Mathematics for computer science

Lecturer:

Tomáš Kroupa

Tutor:

Tomáš Kroupa, Mirko Navara (gar.), Libor Nentvich

Supervisor:

Department of Mathematics

Synopsis:

Basics of probability theory and mathematical statistics. Includes descriptions of probability, random variables and their distributions, characteristics and operations with random variables. Basics of mathematical statistics: Point and interval estimates, methods of parameters estimation and hypotheses testing, least squares method.

Requirements:

Linear Algebra, Calculus, Discrete Mathematics

Syllabus of lectures:

1. Basic notions of probability theory.

2. Independence, conditional probability, Bayes formula.

3. Random variables, random vectors, joint distribution.

4. Description of distributions of random variables.

5. Characteristics of random variables.

6. Basic distributions. Covariance, corellation. Chebyshev inequality.

7. Basic notions of statistics.

8. Parameter estimates and their properties. Sample mean. Central limit theorem.

9. Sample variance. Sample standard deviation.

10. Interval estimates of mean and variance. Method of moments, method of maximum likelihood.

11. Hypotheses testing.

12. Goodness-of-fit tests.

13. Tests of correlation, non-parametic tests.

Syllabus of tutorials:

1. Elementary probability.

2. Mathematical model of probability.

3. Independence, conditional probability, Bayes formula.

4. Description of distributions of random variables. Random vectors, joint distribution.

5. Mixture of random variables.

6. Functions of random variables.

7. Mean and variance of random variables.

8. Operations with random variables. Chebyshev inequality.

9. Central limit theorem.

10. Interval estimates of mean and variance.

11. Method of moments, method of maximum likelihood.

12. Hypotheses testing.

13. Goodness-of-fit tests, tests of correlation.

Study Objective:

Basics of probability theory and their application in statistical estimates and tests.

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:

Time-table for winter semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomKN:E-127 Kroupa T. 12:45–14:15 EVEN WEEK (lecture parallel1) Karlovo nám. Kotkova cvičebna K4
Fri
Thu
Fri

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Computer Technology - Software Engineering- structured studies (compulsory course)
• Computer Technology - System Programming- structured studies (compulsory course)
• Computer Technology - Computer Graphics- structured studies (compulsory course)
• Computer Technology - Computer Network and Internet- structured studies (compulsory course)
• Computer Technology - Designing Digital Systems- structured studies (compulsory course)