Advanced Mathematics for Electrical Engineers B

A tantárgy neve magyarul / Name of the subject in Hungarian: Felsőbb matematika villamosmérnököknek B

Last updated: 2012. november 24.

Budapest University of Technology and Economics
Faculty of Electrical Engineering and Informatics
Course ID Semester Assessment Credit Tantárgyfélév
TE90MX38 1 4/2/0/v 6 1/1
3. Course coordinator and department Dr. Tóth Bálint,
6. Pre-requisites
Kötelező:
NEM ( TárgyEredmény( "BMEVISZMA06" , "jegy" , _ ) >= 2
VAGY
TárgyEredmény("BMEVISZMA06", "FELVETEL", AktualisFelev()) > 0)

A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

8. Synopsis Combinatorial Optimization: Basic concepts of linear programming, Farkas lemma, duality. Integer programming, total unimodularity, applications to matchings in bipartite graphs and network flows.Basic notions of matroid theory, duality, minors, direct sum, sum. Algorithms for matroids. Matroids and graphs, linear representation, Tutte's theorems. Approximation algorithms (set cover, Steiner-trees, travelling salesman problem). Scheduling algorithms (list scheduling, the algorithms of Hu and Coffman and Graham). Engineering applications: design of reliable networks, design of very large scale integrated (VLSI) circuits, the classical theory of electric networks. Stochastics: Review of basic probability theory: random variables, distribution, expectation, covariance matrix, important types of distributions. Generating and characteristic
functions and their applications: limit theorems and large deviations (Bernstein inequality, Chernoff bound,
Kramer's theorem). Basics of mathematical statistics: samples, estimates, hypotheses, important tests, regressions. Basics of stochastic processes: Markov chains and Markov processes. Markov chains with finite state space: irreducibility, periodicity, linear algebraic tools, stationary measures, ergodicity,reversibility, MCMC. Chains with countable state space: transience, recurrence. Application to birth and death processes
and random walks. Basics of continuous time Markov chains: Poisson process, semigroups. Weakly stationary processes: spectral theory, Gauss processes, interpolation, prediction and filtering.
14. Required learning hours and assignment
Kontakt óra
Félévközi készülés órákra
Felkészülés zárthelyire
Házi feladat elkészítése
Kijelölt írásos tananyag elsajátítása
Vizsgafelkészülés
Összesen