Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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    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 rendek grafikus formában itt láthatók.

    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