Mathematics for cybernetics and measurement

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers different chapters of mathematics necessary for Master's degree in cybernetics and measurement that could not be included in the bachelor study due to lack of space and time. It concerns especially z-transformation, some special parts of matrix calculus, basic statistical methods for estimation of distribution parameters and hypotheses testing and elements of the stochastic processes theory. The seminars are aimed at deepening the knowledge of the lecture topics.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1. Series in complex domain, power series, Laurent series.

2. Z-transform.

3. Application of Z-transform to solving difference equations.

4. Minimal polynomial of a matrix, matrix functions.

5. Expressing matrix functions by series.

6. Singular value decompisition.

7. Random sampling, sampling statistics and their distributions.

8. Point estimations. Moment and maximum likelihood estimates.

9. Confidence intervals.

10. Testing hypotheses on expected value and variance.

11. Non-parametric tests.

12. Correlation and regression. Linear regression. Polynomial regression.

13. Stochastic process. Classification of stochastic processes.

14. Stationary processes.

Syllabus of tutorials:

1. Series incomplex domain, power series, Laurent series.

2. Z-transform.

3. Application of Z-transform to solving difference equations.

4. Minimal polynomial of a matrix, matrix functions.

5. Expressing matrix functions by series.

6. Singular value decomposition.

7. Random sampling, sampling statistics and their distributions.

8. Point estimations. Moment and maximum likelihood estimates.

9. Confidence intervals.

10. Testing hypotheses on expected value and variance.

11. Non-parametric tests.

12. Correlation and regression. Linear regression. Polynomial regression.

13. Stochastic process. Classification of stochastic processes.

14. Stationary processes.

Study Objective:

Study materials:

There is no text-book covering the course completely. The lecturer will hint resources to particular topics.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Cybernetics and Measurements - Control Engineering- structured studies (compulsory course)
• Cybernetics and Measurements - Artificial Intelligence- structured studies (compulsory course)
• Cybernetics and Measurements - Measurement and Instrumentation Systems- structured studies (compulsory course)
• Cybernetics and Measurements - Aeronautical Engineering and Control Systems- structured studies (compulsory course)