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Liste over projekter af typen professionsprojekt

Modelling and simulation of the natamycin production in a bioreactor
Professionsprojekt, 2. modul, Vinter 2012, id:447
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
English abstract
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 un-useful 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 two-species model (The two-phase 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 non-producing 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.


Professionsprojekt, 2. modul, Vinter 2011, id:425
Vejleder:Johnny Ottesen
Findes på RUb: Ja
Abstract
English abstract
In this project the HPA-axis 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.

Tikhonov Regularization in Kronecker Product Approximation for Image Restoration with Mean Boundary Conditions
Professionsprojekt, 2. modul, Vinter 2011, id:427
Vejleder:Johnny Ottesen
Findes på RUb: Ja
English abstract
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. 225-237}. 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.


Professionsprojekt, 2. modul, Sommer 2012, id:432
Vejleder:
Findes på RUb: Ja
English abstract
The paper discusses the possibility of improving the teaching of mathematics in the Danish high school by changing the educational practice from a monologue-based dominated communication towards a higher degree of dialogue-based 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 Booss-Bavnbek
Findes på RUb: Ja
Abstract
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.

Sandsynlighed og statistik i gymnasieskolen
Professionsprojekt - formidlervariant, 2. modul, Sommer 2012, id:440
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract

Fortolkning af sandsynlighedsteori
Professionsprojekt formidlervariant, 3. modul, 2014, id:456
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract
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.

Matematikvejlederuddannelsen
Professionsprojekt formidlervariant, 2. modul, 2013, id:471
Vejleder:Uffe Thomas Jankvist og Mogens Allan Niss
Findes på RUb: Ja
Abstract

Eksamensrapport Matematikvejlederuddannelsen
Professionsprojekt formidlervariant, 2. modul, 2013, id:470
Vejleder:Mogens Allan Niss & Uffe Thomas Jankvist
Findes på RUb: Ja
Abstract

Matematikvejlederrapport
Professionsprojekt formidlervariant, 2. modul, 2013, id:472
Vejleder:Mogens Niss og Uffe Jankvist
Findes på RUb: Ja
Abstract

Matematikvejledning
Professionsprojekt formidlervariant, 2. modul, 2013, id:473
Vejleder:Uffe Jankvist og Mogens Niss
Findes på RUb: Ja
Abstract

Matematikvejlederprojekt
Professionsprojekt formidlervariant, 2. modul, 2013, id:474
Vejleder:Mogens Niss og Uffe Thomas Jankvist
Findes på RUb: Ja
Abstract

Matematikvejledning i gymnasiet
Professionsprojekt formidlervariant, 2. modul, 2013, id:475
Vejleder:Mogens Niss og Uffe jankvist
Findes på RUb: Ja
Abstract
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 equation-solving 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 building-up 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 A-level (the higher level), while students with major problems in this area choose it at a B-level. 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 HTX-program. 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 class-based 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 class-based intervention with focus on pre-mathematizing 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 class-based 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.

Matematikvejledning i htx
Professionsprojekt formidlervariant, 2. modul, 2013, id:476
Vejleder:Mogens Allan Niss og Uffe Thomas Jankvist
Findes på RUb: Ja
Abstract
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
Abstract
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.

Matematisk modellering i de gymnasiale uddannelser
Profession, formidler-variant, 3. modul, 2009/10, id:393
Vejleder:
Findes på RUb: Ja
Abstract
English abstract

Matematisk metodologisk paradigmestrid
Profession - forskning, 3. modul, 2008/09, id:377
Vejleder:
Findes på RUb: ja
Abstract
English abstract


Profession - formidlervariant, 3. modul, 2008, id:369
Vejleder:Tinne Hoff-Kjeldsen
Findes på RUb: Ja
Abstract
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 2007-2008 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.


Profession - formidlervariant, 3. modul, 2007/2008, id:365
Vejleder:
Findes på RUb: Ja
English abstract
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
Abstract
English abstract
In this project I study the advantages and the disadvantage by the use of Spectral-methods for the solution of the Navier-Stokes-equations. My case will be the formation and dynamics of rings of smoke. I conclude that the Spectral-methods are too dependent on good conditions. And therefore my model is not particularly suitable for the simulation of rings of smoke


Profession - modelbygger, 3. modul, 2006, id:345
Vejleder:
Findes på RUb: Ja
Abstract
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 SEIR-models that descripe the dynamical pattern in a population exposed to a given disease. This paper contains an expansion of the SIR-model to a TSIR-model that incorporates timeseries, and the model is used on a set of data consisting of births and easles infected individuals in the years 1900-1967 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.


Profession, 3. modul, 2005, id:320
Vejleder:Anders Madsen
Findes på RUb: Nej
Abstract


Profession - formidling, 3. modul, 2005, id:341
Vejleder:Poul Winther Andersen
Findes på RUb: 
Abstract

Kan matematik blive interessant for piger?
Profession, 3. modul. modul, 2004/05, id:322
Vejleder:Mogens Niss
Findes på RUb: ja


Professionsprojekt, modelbygger, 3. modul, 2003, id:282
Vejleder:Johnny Ottesen
Findes på RUb: Nej
Abstract

Den selvundvigende vandring
Professionsprojekt, Forsknings-varianten, 3. modul, 2000, id:237
Vejleder:John Villumsen og Viggo Andreasen
IMFUFA-tekst: 382
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


Professionsprojekt, Modelbygger-varianten, 3. modul, 2000, id:240
Vejleder:Johnny Ottesen
IMFUFA-tekst: 380
Findes på RUb: Nej
Abstract
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.

A Quantitative Description of Glycolysis by Normal Forms
Professionsprojekt, Formidler-varianten, 3. modul, 2000, id:244
Vejleder:
Findes på RUb: Ja
English abstract
In this report a high dimensional model of glycolysis is described by the Stuart-Landau 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 Stuart-Landau approximation with the original model. This is possible because a way to transform the Stuart-Landau 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 Stuart-Landau approximation and the original model are compared.


Professionsprojekt, Modelbygger-varianten, 3. modul, 2000, id:247
Vejleder:Jesper Larsen
Findes på RUb: Ja
Abstract


Professionsprojekt, formidler-varianten, 3. modul, 2000, id:251
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract

Matematik og Almenhed
Professionsprojekt, formidler-variant, 3. modul, 2000, id:253
Vejleder:Oluf Danielsen og Mogens Niss
Findes på RUb: Ja
English abstract

Hilberts matematikfilosofi
Professionsprojekt, formidlervariant, 3. modul, 2000, id:254
Vejleder:Stig Andur Pedersen
IMFUFA-tekst: 393
Findes på RUb: Ja
English abstract


Professionsprojekt, Formidlervariant, 3. modul, 2000, id:255
Vejleder:Tine Wedege
IMFUFA-tekst: 395 og 396
Findes på RUb: Ja
Abstract
English abstract

Matematik i gymnasiet - Selvvirksomhed, kontekst og undervisningsvejledning
Professionsprojekt, Formidler-varianten, 3. modul, 1999-2000, id:243
Vejleder:Erik von Essen
Findes på RUb: Nej
Abstract
English abstract


Professionsprojekt, formidler-varianten, 3. modul, 1999, id:219
Vejleder:Mogens Niss
Findes på RUb: Ja
Abstract


Professionsprojekt, modelbygger-varianten, 3. modul, 1999, id:225
Vejleder:Carsten Lunde Petersen
Findes på RUb: Ja
Abstract


Professionsprojekt, 3. modul, 1999, id:226
Vejleder:Mogens Niss
IMFUFA-tekst: 371
Findes på RUb: Ja
Abstract

Designerkurver
Professionsprojekt, formidler-varianten, 3. modul, 1999, id:229
Vejleder:Erik von Essen
Findes på RUb: Ja
Abstract


Professionsprojekt, 3. modul, 1999, id:233
Vejleder:Stig Andur Pedersen
Findes på RUb: Ja
Abstract

Dynamics of Complex Quadratic Correspondences
Professionsprojekt, Forsker-varianten, 3. modul, 1999, id:235
Vejleder:Carsten Lunde Petersen
IMFUFA-tekst: 369
Findes på RUb: Ja
Abstract
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 arithmetic-geometric 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, Modelbygger-varianten, 3. modul, 1999, id:236
Vejleder:Jesper Larsen
Findes på RUb: Ja
Abstract
English abstract

Elliptisk Kurve Kryptering
Professionsprojekt, Modelbygger-varianten, 3. modul, 1999, id:238
Vejleder:Jesper Larsen
Findes på RUb: Ja
Abstract

Valgemner i matematik i det almene gymnasium og HTX
Professionsprojekt, 3. modul, 1999, id:459
Vejleder:Viggo Andreasen
Findes på RUb: Ja
Abstract

Graflommeregneren i det matematiske gymnasium
Professionsprojekt - formidlervarianten, 3. modul, 1998, id:209
Vejleder:Erik von Essen
Findes på RUb: Ja
Abstract

Logicisme: Tilblivelse og sammenbrud
Professionsprojekt - speciale, 3. modul, 1998, id:216
Vejleder:Stig Andur Pedersen
Findes på RUb: Ja
Abstract


Professionsprojekt, modelbygger-varianten, 3. modul, 1998, id:217
Vejleder:Bernhelm Booss-Bavnbek
Findes på RUb: Ja
Abstract

Funktionsbegrebet i det matematiske gymnasiums 1. G.
Professionsprojekt, formidler-variant, 3. modul, 1997, id:194
Vejleder:Erik von Essen
Findes på RUb: Ja
Abstract

Matematisk Kompetence i filosofisk og didaktisk perspektiv
Professionsprojekt -formidler-variant, 3. modul, 1997, id:199
Vejleder:
Findes på RUb: Ja
Abstract

Flexundervisning i matematik
Professionsprojekt, formidler-variant, 3. modul, 1997, id:200
Vejleder:
Findes på RUb: Nej
Abstract


Proffession, formidler-variant., 3. modul, 1997, id:201
Vejleder:Erik von Essen
Findes på RUb: Nej


Professionsprojekt - modelbyggervariant, 3. modul, 1996/97, id:186
Vejleder:Jacob M. Jacobsen og Jesper Larsen
IMFUFA-tekst: 331
Findes på RUb: Ja
Abstract

Modelling the Respiratory System
Professionsprojekt -, 3. modul, 1996, id:183
Vejleder:Viggo Andreasen og Michael Danielsen
IMFUFA-tekst: 318
Findes på RUb: Ja
English abstract
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:
IMFUFA-tekst: 321
Findes på RUb: Ja
Abstract

Retorik eller realitet?
Professionsprojekt - formidlervariant, 3. modul, 1996, id:185
Vejleder:Mogens Niss
IMFUFA-tekst: 325
Findes på RUb: Ja
Abstract


Professionsprojekt - formidlervarianten, 3. modul, 1996, id:174
Vejleder:
Findes på RUb: nej
Abstract

Database opslag den: 21-09-2017