Mathematics 6D

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Basic concepts of graph theory. Topological ordering of edges and vertices. Dept-first and breadth-first searches. Spanning tree. Shortest path problem. Dijsktra and Floyd algorithms. Complexity, P and NP problems. Existence of algorithmically nonsolvable problems. Random variables, random vectors. Empirical distribution function, histogram. Point and interval estimation. Tests of means and variances. Goodness-of-fit test, nonparametric tests.

Requirements:

Syllabus of lectures:

1. Basic concepts of graph theory

2. Topological ordering of edges and vertices

3. Dept-first and breadth-first searches

4. Spanning tree

5. Shortest path problem

6. Dijsktra and Floyd algorithms

7. Complexity, P and NP problems

8. Existence of algorithmically nonsolvable problems

9. Random variables, random vectors

10. Empirical distribution function, histogram

11. Point and interval estimation

12. Tests of means and variances

13. Goodness-of-fit test, nonparametric tests

Syllabus of tutorials:

1. Basic concepts of graph theory

2. Topological ordering of edges and vertices

3. Dept-first and breadth-first searches

4. Spanning tree

5. Shortest path problem

6. Dijsktra and Floyd algorithms

7. Complexity, P and NP problems

8. Existence of algorithmically nonsolvable problems

9. Random variables, random vectors

10. Empirical distribution function, histogram

11. Point and interval estimation

12. Tests of means and variances

13. Goodness-of-fit test, nonparametric tests

Study Objective:

Study materials:

[1] M. K. Ochi: Applied Probability & Stochastic Processes in Engineering. Wiley 1989.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Technická kybernetika-inženýrský blok (compulsory course)
• Biomedicínské inženýrství - inženýrský blok (compulsory course)
• Biomedicínské inženýrství - inženýrský blok (compulsory course)
• Technická kybernetika-inženýrský blok (compulsory course)