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Liste over projekter af typen videnskabsfagsprojekt


Videnskabsfagsprojekt, 1. modul, Vinter 2012, id:441
Vejleder:Anders Madsen
Findes på RUb: Ja
Abstract
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 Turing-machine. 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.

Concept image and concept definition of functions
Videnskabsfagsprojekt, 1. modul, Vinter 2012, id:442
Vejleder:Mogens A. Niss
Findes på RUb: Ja
English abstract

Matematikkens fundament i krise
Videnskabsfagprojekt, 1. modul, Vinter 2012, id:443
Vejleder:Anders Madsen
Findes på RUb: Ja
Abstract
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.

Problemer vs. Teoremer
Videnskabsfagsprojekt, 1. modul, Vinter 2011, id:421
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
Abstract
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.

Continuum hypothesis and its influence on the decelopment of the set theory.
Videnskabsfagsprojekt, 1. modul, Vinter 2011, id:423
Vejleder:Viggo Andreasen
Findes på RUb: Ja
English abstract
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
Abstract
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.

Henstockintegralet - et overset integral ?
Videnskabsfagsprojekt, 1. modul, Vinter 2011, id:426
Vejleder:Viggo Andreasen
Findes på RUb: Ja
Abstract
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.

Radon's Merge of the Stieltjes and Lebesgue integral
Videnskabsfagsprojekt, Modul 1. modul, Vinter 2011, id:429
Vejleder:Viggo Andreasen
Findes på RUb: Ja
English abstract
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.

Holomorf Dynamik - et historisk perspektiv
Videnskabsfagsprojekt, 2. modul, Vinter 2010, id:409
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
Abstract
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 mid-1920'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 mid-1970'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 quasi-conformal 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.


Videnskabsfagsprojekt, 2. modul, Vinter 2010, id:412
Vejleder:
Findes på RUb: Ja
Abstract
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 object-level manages the complex plane to dissolve the anomaly as the complex numbers has hitherto been, but at the meta-level 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.


Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:448
Vejleder:Anders J. Hede Madsen
Findes på RUb: Ja
Abstract
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.

Riemann hypotesen
Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:450
Vejleder:Anders J. Hede Madsen
Findes på RUb: Ja
Abstract
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 Basel-problem. 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 1859-paper 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.

Matematiske discipliner mellem 1870-1940
Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:451
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 1. modul, Sommer 2013, id:452
Vejleder:
Findes på RUb: Ja
Abstract
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.

I et historisk perspektiv: Eksperimenters rolle i matematisk vidensproduktion belyst ved udvalgte cases af Leonhard Euler og Carl Friedrich Gauss
Videnskabsfagsprojekt, 1. modul, Sommer 2012, id:435
Vejleder:
Findes på RUb: Ja
Abstract
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 Arithmetic-Geometric 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.

Comparison of two epidemiological models
Videnskabsfagsprojekt, 1. modul, Sommer 2012, id:437
Vejleder:Viggo Andreasen
Findes på RUb: Ja
Abstract
English abstract
This project is based on the article "Natural immune boosting in pertussis dynamics and the potential for long-term 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
Abstract
English abstract
In this project we investigate whether or not there excist correlations for a bead-spring 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.

The Link between Algebra and Geometry. How Does Our Brain Function ?
Videnskabsfagsprojekt, 1. modul, Sommer 2011, id:413
Vejleder:Johnny Ottesen
Findes på RUb: Ja
English abstract
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.

Udvikling af vektorbegreberne i gymnasiernes matematikundervisning i 1900-tallet
Videnskabsfagsprojekt, 1. modul, Sommer 2011, id:418
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
Abstract
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: 1900-1935, 1935-1959, 1960-1990 and 1991-2005. 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.

Distributioner og currents
Videnskabsfagsprojekt, 1. modul, Sommer 2011, id:420
Vejleder:Carsten Lunde Pedersen
Findes på RUb: Ja
Abstract
English abstract
The report deals with the historic development of two mathematical concepts, distributions and currents, which were formalised in the period 1930-1955 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.


Videnskabsfagsprojekt, 1. modul, 2013, id:465
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
Abstract
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.

Udviklingen af det moderne uendelighedsbegreb
Videnskabsfagsprojekt, 1. modul, 2013, id:467
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract
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.

Validation of Mathematical Models in Biology
Videnskabsfag, 2. modul, 2010, id:399
Vejleder:Johnny Ottesen
Findes på RUb: Ja
Abstract
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 Hypothalamo-Pituitary-Adrenal (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 cross-validation 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.

The mathematical foundations for training and designing neural networks
Videnskabsfag, 2. modul, 2010, id:402
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
English abstract
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.

Der er en hestesko i dynamikken
Videnskabsfag, 2. modul, 2010, id:403
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
Abstract
English abstract


Videnskabsfag, 2. modul, 2009/10, id:391
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract
English abstract

The effect of Computers on Pure Mathematics
Videnskabsfag, 2. modul, 2009/10, id:394
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: 
English abstract
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 Four-Colour Theorem, then the famous Jaffe-Quinn 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.


Videnskabsfag, 2. modul, 2009/10, id:398
Vejleder:
Findes på RUb: Ja
Abstract
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 measure-theoretic approach from 1933 and on Shafer and Vovk's game-theoretic 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.

Mathematical and historical research about the theory of population dynamics
videnskabsfag, 2. modul, 2009, id:384
Vejleder:Anders Madsen
Findes på RUb: 
Abstract
English abstract


Videnskabsfag, 2. modul, 2008, id:368
Vejleder:
Findes på RUb: Nej
Abstract
English abstract


Videnskabsfag, 2. modul, 2008, id:370
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
Abstract
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.


Videnskabsfag, 2. modul, 2007/2008, id:362
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
English abstract
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.


Videnskabsfag, 2. modul, 2007/2008, id:364
Vejleder:
Findes på RUb: Ja


Videnskabsfag, 1 og 2. modul, 2007, id:353
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract

Variationsregningens tidlige udvikling
Videnskabsfag, 2. modul, 2007, id:355
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
Abstract
English abstract

Matematiske Beviser - Kravene til dem og brugen af dem
Videnskabsfag, 3. modul, 2007, id:356
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract
English abstract


Videnskabsfag, 1. modul, 2007, id:359
Vejleder:Mogens Niss
Findes på RUb: 


Videnskabsfag, 2. modul, 2006/2007, id:347
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: 
Abstract
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?

Kompetencespring i matematikken
Videnskabsfag, 1 + 2. modul, 2006, id:374
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: 
Abstract
English abstract

Gymnasiematematik 2005 - i historisk perspektiv
Videnskabsprojekt, . modul, 2005, id:326
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract

Hvordan skabes faglig dygtige matematikelever?
Videnskabsfagsprojekt, . modul, 2005, id:329
Vejleder:Moges Niss
Findes på RUb: 
Abstract


videnskabsprojekt, . modul, 2005, id:336
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: 
Abstract
English abstract

Matematisk empirisme
Videnskabsfag, 1. modul, 2004/2005, id:313
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: Ja
Abstract
English abstract

Matematisk strukturalisme og matematikkens ontologi
Videnskabsfag, 1 + 2. modul, 2004/05, id:312
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract
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
Abstract

Uendelighed og "integration" i antikken
Videnskabsfag, 2. modul, 2004/05, id:315
Vejleder:Anders Madsen
Findes på RUb: Ja

Distributionsteoriens udbredelse siden 1950
videnskabsfag, 1. modul, 2004, id:288
Vejleder:Anders Madsen
Findes på RUb: Ja
Abstract
English abstract


Videnskabsfag, 1. modul, 2004, id:289
Vejleder:Bernhelm Boss-Bavnbek
Findes på RUb: Nej
Abstract
English abstract


Videnskabsfag, 1. modul, 2004, id:293
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
Abstract
English abstract

Minkowski & udviklingen af den specielle relativitetsteori
Videnskabsfag, 1. modul, 2004, id:294
Vejleder:
Findes på RUb: Nej
Abstract

Formidling af vektorer i gymnasiet
Videnskabsfagsprojekt, 1. modul, 2004, id:298
Vejleder:Jacob Jacobsen
Findes på RUb: Ja
Abstract

Runge-Kutta Metodens historie - Baggrund og oprindelse
Videnskabsfagsprojekt, 1. modul, 2004, id:299
Vejleder:
Findes på RUb: Ja
Abstract

Udvikling, accept og anvendelse af matematiske teorier og modeller belyst af et eksempel.
Videnskabsfagsprojekt, 1. modul, 2004, id:304
Vejleder:Jesper Larsen
Findes på RUb: Ja
Abstract

Matematik i Det Virtuelle Gymnasium
Videnskabsfagsprojekt, 2. modul, 2004, id:305
Vejleder:Poul Winther Andersen
Findes på RUb: Nej
Abstract


Videnskabsfagsprojekt, 2. modul, 2003, id:284
Vejleder:
Findes på RUb: Ja
Abstract

Modeller - glade tanker eller videnskab
Videnskabsfagsprojekt, 1. modul, 2003, id:286
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
Abstract
English abstract

Infinitesimalregningen hos Newton og Leibniz
Videnskabsfagsprojekt, 2. modul, 2003, id:287
Vejleder:
Findes på RUb: Ja
Abstract

Kinesisk matematik
Videnskabsfagsprojekt, 2. modul, 2002, id:267
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja

Invarians - om anvendelser og anvendelighed
Videnskabsfag, 1. modul, 2002, id:270
Vejleder:
Findes på RUb: Ja
Abstract


Videnskabsfag, 2. modul, 2002, id:272
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
Abstract

Kinesisk Matematik
Videnskabsfagsprojekt, modul 2. modul, 2002, id:275
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
Abstract

Brouwers intuitionisme
Videnskabsfagsprojekt, 2. modul, 2002, id:278
Vejleder:
Findes på RUb: Ja
Abstract

Fourier og Funktionsbegrebet - overgangen fra Eulers til Direchlets funktionsbegreb
Videnskabsfag, 1 og 2. modul, 2002, id:279
Vejleder:Erik von Essen
IMFUFA-tekst: 416
Findes på RUb: Ja
Abstract

Aksiomatisering af euklidisk geometri
Videnskabsfag, 1. modul, 2001, id:260
Vejleder:Erik Von Essen
Findes på RUb: Ja


Videnskabsfag, 2. modul, 2001, id:265
Vejleder:Tinne Hoff Kjeldsen Bernhelm Booss-Bavnbek
IMFUFA-tekst: 403
Findes på RUb: Ja
Abstract

Beviser i matematik
Videnskabsfags- og prof.projekt, Formidler-variant, 1 + 3. modul, 2000, id:239
Vejleder:Mogens Niss
IMFUFA-tekst: 383
Findes på RUb: Ja
Abstract

Potentialeteoriens historie
Videnskabsfagsprojekt, 2. modul, 2000, id:248
Vejleder:Anders Madsen
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 1 og 2. modul, 2000, id:249
Vejleder:Anders Madsen
Findes på RUb: Ja
Abstract

Uendelighedens Paradokser
Videnskabsfagsprojekt, 1. modul, 2000, id:250
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract

Hyperbolsk Geometri
videnskabsfagsprojekt, 1. modul, 2000, id:252
Vejleder:John Villumsen
Findes på RUb: Ja
Abstract


Videnskabsfag, 1. modul, 2000, id:257
Vejleder:Erik von Essen
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 1. modul, 1999, id:218
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 1 + 2. modul, 1999, id:221
Vejleder:Johnny Ottesen
Findes på RUb: Nej
Abstract

Hvad matematikken og fysikken gjorde for vektorregningen
Videnskabsfagsprojekt, 1 + 2. modul, 1999, id:241
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
Abstract

Cayleys Problem
Videnskabsfagsprojekt, 1. modul, 1998, id:210
Vejleder:Jesper Larsen
IMFUFA-tekst: 357
Findes på RUb: Ja
Abstract

Den aksiomatiske metode
Videnskabsfagsprojekt, 2. modul, 1998, id:212
Vejleder:
Findes på RUb: Nej
Abstract

Hodgkin og Huxleys matematiske model - en modelteoretisk behandling
Model- og videnskabsfagsprojekt, 2. modul, 1998, id:214
Vejleder:Johnny Ottesen
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 2. modul, 1998, id:215
Vejleder:
IMFUFA-tekst: 362
Findes på RUb: Ja
Abstract

From Cayley to the Erlanger Programm
Videnskabsfagsprojekt, 1 + 2. modul, 1998, id:223
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
English abstract


Videnskabsfagsprojekt, 2. modul, 1997, id:195
Vejleder:Jacob Jacobsen
Findes på RUb: Ja
Abstract

Grafiske modeller - et matematikhistorisk projekt
Videnskabsfagsprojekt, 1. modul, 1997, id:206
Vejleder:Stig Andur Pedersen
Findes på RUb: Ja
Abstract

Kaos og universalitet
Videnskabsfagsprojekt, 2. modul, 1996, id:175
Vejleder:Mogens Brun Heefelt
Findes på RUb: Ja
Abstract

Den tidlige historiske udvikling af spilteorien.
Videnskabsfagsprojekt, 1. modul, 1996, id:178
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: Ja
Abstract

Bolzano og Cauchy - Et matematikhistorisk projekt.
Videnskabsfagsprojekt, 1. modul, 1996, id:179
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 1. modul, 1996, id:180
Vejleder:Anders Madsen
Findes på RUb: Ja
Abstract

Forholdet mellem matematik og virkelighed - belyst ved fremkomsten af ikke-euklidisk geometri
Videnskabsfagsprojekt, . modul, 1996, id:181
Vejleder:
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, modul 1. modul, 1996, id:189
Vejleder:
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 3. modul, 1996, id:161
Vejleder:Anders Madsen
IMFUFA-tekst: 317
Findes på RUb: 
Abstract


Videnskabsfagsprojekt, . modul, 1996, id:169
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: Ja
Abstract

Hamiltons Quaternioner - En vurdering af deres anvendelighed
Videnskabsfagsprojekt, 1. modul, 1996, id:171
Vejleder:Anders Hede Madsen
Findes på RUb: Ja
Abstract


A: Projekt B: Videnskabsfagsmodul, A: Modul 1. modul, 1995, id:143
Vejleder:A: Bernelm Booss-Bavnbek. B: Jacob Jacobsen.
Findes på RUb: B: Nej

Gymnasiets matematik set i lyset af EDB
Videnskabsprojekt, Bachelor. modul, 1995, id:151
Vejleder:Viggo Andreasen
Findes på RUb: Nej
Abstract

Matematikundervisning i en computertidsalder
Videnskabsprojekt, 2. modul, 1995, id:156
Vejleder:Lars Kadison
Findes på RUb: Nej


Videnskabsprojekt, Bachelormodul. modul, 1995, id:160
Vejleder:Anders Madsen
Findes på RUb: Nej
Abstract

Hermann Weyls intuitionistiske matematik
Videnskabsfagsprojekt, . modul, 1995, id:170
Vejleder:
Findes på RUb: Ja
Abstract

Riemann integralet set i et historisk perspektiv
Videnskabsfagsprojekt, 1. modul, 1994, id:131
Vejleder:Anders Madsen
Findes på RUb: Ja
Abstract


Videnskabsfagsprojekt, 2. modul, 1994, id:138
Vejleder:Viggo Andreasen og Jesper Larsen
Findes på RUb: Ja

Vektoranalysens udvikling
Videnskabsfagsprojekt, . modul, 1994, id:140
Vejleder:Johnny Ottesen
Findes på RUb: 


Videnskabsfagsprojekt, . modul, 1994, id:146
Vejleder:Anders Madsen
Findes på RUb: 
Abstract

Wavelets
Videnskabsfagsprojekt, 1. modul, 1993, id:132
Vejleder:Anders Hede Madsen
Findes på RUb: Ja
Abstract

Matematik i gymnasiet fra 1903 til 2005
Videnskabsfag, 1. modul, 2006, id:342
Vejleder:Tinne Hoff Kjeldsen
Findes på RUb: Ja
Abstract
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.

Populationsbiologiens Matematik
Videnskabsfagsprojekt, 2. modul. modul, , id:323
Vejleder:
Findes på RUb: ja
Abstract

Database opslag den: 19-11-2017