General information about the Department of Mathematics and Physics Name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Department of Mathematics and Physics Department - / course locations . . . . . . . . . . . Eskilstuna and Västerås. Students / faculty and staff . . . . . . . . . . . . . . Full time students 620, teachers and staff 60. Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aeronautical Engineering, Chamber Music, Mathematics/ Applied Mathematics, Physics. Equipment / labs. / computer rooms . . . . . . . Yes. Computer access for students / e-mail . . . . . Yes, 24-hour access. Teaching methods . . . . . . . . . . . . . . . . . . . . . . Lectures, group lectures, projects, laboratory work, etc. Examinations . . . . . . . . . . . . . . . . . . . . . . . . . . Written- and oral examinations, assignments, seminars, projects, laboratory work. Grades awarded (Swedish system) . . . . . . . . Fail, 3, 4, 5. Study Advisors . . . . . . . . . . . . . . . . . . . . . . . . . Aeronautics: Mirko Senkovski Tel: +46 (0)21 101661 Fax: +46 (0)21 101330 [email protected] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematics (Eskilstuna): Bengt Rydström Tel: +46 (0)16 153473 Fax: +46 (0)16 153460 [email protected] Chamber Music: Per-Olov Sahl Tel: +46 (0)21 103196 Fax: +46 (0)21 101330 [email protected]

Mathematics (Västerås): Erik Janse Tel: +46 (0)21 101537 Fax: +46 (0)21 101330 [email protected] Physics (Västerås): Anders Alm Tel: +46 (0)21 101332 Fax: +46 (0)21 101330 [email protected]

Physics (Eskilstuna): Sten Lindstam Tel: +46 (0)16 153655 Fax: +46 (0)16 153460 [email protected]

Postgraduate studies: Benjamin Baumslag Tel: +46 (0)21 101663 Fax: +46 (0)21 101330 [email protected]

Address to the Department . . . . . . . . . . . . . . . Mälardalen University Mälardalen University Dep. of Mathematics Dep. of Mathematics and Physics and Physics P O Box 883 P O Box 325 SE-721 23 Västerås SE-631 05 Eskilstuna Sweden Sweden Descriptions of the levels in the Swedish system . . . . . . . . . . . . . . . . . . . . . . . . A-level Basic level B-level Intermediate level C-level Advanced level D-level Specialized level Study periods: Study period 1: 25.08.2003-02.11.2003 Study period 2: 03.11.2003-18.01.2004 Study period 3: 19.01.2004-28.03.2004 Study period 4: 29.03.2004-13.06.2004 Autumn semester = Study period 1 and 2 Spring semester = Study period 3 and 4 Most students study two 5 point courses in each period. Examinations are held at the end of each study period. Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

DEPARTMENT OF MATHEMATICS AND PHYSICS

89

90

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Current Research at the Department Professor Kimmo Eriksson Applied combinatorics. Combinatorics is a relatively new branch of mathematics which focuses on the studies of different discrete structures and the relations between them. Typical examples of the objects of our studies are (i) graphs, i.e., structures built of points and the possible links which connect them and (ii) permutations, i.e., arrangements of objects in a queue. Currently, we investigate applications of combinatorics within mathematics as well as in other sciences like bioinformatics (analysis of data in molecular biology) and economics (game theory). Professor Dmitrii Silvestrov Stochastic processes and analytical finance. We conduct both theoretical and applied research. The theoretical projects concentrate on limit and ergodic theorems for stochastic processes and on the studies of quasi-stationary phenomena in stochastic systems with nonlinear perturbations. In the applied projects we investigate and develop: (i) nonlinear dynamical models of pricing processes, (ii) Monte Carlo algorithms, (iii) algorithms and computer programs for the prediction of pricing processes and for optimal option pricing. Professor Kenneth Holmström Applied Optimization. We develop numerical algorithms and solutions for practical optimization problems. Currently, out projects focus on global, non-convex optimization of cost- and CPUintensive financial and industrial problems, e.g. the optimal design of a passenger train set. We are also involved in nonlinear parameter estimation. There, we usually use models of exponential type that occur e.g. in chemical equilibria and kinetics. Finally, we build models for predictions of financial time serieses, like those of stock market prices and movements. Professor Benjamin Baumslag Group Theory. Our focus is on Coxeter groups with one additional relator. Teaching mathematics and… We investigate how mathematics is used in finance companies.

Dr Anatoliy Malyarenko Random fractals and analytical finance. Random functions arising in mathematical finance have extremely irregular sample paths. In particular, random sets connected to their trajectories have non-integer Hausdorff dimension. Calculation of this dimension helps to solve different interesting problems in mathematics and in economics. Dr Evelina Silvestrova Stochastic automata. The studies are concentrated on the models of stochastic processes controlled by stochastic automata and their applications to stochastic modeling and statistical studies of pricing processes. Dr Richard Bonner Computational models in informatics and economics. We build and analyze, e.g., (i) models of decision processes which include costs of information and costs of modeling; (ii) models of learning (Artificial Intelligence) and their complexity, or (iii) recursive (incremental) models. Quantum computation and learning: We study, e.g., learning by quantum automata. Dr Piotr Badziag Quantum mechanics and information. We try to answer questions concerning quantum communication (QC), i.e., nearly magic communication, which includes e.g., teleportation. Some of the typical questions for us? What can separated friends Alice and Bob do locally to improve quality of their QC channel? How to identify those quantum states which, at least in principle, allow for QC? etc. Dr Peter Gustafsson Context and Conversation in Physics Education. In this project, supported by The Swedish Research Council, we investigate students’ interest in physics and their understanding of physics’ concepts. For that, we analyse the behaviour of small cooperative groups of students solving context rich problems. Video recordings, questionnaires and interviews are our main tools for the data collection. The project is conducted in cooperation with Umeå University and a number of high schools.

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

91

Courses given in Swedish Code

Title

ECTS credits:

Code

Title

MT1080

Aeronautical Engineering Basic level MG1190 Aircraft Engine Technology . . . . . . . . . . . . . . . . 7.5 Flygmotorteknik MG1090 Introductory Course (Aeronautical Engineering) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Introduktion (flygteknik) Intermediate level MG1020 Aerodynamics and Applied Flight Mechanics . . Aerodynamik och tillämpad flygmekanik MG1170 Aircraft Systems Engineering . . . . . . . . . . . . . . . Flygsystemteknik MG1100 Avionics I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Avionik I MG1110 Fluid Mechanics for Aeronautical Engineering . . Flygteknisk strömninglära

7.5 7.5 7.5 7.5

Advanced level MG1130 Aerodynamics Extended course . . . . . . . . . . . . . 7.5 Aerodynamik, pk MG1140 Degree Project (Aeronautics) . . . . . . . . . . . . . . . 15 Examensarbete (flygteknik)

Mathematics/Applied Mathematics Basic level MM1700 Calculus I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential- och integralkalkyl I MM1510 Discrete Mathematics . . . . . . . . . . . . . . . . . . . . . Diskret matematik MM1690 Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . Linjär algebra MM1420 Mathematical Logic . . . . . . . . . . . . . . . . . . . . . . . Matematisk Logik Intermediate level MM1710 Calculus II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential- och integralkalkyl II MM1720 Calculus III Differential- och integralkalkyl III . . . . . . . . . . . MT1090 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . Numeriska metoder MT1060 Probability Theory and Statistical Inference . . . Sannolikhetslära och statistisk teori Advanced level MM1010 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algebra MM1150 Complex Analysis . . . . . . . . . . . . . . . . . . . . . . . . Komplex analys MM1120 Degree Project in Mathematics . . . . . . . . . . . . . . Examensarbete i matematik MM1490 Differential Equations . . . . . . . . . . . . . . . . . . . . . Differentialekvationer MM1380 Elementary Algebraic Topology . . . . . . . . . . . . . Elementär algebraisk topologi MT1200 General Relativity . . . . . . . . . . . . . . . . . . . . . . . . Allmän relativitetsteori MT1190 Linear and Nonlinear Optimization . . . . . . . . . . Linjär och ickelinjär optimering MM1840 Information and Coding Theory . . . . . . . . . . . . Information- och kodningsteori

7.5 7.5 7.5 7.5

7.5 7.5 7.5 7.5

7.5 7.5 15

ECTS credits:

Numerical Linear Algebra . . . . . . . . . . . . . . . . . . Numerisk linjär algebra MT1220 Numerical Methods, extended course . . . . . . . . Numeriska metoder, fortsättningskurs MT1110 Operations Research . . . . . . . . . . . . . . . . . . . . . . Operationsanalys MT1130 Optimization Theory . . . . . . . . . . . . . . . . . . . . . . Optimeringslära MM1480 Project in Mathematics . . . . . . . . . . . . . . . . . . . . Projektarbete i matematik

7.5 7.5 7.5 7.5 7.5

Specialized level MM1390 Algebraic Topology . . . . . . . . . . . . . . . . . . . . . . . 7.5 Algebraisk topologi MT1250 Algortihms for Learning Machines . . . . . . . . . . 7.5 Algoritmer för självlärande maskiner MT1330 Applied Mathematics, Theory and Methods . . . 7.5 Tillämpad matematik, teori och metoder MT1230 Computational Complexity I . . . . . . . . . . . . . . . 7.5 Komplexitetsteori I MT1240 Computational Complexity II . . . . . . . . . . . . . . . 7.5 Komplexitetsteori II MM1350 Degree Project in Mathematics . . . . . . . . . . . . 15/30 Examensarbete i matematik MM1110 Differential Geometry . . . . . . . . . . . . . . . . . . . . . 7.5 Differentialgeometri MM1520 Functional Analysis . . . . . . . . . . . . . . . . . . . . . . . 7.5 Funktionalanalys MM1770 Galois Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Galoisteori MT1210 General Relativity, extended course . . . . . . . . . . 7.5 Allmän relativitetsteori, fk MT1300 Global Optimization . . . . . . . . . . . . . . . . . . . . . . 7.5 Global optimering MT1310 Integer Programming . . . . . . . . . . . . . . . . . . . . . 7.5 Heltalsoptimering MM1650 Integration Theory . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Integrationsteori MT1270 Mathematical Theories of Learning . . . . . . . . . . 7.5 Inlärningsteorins matematiska grunder MT3020 Mixed-Integer Non-Linear Programming . . . . . 7.5 Blandad ickelinjär och linjär heltalsoptimering MT1260 Modelling with Neural Nets . . . . . . . . . . . . . . . . 7.5 Modellering med neurala nät MT1290 Optimization Algorithms . . . . . . . . . . . . . . . . . . 7.5 Optimeringsalgoritmer MM1640 Partial Differential Equations . . . . . . . . . . . . . . . 7.5 Partiella differentialekvationer MT1340 Practical Methods in Optimization . . . . . . . . . . . 7.5 Praktiska metoder för optimering MM1300 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Topologi

7.5 7.5 7.5 6.0 7.5

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

92

Code

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Title

ECTS credits:

Code

Title

ECTS credits:

Physics

Degree Programs

Basic Level MF1370 Classical Physics A1 . . . . . . . . . . . . . . . . . . . . . . . 7.5 Klassisk fysik A1 MF1380 Classical Physics A2 . . . . . . . . . . . . . . . . . . . . . . 7.5 Klassisk fysik A2 . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 MF1510 Principles of Physics Fysikaliska principer

Aeronautical Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . 180 Flygingenjörsprogrammet

Intermediate level MF1730 Classical Mechanics I . . . . . . . . . . . . . . . . . . . . . . Mekanik MF1750 Classical Mechanics II . . . . . . . . . . . . . . . . . . . . . Mechanik II MF1520 Computer Simulation of Physical and Technical Problems I . . . . . . . . . . . . . . . . . . . . . . Datorsimulering av fysikaliska system I, MF1530 Computer Simulations of Physical and Technical Problems II . . . . . . . . . . . . . . . . . . . . . . Datorsimulering av fysikaliska och tekniska problem II MF1050 Electromagnetism I . . . . . . . . . . . . . . . . . . . . . . . Elektricitetslära I MF1030 Electromagnetism and the Physics of Waves . . . Elektromagnetism och vågrörelselära MF1740 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . Elektromagnetiska vågor MF1620 Electrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elektrofysik MF1150 Modern Physics . . . . . . . . . . . . . . . . . . . . . . . . . . Modern fysik MF1190 Physics of Waves and Optics . . . . . . . . . . . . . . . Vågrörelselära och optik MF1230 Thermodynamics and Kinetic Gas Theory . . . . Värmelära MF1670 Quantum Physics . . . . . . . . . . . . . . . . . . . . . . . . . Kvantfysik I Advanced level MF1690 Classical Mechanics III . . . . . . . . . . . . . . . . . . . . Mekanik, f.k. MF1250 Degree Project in Physics . . . . . . . . . . . . . . . . . . Examensarbete i fysik MF1390 Mathematical Methods in Physics . . . . . . . . . . . Matematiska metoder i fysik MF1430 Physical Foundations of VLSI-Technology . . . . VLSI-teknikens fysikaliska grunder

Chamber Music and other subjects . . . . . . . . . . . . . . . . . . . 180 Kammarmusik Engineering Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180-240 Teknisk fysikprogrammet

7.5 7.5

Degree Program in English Analytical Finance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5

7.5 15 7.5 7.5

Specialized level MF1600 Quantum Information Theory . . . . . . . . . . . . . . 7.5 Kvantmekanik och informationsteori

Chamber Music Basic level MK 1020 Chamber Music . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Kammarmusik Intermediate level MK 1030 Chamber Music . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Kammarmusik Advanced level MK 1040 Chamber Music . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Kammarmusik

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

93

Courses given in English Mathematics for Economics and Business Code:

MM1980

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

50

Study period:

1

Level:

Basic

Location:

Västerås

Examination:

Projects and seminars.

Language:

English

Prerequisites:

Mathematics from 3 years upper secondary school or equivalent.

Numerical Methods with MATLAB Code:

MT1370

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

12

Course content:

Elementary algebra. Equations and polynomials. The concept of functions and especially exponential- logarithmicand trigonometric functions. Differentiation and integration. Applications to Economics and business.

Contact person:

Torgöt Berling [email protected]

Literature:

Hughes-Hallett, Gleason, Lock, Flath, Et AL., Applied calculus. - John Wiley & sons, INC, 1998, 1 ed. - ISBN 0-471-10876-6

Course content:

A brief introduction to MATLAB. Vectors and plotting. Building exploratory environments. Designing functions. More refined graphics. Nature of numerical computation. Working with a finite precision arithmetic. Number representation, rounding, and truncation. Analysing and computing cash flow streams. Non-linear equations. Bisection method, Newton_s method. MATLAB functions for analysing and computing cash flows. Valuation of fixed-income securities. Linear systems. Gaussian elimination, LU-decomposition. MATLAB function to deal with fixed-income securities. BlackScholes model. Polynomial interpolation. Black-Scholes sensitivity to changing underlying parameters. MATLAB functions for pricing and analysing derivatives. Pricing American options by binomial lattices. Binomial put and call pricing in MATLAB. Option valuation by Monte Carlo simulation. Simulating asset price dynamics.

Contact person:

Anatoliy Malyarenko [email protected]

Literature:

Getting started with MATLAB, Version~6, The MathWorks, Inc., 2001. Available online. P.Brandimarte, Numerical methods in finance: a MATLAB-based introduction, Wiley, 2001.

Laboratory hours 44 Study period:

1

Level:

Intermediate

Location:

Västerås

Examination:

Projects and seminars.

Language:

English

Prerequisites:

Introduction to financial mathematics, Calculus I or equivalent.

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

94

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Algebra Code:

MM1800

Swedish points:

5

ECTS credits:

7.5

Study period:

Late Fall

Level:

Basic

Location:

Västerås

Language:

English

Examination:

Projects and seminars.

Prerequisites:

Mathematics from 3 years upper secondary school or equivalent.

Complex Analysis Code:

MM1150

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

14

Course content:

Systems of linear equations, Gaussian elimination, coefficient and total matrix, matrix operations. Matrices, matrix arithmetic, matrix equations, transposes, inverses. Vectors in 2-space and 3-space. Scalar product, cross product, lines and planes, projection, linear dependence and independence, bases, coordinates, orthogonality.

Contact person:

Eric Janse [email protected]

Literature:

Anton, Howard, Rorres, Chris, Elementary linear algebra: applications version. - New York: Wiley , 2000/8. ed. . - ISBN 0-471-17052-6 The department for Mathematics and Physics may decide to change the above literature.

Language:

English

Prerequisites:

Calculus, Differential equations or equivalent

Course content:

Basic topological concepts. Complex, and especially analytical functions of one complex variable. Elementary analytical functions. Integration. Taylor and Laurent series. Residue calculus. The argument principle. Conformal mapping. Applications: Distribution of zeros. Fluids and potentials.

Contact person:

Anatoliy Malyarenko [email protected]

Literature:

Wunsch, David A., Complex Variables with Applications. - Addison-Wesley, 1994. - ISBN 0-201-12299-5

Laboratory hours 42 Study period:

2

Level:

Advanced

Location:

Västerås

Examination:

Home assignments and written exam.

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

function, Probability Density, Expected Value, Variance, Standard Deviation. Special Discrete and Continuous Distributions: Binomial, Poisson, Geometrical, Hyper-geometrical, Uniform, Exponential, Gamma. Normal Distribution and Limit Theorems: Normal Distribution, Law of Large Numbers, Central Limit Theorem. Inference: Tests of Significance, Tests for Binomial Model, Tests based on Normal Distribution. Confidence Intervals, Linear Regression, Chi-squared Tests.

Probability and Statistics Code:

MT1380

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

11

95

Laboratory hours 45 Study period:

2

Level:

Basic

Location:

Västerås

Examination:

Projects and seminars.

Language:

English

Prerequisites:

Calculus I or equivalent.

Course content:

Data Analysis and Descriptive Statistics: Tables and Diagrams, Boxplots, Median, Quartiles, Transformation of data, Sample Mean, Sample Variance, Bivariate data. Combinatorics: The multiplication Principle, Permutations, Combinations, Sampling. Elements of Probability: Sample space and events, Axioms of Probability, Conditional Probability, Bayes' Formula, Independence. Random Variables and Expectation: Types of Random Variables, Distribution

Calculus I Code:

MM1820

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

50

Study period:

3

Level:

Basic

Location:

Västerås

Examination:

Projects and seminars.

Language:

English

Prerequisites:

Mathematics from 3 years upper secondary school or equivalent.

Contact person:

Dmitrii Silvestrov, [email protected]

Literature:

1. C.M. Grinstead, J.L. Snell, Introduction to Probability. The Chance Project. - Dartmouth College, http://www.dartmouth.edu/~chance/tea ching_aids/articles.html, 2002, Reference for further reading. 2. M.C. Phipps, M.P. Ouine, A Primer of Statistics: Data Analysis. Probability. Inferense. - Pearson Education Australia. Sydney, 2001 4 th edition. – ISBN 1-74009-626-6 3. Arne Frennelius, Sannolikhetslära och statistisk inferens för tekniska utbildningar. - Västerås Statistikutbildning, 2002. - ISBN 91-630-9573-4, Reference for further reading.

Course content:

Real valued functions of a real variable. Continuity. Derivatives. Techniques of derivation. Extremal value problems. Elemantary functions, notably the logarithm and the exponential funcion. Anti-derivatives. Integrals. Techniques of integration. Computer aided calculations. Numerous applications of calculus to problems in business and economics

Contact person:

Torgöt Berling [email protected]

Literature:

Larry J. Goldstein, David C. Lay, David I. Schneider, Calculus and Its Applications. - Pearson Higher Education, UK, 200009. - ISBN 0-13-087304-7

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

96

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Calculus II

Language:

English

Code:

MM1960

Prerequisites:

Linear algebra, Calculus I or equivalent

Swedish points:

5

Course content:

ECTS credits:

7.5

Lecture hours:

11

This course is devoted to basic theory of functions of more than one variable, sequences, series, differential equations and applications in economics and business.

Contact person:

Anatoliy Malyarenko [email protected]

Literature:

Larry J. Goldstein, David C. Lay, David I. Schneider, Calculus and its Applications. - Pearson Higher Education, UK, 2000. - ISBN 0-13-087304-7

Prerequisites:

Complex analysis, analysis in one and several variables or equivalent.

Course content:

Theory and solution methods of ordinary differential equations (ODEs) are studied as well as systems of ODEs and transform methods (Fourier series, Fourier, Laplace and z-transforms) with applications to ODEs, partial differential equations (PDEs) and difference equations. For more information see http://www.ima.mdh.se

Contact person:

Lars-Göran Larsson, [email protected]

Literature:

Differential equations with applications and historical notes (2nd ed.) G.F. Simmons, McGraw Hill 1991

Course content:

The real number system, the Lebesgue measure of R and R^n, measurable f unctions, the Lebesgue integral of R and R^n. Introduction to abstract theory of measure and integration. Fubini's theorem, the monotone convergence theorem and the dominated convergence theorem. Additionally, the course covers some of the following topics: differentiaition and integration on the real line, geometry of the Lebesgue measure, variable substitutions in Lebesgue integrals, the Radon-Nikodym theorem and Riesz representation theorem.

Contact person:

Anatoliy Malyarenko [email protected]

Literature:

Friedman, Avner, Foundations of Modern Analysis. - Dover, New York , 1982. - ISBN 0-486-64062-0

Laboratory hours 45 Study period:

3

Level:

Intermediate

Location:

Västerås

Examination:

Projects and seminars.

Differential Equations Code:

MM1490

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

60

Study period:

3

Level:

Advanced

Location:

Västerås

Language:

English

Examination:

Written examination and assignments.

Theory of Integration Code:

MM1650

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

14

Laboratory hours 16 Study period:

3

Level:

Advanced

Location:

Västerås

Examination:

Oral or written examination.

Language:

English

Prerequisites:

Linear algebra, Calculus, Real Analysis or Mathematical Analysis III or equivalent.

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Actuarial Mathematics Code:

MT1390

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

13

Course content:

Cash flow and accounting insurance models. Premiums. Claims. Insurance process. Number of claims. Poisson distribution. Negative binomial distribution. Mixed Poisson distribution. Normal approximation. Aggregate claim amount. Compound distributions. Claim size distribution. Gamma distribution. Pareto distribution. Reinsurance models. Simulation methods. Evaluation of ruin probabilities. Short-term claim fluctuation. Evaluating capital at risk. Lifetime distributions, Life tables. Basics of life insurance.

Contact person:

Dmitrii Silvestrov, [email protected]

Literature:

1. C.D. Daykin, T. Pentikäinen, M. Pesonen, Practical Risk Theory for Actuaries. Chapman & Hall. London 1994. - ISBN 0-412-42850-4 2. G: H.U. Gerber, Life Insurance Mathematics. Springer. Berlin. 3-th edition, 1997. – ISBN 3-540-62242-X 3. S: E. Straub, Non-Life Insurance Mathematics. Springer. Berlin. 1997. – ISBN 3-540-18787-1

Course content:

Curves: tangents, curvature and torsion, the Frenet--Scherret equations and the fundamental theorem for curves. Spherical contact, spherical curves, involutes and evolutes. Regular surfaces: charts, tangent plane. The first fundamental form, normal and geodesic curvature, Gauss's formulas, geodesics and parallel transport. The second fundamental form: Weingarten's equations. Principal, Gaussian, mean and normal curvatures, minimal surfaces and developable surfaces. Riemannian curvature and Gauss's Theorema Egregium: Riemann's tensor, Ricci's tensor and Codazzi--Mainardi's equations. Isometrics and conformal mappings. Gauss--Bonnet theorem.

Contact person:

Anatoliy Malyarenko [email protected]

Literature:

Struik, D J., Lectures on Classical Differential Geometry. - Dover, 1988. - ISBN 0-486-65609-8

Prerequisites:

Mathematics from 3 years upper secondary school or equivalent

Course content:

Elementary discrete probability. Normal distribution. Geometrical Brownian motion and modelling of pricing processes. Interest rates. Present value analysis. Pricing contracts via arbitrage. Multiperiod pricing model. European and American options. Black-Scholes formula.

Contact person:

Dmitrii Silvestrov [email protected]

Literature:

Jarrow, Robert, Turnbull, Stuart, Derivative Securities. - South-Western, 1999, 2nd ed. - ISBN 0-538-87740-5 Ross, Sheldon M., An introduction to Mathematical Finance. - Cambridge University Press, 1999. - ISBN 0-521-77043-2.

Laboratory hours 50 Study period:

4

Level:

Basic

Location:

Västerås

Examination:

Projects and seminars.

Language:

English

Prerequisites:

Calculus I, Calculus II, Probability and Statistics or equivalent.

Differential Geometry Code:

MM1110

Swedish points:

5

ECTS credits:

7.5

Lecture hours:

14

Laboratory hours 16 Study period:

4

Level:

Advanced

Location:

Västerås

Examination:

Written exam.

Language:

English

Prerequisites:

Linear algebra, Calculus, Differential equations or equivalent.

Introduction to Financial Mathematics Code:

MM1810

Swedish points:

5

ECTS credits:

7.5

Study period:

Late Spring

Level:

Basic

Location:

Västerås

Language:

English

Examination:

Projects and seminars.

97

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

98

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Algorithms for Self-instructive Machines Code:

MT1250

Swedish points:

5

ECTS credits:

7.5

Study period:

No fixed period.

Level:

Specialized

Location:

Västerås

Language:

Swedish

Examination:

Assignments and student seminars.

Prerequisites:

Computational Complexity I, or equivalent.

Computational Complexity I Code:

MT1230

Swedish points:

5

ECTS credits:

7.5

Study period:

No fixed period.

Level:

Specialized

Location:

Västerås

Language:

Swedish

Examination:

Assignments and student seminars.

Computational Complexity II Code:

MT1240

Swedish points:

5

ECTS credits:

7.5

Study period:

No fixed period.

Level:

Specialized

Location:

Västerås

Language:

Swedish

Examination:

Assignments and student seminars.

Prerequisites:

Computational Complexity I, or equivalent.

Course content:

Introductory notions and instances of learning, such as the learning of concepts, decision trees, functions, probability distributions, rules, etc. Short accounts of Computational Learning Theory (known as COLT), Artificial Neural Networks, and Genetic Algorithms. Account of inductive vs analytical learning. Reinforcement learning. Presentation of further applications, for example in Knowledge Discovery and Data Mining.

Contact person:

Richard Bonner [email protected]

Literature:

Bergadano, Francesco, Gunetti, Daniele, Inductive Logic Programming. - MIT Press, 1996. - ISBN 0-262-02393-8 Fayyad, Usama M. m fl, Advances in Knowledge Discovery and Data Mining. - MIT Press, 1996. - ISBN 0-262-56097-6 Mitchell, Tom Michael, Machine Learning. - McGraw-Hill, 1997. - ISBN 0-07-042807-7 The litterature may be subject to changes.

Prerequisites:

To follow this course it is necesary to have a solid background in undergraduate mathematics course correspondning to for example Linear Algebra, Calculus and Real Analysis or Mathematical Analysis III.

Course content:

Notions of problem, algorithm, and computability with respect to Turing machines. Boolean and first order logic, notions of completeness and undecidability. Complexity classes, notions of P- and NPcompleteness.

Contact person:

Richard Bonner [email protected]

Literature:

Papadimitriou, C.H., Computational Complexity. - Addison-Wesley, 1995. - ISBN 0-201-53082-1 Smith, C.H., A Recursive Introduction to the Theory of Computation. - Springer, 1994. - ISBN 3-540-94332-3 The litterature may be subject to changes.

Course content:

P and NP - randomised computation, cryptography, approximability. Inside P - parallel computation and logarithmic space. Beyond NP.

Contact person:

Richard Bonner [email protected]

Literature:

Papadimitriou, C.H., Computational Complexity. - Addison-Wesley, 1995. - ISBN 0-201-53082-1 The litterature may be subject to changes.

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Mathematical Theories of Learning Code:

MT1270

Swedish points:

5

ECTS credits:

7.5

Study period:

No fixed period.

Level:

Specialized

Location:

Västerås

Language:

Swedish

Examination:

Assignments and student seminars.

Prerequisites:

Representation of abstract knowledge by mathematical structures. Dynamics in abstract structures. Algebraic complexity. Computational approaches to learning. Inductive logic programming.

Modelling with Neural Nets Code:

MT1260

Swedish points:

5

ECTS credits:

7.5

Study period:

No fixed period.

Level:

Specialized

Location:

Västerås

Language:

Swedish

Examination:

Assignments and student seminars.

99

Course content:

Elementary discrete probability. Normal distribution. Geometrical Brownian motion and modelling of pricing processes. Interest rates. Present value analysis. Pricing contracts via arbitrage. Multiperiod pricing model. European and American options. Black-Scholes formula.

Contact person:

Richard Bonner [email protected]

Literature:

Burgisser, Peter m fl, Algebraic Complexity Theory. - Springer, 1997. - ISBN 3-540-60582-7 Li, Ming, Vitanyi, Paul, An Introduction to Kolmogorov Complexity and Its Applications. - Springer, 1997, 2nd ed. - ISBN 0-387-94868-6 Lorentz, Georg G. m fl, Constructive Approximation. - Springer, 1996. - ISBN 3-540-57028-4 Vapnik, Vladimir Naumovic, The Nature of Statistical Learning Theory. - Springer, 1995. - ISBN 0-387-94559-8 Vidyasagar, M., A Theory of Learning and Generalization. - Springer, 1997. - ISBN 3-540-76120-9 The litterature may be subject to changes.

Prerequisites:

Neural nets as dynamical systems. The dynamics of learning and recall. Feed-forward (discrete) networks and constructive approximation of functions. Stochastic models. Connections to theories of complexity.

Course content:

Elementary discrete probability. Normal distribution. Geometrical Brownian motion and modelling of pricing processes. Interest rates. Present value analysis. Pricing contracts via arbitrage. Multiperiod pricing model. European and American options. Black-Scholes formula.

Contact person:

Richard Bonner [email protected]

Literature:

Haykin, Simon S., Neural Networks - A Comprehensive Foundation. - Prentice-Hall, 1994 eller senare. - ISBN 0-02-352761-7 Landau, L.J., Taylor, J.G., Concepts for Neural Networks. - Springer, 1998. - ISBN 3-540-76163-2 The litterature may be subject to changes.

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004

100

D E PA R T M E N T O F M AT H E M AT I C S A N D P H Y S I C S

Degree Program in English Analytical Finance Swedish points:

120-160

ECTS credits:

180-240

Study period:

Start every autumn duration 3-4 years

Level:

A whole program

Location:

Västerås

Language:

English

Examination:

Written examination, written assignments, oral presentations, group work.

Prerequisites:

Science mathematics 3 years in upper secondary education, TOEFL 213 (or 550 in the old system).

Course content:

The Analytical Finance programme prepares you for a challenging career in the international world of finance.You will learn to make mathematical models of economic processes, study the models with state-of-the-art software, and use the results in decision making. You will see economics in different perspectives from accounting in firms, to risk analysis in financial markets. If you are good at analytical thinking and solving problems, this programme could be your stepping stone to an exciting future. A degree in Analytical Finance will give you a general base in Mathematics, Business Administration, Economics and Computer Science. The focus of the programme, however, is on real-life problems and the textbooks have been chosen to support this approach. Advanced financial software is used in the teaching. In general, students work in groups of four with support from one or several teachers. The programme has built-in flexibility and allows students to choose from a selection of subjects during all four years of study. Mälardalen University has a strong group of researchers and graduate students in the fields of Mathematical and Computational Economics. This group developed the Analytical Finance programme after discussions with major financial institutions in Sweden. The programme is a response to the acute and growing need for qualified people in the finance industry. As a graduate of Analytical Finance you will be in demand with banks, financial institutions, insurance companies and government organizations, as well as innovation firms operating in the financial market. Depending on our specialisation, you may be particularly attractive to financial institutions working in the international arena.

Contact person:

Magnus Strandås [email protected]

Study periods Period 1: 25.08.2003 – 02.11.2003

Period 2: 03.11.2003 – 18.01.2004

Period 3: 19.01.2004 – 28.03.2004

Period 4: 29.03.2004 – 13.06.2004