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Course, academic year 2018/2019
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Advanced Linear Algebra for Physicists - NMAF037
Title in English: Pokročilá lineární algebra pro fyziky
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Miloš Zahradník, CSc.
Classification: Physics > Mathematics for Physicists
Annotation -
Last update: T_KMA (22.05.2008)
Advanced topics of linear algebra for physicists.. A complement to the basic course of mathematics for physicists.
Literature -
Last update: T_KMA (15.05.2008)

L. Motl, M. Zahradník: Pěstujeme lineární algebru, skriptum MFF UK

K. Výborný, M. Zahradník: Používáme lineární algebru, skriptum MFF UK

J. Matoušek, J. Nešetřil: Kapitoly z diskrétní matematiky, Praha 2007

R.P. Feynman: Statistical Mechanics, A Set of Lectures., Addison-Wesley Publishing Company, 1972.

F.R. Gantmacher: The theory of matrices, 1999.

I. Daubechies: Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, 1992.

M.L. Mehta: Random matrices, 2004.

Requirements to the exam - Czech
Last update: doc. RNDr. Miloš Zahradník, CSc. (13.10.2017)

Zkouška bude ústní, po předběžné domluvě studenta s přednášejícím půjde o rozvinutí některého z témat na přednášce probraných

Syllabus -
Last update: T_KMA (15.05.2008)

Theory of determinants and Combinatorics. Trees, Kirchhoff theorem.

Probability and Stochastic matrices. Markov chains. Spectral properties of positive matrices,

Frobenius theorem, spectral gap.

Laplacian and the potential theory on lattices and graphs (Dirichlet forms, Coulomb potentials,

random walks). Gaussian measures, Wick formulas.

Heat equation on lattices, path integrals, Feynman Kac formulas.

Discrete Fourier transform. Introduction to waveletts.

Operators on finite dimensional spaces, functions of operators, Laurent series

of the resolvent, Jordan normal form, spectral decomposition. Introduction

to unbounded operators (and corresponding quadratic forms) on Hilbert space.

Random matrices and their spectra.

Pfaffian. Introduction to the calculus of anticommuting variables.

Linear algebra and statistical physics. Mayer expansion. Determinants of Laplace operators.

Onsager solution of the Ising model.

 
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