BME VIK - A számítástudomány alapjai

A tantárgy neve magyarul / Name of the subject in Hungarian: A számítástudomány alapjai

3. Course coordinator and department Dr. Katona Gyula,

Web page of the course http://www.cs.bme.hu/sza

4. Instructors Dr. Attila Sali, associate professor, Department of Computer Science and Information Theory

6. Pre-requisites

Kötelező:

NEM ( TárgyEredmény( "BMEVISZA105", "jegy" , _ ) >= 2
VAGY TárgyEredmény("BMEVISZA105", "FELVETEL", AktualisFelev()) > 0
VAGY TárgyEredmény( "BMEVISZAA02", "jegy" , _ ) >= 2
VAGY TárgyEredmény("BMEVISZAA02", "FELVETEL", AktualisFelev()) > 0
VAGY TárgyEredmény( "BMEVISZAA02" , "aláírás" , _ ) = -1)

ÉS (Training.Code=("5N-A7") VAGY Training.Code=("5N-A7H") VAGY Training.Code=("5NAA7"))

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

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

7. Objectives, learning outcomes and obtained knowledge

The objective is to provide the students with the required theoretical background in combinatorics, algorithmics, elementary cryptography, and graph theory for further studies in electrical engineering.

Obtained skills and expertise:

Theoretical knowledge and problem solving skills in the treated fields of mathematics.

8. Synopsis

Week 1: Basic concepts of combinatorics: permutations, variations, combinations, binomial coefficient, nimonial theorem

Week 2: Basic concepts of graph theory (vertex, edge, degree, isomorphism). Path, circuit, connectivity, trees.

Week 3: Shortest path, BFS, Dijkstra, Ford, Floyd algorithms, widest paths in directed and undirected graphs

Week 4: DFS, directed cycles, fundamental system of cycles and cuts, PERT

Week 5: Euler- and Hamiltonian circuits, sufficient and necessary conditions for the existence. Dirac, Ore theorems,

Week 6: Graph coloring problems (vertex, edge and map coloring). Bipartite graphs. Flows, Ford-Fulkerson theorem, algorithm to find a maximal flow. Integral maximum flow lemma.

Week 7: Multiple source flows, vertex capacities, undirected flows.

Week 8: Bipartite graphs, matchings, Hall's theorem, algorithm to find a maximal matching. Independent and covering vertex and edge sets, König's and Gallai's theorems.

Week 9: Planar graphs, duality. Euler's Theorem, Kuratowski's theorem, four color theorem.

Week 10: Basic concepts of algorithms and complexity. Polynomially solvable and NP-complete problems, coNP.

Week 11: Karp-reduction, Cook-Levin theorem, famous NP-complete problems: SAT, HAM, 3-COLOR, k-COLOR, MAXSTABLE, MAXCLIQUE, HAMPATH.

Week 12: Basic concepts in number theory: divisibility, primes, fundamental theorem of number theory, number of divisors, distribution of primes

Week 13: Congruences, diophantine equations, Euler-Fermat theorem,

Week 14: Algorithms in number theory: prime tests, public key cryptography, RSA.

9. Method of instruction 2 hours lecture, 2 hours problem solving

10. Assessment

Signature:

2 midterms during the semester. Both must be at least 30% and at least 40% in average.

Final:

Oral exam.

Final grade: 40% midterms, 60% oral exam.

11. Recaps 2 occasions for retake the midterms, each time either one of the test can be retaken.

12. Consultations By appointment.

13. References, textbooks and resources M. O. Albertson, J. P. Hutchinson: Discrete Mathematics with Algorithms, Wiley, 1988

14. Required learning hours and assignment

In class	56
Preparation for classes	28
Preparation for midterms	18
Homework
Reading assignment
Preparation for final	48
Total	150

15. Syllabus prepared by

Dr. Tamás Fleiner, associate professor

Department of Computer Science and Information Theory

Dr. Gyula Katona, associate professor

Department of Computer Science and Information Theory

Dr. András Recski, professor

Department of Computer Science and Information Theory