Advanced Mathematics for Informaticians D

A tantárgy neve magyarul / Name of the subject in Hungarian: Felsőbb matematika informatikusoknak D

Last updated: 2012. november 24.

Budapest University of Technology and Economics
Faculty of Electrical Engineering and Informatics
Course ID Semester Assessment Credit Tantárgyfélév
TE90MX43 1 4/0/0/v 4 1/1
3. Course coordinator and department Dr. Tóth Bálint,
6. Pre-requisites
Kötelező:
NEM ( TárgyEredmény( "BMETE90MX58" , "jegy" , _ ) >= 2
VAGY
TárgyEredmény("BMETE90MX58", "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 Stochastics 1: Existence proofs and randomness: Erdõs' method through examples (2-coloring of hypergarphs,
Ramsey numbers) with algorithmic aspects. Turán's theorem. Derandomization. Lovász's local lemma and applications. Analysis of randomized algorithms (expected time of quicksort, Rabin-Miller primality test, Schwartz-Zippel lemma and applications, pattern matching, treaps, minimum spanning trees, computing planar autopartitions and convex hulls). Random walks and algorithms, ranking pages in the internet.
Randomness and complexity classes (RP, Las Vegas, interactive protocols, IP, BPP, RL with examples, IP=PSPACE). Zero knowledge proofs. Random graphs (Erdõs-Rényi model, Albert-Barabási model). Properties of large networks. Stochastics 2: Review of basic probability theory: random variables, distribution, expectation, covariance matrix, important types of distributions. Types of convergence: stochastic, L^p, almost sure. Borel-Cantelli lemmas. Laws of large numbers, weak convergence of distributions, limit theorems. Generating and characteristic functions and their applications: limit theorems and large deviations (Bernstein inequality, Chernoff bound, Kramer's theorem). 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. Additional topics: percolation, random graphs, phase transition.
14. Required learning hours and assignment
Kontakt óra
Félévközi készülés órákra
Felkészülés zárthelyire
Házi feladat elkészítése
Kijelölt írásos tananyag elsajátítása
Vizsgafelkészülés
Összesen