldsen 
Findes på RUb:  Ja 
English abstract
In this report we will examine mathematics as a subject in the danish hig school, how it has been presented in law and school books. We will focus on the years 1906, 1935, 1961/71, 1987 and 2005. On the basis of this analysis we can conclude that there is a tencency that mathematics change from being strictly pure to focus on the applications of mathematical theory in concrete problems. The most widely used school books, however, are very conservative and are focused mainly  or only  on pure mathematics. After 1987 meta mathematical aspects are also included to be a part of the teaching programme.
Videnskabsfagsprojekt, 2. modul. modul, , id:323  
Vejleder:  
Findes på RUb:  ja 