Kezdőlap Rólunk Munkatársak Oktatás Kutatás Elérhetőség

© Katona Gyula Y.

Foundation of Computer Science (BMEVISZA105, semester 1, 4/2/0/v/6 c. p.)

Dr. Gyula Katona

Basic concepts of combinatorics (permutations, variations, combinations). Basic concepts of graph theory (vertex, edge, degree, isomorphism). Path, circuit, connectivity, trees. Planar graphs, duality. Algorithms in graph theory (minimum cost tree, shortest path, maximum matching, flow problems, topological sorting, PERT method). Higher connectivity numbers of graphs. Graph coloring problems (vertex, edge and map coloring). Euler- and Hamiltonian circuits. Basic concepts of algorithms and complexity. Polynomially solvable and NPcomplete problems. Basic concepts in number theory  (divisibility, primes, congruencies, Euler-Fermat theorem), algorithms in number theory (prime tests, public key cryptography). Basic concepts of abstract algebra (operations, structures), semigroups. Groups, their relations to transformations, important special groups, factor group. Rings and fields.

Introduction to the Theory of Computing 1 (BMEVISZA103, semester 1, 2/2/0/v/5 c. p.)

Dr. András Recski

Scalars, vectors, analytic geometry of 2- and 3- dimensional space. Solvability of systems of linear equations with Gauss elimination. Unicity. Determinants, their properties. Complex numbers. Vector spaces, linear independence, base, dimension. Linear transformations and their matrices, rank, inverse. Eigenvalues and eigenvectors of linear transformations. Quadratic forms, definiteness. Equivalence and cardinality of infinite sets. Countable and continuum. Power set. Basic concepts of combinatorics (permutations, variations, combinations). Basic concepts of graph theory (vertex, edge, degree, isomorphism). Path, circuit, connectivity, trees. Planar graphs, duality.  

Introduction to the Theory of Computing 2 (BMEVISZA110, semester 2, 2/2/0/v/4 c. p.)

Dr. András Recski

Algorithms in graph theory (minimum cost tree, shortest path, maximum matching, flow problems, topological sorting, PERT method). Higher connectivity numbers of graphs. Graph colouring problems (vertex, edge and map colouring). Euler- and Hamiltonian circuits. Basic concepts in number theory (divisibility, primes, congruencies, Euler-Fermat theorem), algorithms in number theory (prime tests, public key cryptography). Basic concepts of abstract algebra (operations, structures), semigroups. Groups, their relations to transformations, important special groups, factor group. Rings and fields.

Probability Theory (BMEVISZA208, semester 3, 3/1/0/v/4 c. p., SZIT)

Dr. László Ketskeméty

Probability: Elements (random experiment, outcomes, sample space, event, probability). Conditional probability, independence of events. The law of total probability and Bayes' rule. Random variables, probability distribution function. Discrete random variables (binomial, geometric, Poisson, hypergeometric). Continuous random variables (uniform, exponential, normal). Expectation and variance. Markov's and Chebyshev's inequalities. Joint distributions and independence. Covariance and correlation coefficient. Linear regression. Law of large numbers. Central limit theorem. Statistics: Elements (sample, estimators, unbiased and consistent estimators). Confidence intervals (examples in normal data). Statistical tests (null hypotheses, type I and type II errors, test statistics, critical value, the u- and t- tests).  

Theory of Algorithms (BMEVISZA213, semester 4, 2/2/0/v/5 c. p.)

Mrs. Dr. Katalin Friedl

Algorithms. Sequential and binary search. Search with some basic data structures, like search tree, AVL tree, B-tree, hash table. Sorting by insertion, merge sort, heap sort, quicksort, bin sort, radix sort and the analysis of these methods. The complexity of sorting. Basic graph theoretical algorithms: BFS, DFS and their applications to determine (strongly) connected components. Algorithms for acyclic graphs. Finding maximal matching in bipartite graphs. Determining shortest paths by methods of Bellman-Ford, Dijkstra, and Ford. Minimal spanning tree algorithms and the union-find data structure. General algorithmic methods: branch and bound, divide and conquer, dynamic programming. Efficient approximation algorithms. Algorithmically hard problems, the notion of NP and NP-completeness.  

Data Mining Laboratory (BMEVISZA384, semester 6, 0/0/2/f/2 c. p.)

Dr. Krisztián Buza

The course is concerned with the essential data mining problems and algorithms. The laboratory gives practical knowledge about data mining methods and skills to be able to make data mining analysis in several fields, such as commerce, finance, medical data mining. The data mining software Weka is introduced and used for preprocessing,  data transformations, classification (with nearest neighbor rule, decision rules, decision trees, neural networks, bayesian networks, support vector  machine), clustering, searching for frequent item sets, association rules.

Declarative Programming (VISZA402, semester 7, 3/1/0/v/5 c. p.)

Dr. Péter Szeredi

Comparison of the imperative and the declarative (functional and logical) programming. Functional programming in Erlang language. The basics of the Erlang language. Logical programming in Prolog language. The basics of the Prolog language.

Combinatorics and Graph Theory 1 (BMEVISZA030, semester 1, 2/1/0/v/4 c. p.)

Dr. András Recski

Basic concepts of combinatorics (permutations, variations, combinations). Recursions and generating functions. Fibonacci numbers, homogen linear recursions. Catalan numbers.  Basic concepts of graph theory (vertex, edge, degree, isomorphism). Path, circuit, connectivity, trees. Minimum cost tree, Kruskal’s theorem. Bipartite graphs, matchings, Tutte’s theorem, König-, Gallai-thorems. Flows, Ford-Fulkerson-theorem, Edmonds-Karp-thorem. Menger’s theorem, higher connectivity.

shortest path, maximum matching, flow problems, topological sorting, PERT method). Higher connectivity numbers of graphs.  Euler- and Hamiltonian circuits, sufficient conditions (Dirac, Ore, Pósa, Chávtal).

Combinatorics and Graph Theory 2 (BMEVISZA031, semester 2, 2/1/0/f/3 c. p.)

Dr. András Recski

Planar graphs, duality, Euler’s formula, Kuratowski’s thorem, weakly isomorphic graphs, Whitney’s thorems. Graph coloring problems (vertex, edge and map coloring), Mycielski’s constructions, Brooks-thorem. Five-color theorem. Vizing thorem. Dinitz-problem, list-coloring, Galvin’s thorem. Perfect graphs, interval graphs, perfect graph theorem.  Ramsey-thory, Erdõs-Szekeres theorem. Turán-thorem, Erdõs-Stone -thorem, Erdõs-Simonovits-theorem. Hypergraphs, Erdõs-Ko-Rado thorem, Sperner’s thorem, LYM inequality. De Brujin-Erdõs thorem, finite geometries, Bruck-Ryser theorem.