Mathematics for computer science

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Basics of probability theory, in particular conditional probability and Bayesian approach. Notions needed for statistics: Descriptions of random variables and vectors, laws of large numbers. Basics of mathematical statistics: Point and interval estimates, methods of parameters estimation and hypotheses testing. Basic notions and results of the theory of Markov chains.

Requirements:

Active participation at seminars and a fulfilled project - an ordinary statistical task trained at seminars, based on real data. Will be specified at seminars by tutors.

Syllabus of lectures:

1. Basic notions of probability theory.

2. Random variables and their description.

3. Characteristics of random variables.

4. Basic distributions of random variables.

5. Random vector, joint distribution.

6. Binary operations with random variables, mixture of distributions.

7. Basic notions of statistics.

8. Method of moments, method of maximum likelihood.

9. EM algorithm. 10. Interval estimates of mean and variance.

11. Hypotheses testing.

12. Goodness-of-fit tests, tests of correlation, non-parametic tests.

13. Markov chains.

14. Classification of states of Markov chains.

Syllabus of tutorials:

1. Basic notions of probability theory.

2. Random variables and their description.

3. Characteristics of random variables.

4. Basic distributions of random variables.

5. Random vector, joint distribution.

6. Binary operations with random variables, mixture of distributions.

7. Basic notions of statistics.

8. Method of moments, method of maximum likelihood.

9. EM algorithm.

10. Interval estimates of mean and variance.

11. Hypotheses testing.

12. Goodness-of-fit tests, tests of correlation, non-parametic tests.

13. Markov chains.

14. Classification of states of Markov chains.

Study Objective:

Study materials:

1. Spiegel, Murray R. and Schiller, John J. and Srinivasan, R. Alu: Probability and Statistics, McGraw-Hill, 2000, ISBN 0-07-135004-7

2. Hsu, Hwei P.: Probability, random variables, and random processes, McGraw-Hill, 1996, ISBN 0-07-030644-3

3. Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics. 3rd ed., McGraw-Hill, 1974.

4. Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Computer Science and Engineering (compulsory course)