Mathematics I (FSI-9MA1)

Academic year 2022/2023
Supervisor: doc. RNDr. Libor Žák, Ph.D.  
Supervising institute: ÚM all courses guaranted by this institute
Teaching language: Czech or English
Aims of the course unit:
Students will acquaint with testing statistical hypotheses and with real applications of linear regression methods in technical practice. Formation of a stochastic way of thinking for the creation of mathematical models with an emphasis on engineering disciplines.
Learning outcomes and competences:
Students acquire needed knowledge from important parts of the probability theory and mathematical statistics, which will enable them to evaluate and develop stochastic models of technical phenomena and processes based on these methods and realize them on PC.
Prerequisites:
Rudiments of descriptive statistics, probability theory and mathematical statistics.
Course contents:
Normal distribution.
Estimation of parameters.
Hypothesis testing.
Analysis of variances.
Tukey's method and Scheffe method.
Linear model.
Coefficient of correlation.
Teaching methods and criteria:
The course is taught through consultations to explanation of basic principles and theories of the discipline.
Assesment methods and criteria linked to learning outcomes:
Use of the above-mentioned statistical methods for solving specific problems. Specific problems are selected in agreement with the student. Student's area of study is preferred. The solved, calculated and elaborated tasks serve to evaluate the student.
Controlled participation in lessons:
Teaching is a form of consultation.
Type of course unit:
    Lecture  10 × 2 hrs. optionally                  
Course curriculum:
    Lecture 1. Collection of data.
2. Variance.
3. Pareto analysis.
4. Probability density and probability distribution.
5. Normal distribution.
6. Distribution of averages
7. Estimation of parameters.
8. Hypothesis testing.
9. Analysis of variances. One way testing,
10. Two way testing.
11. Tukey's method. Scheffe method.
12. Linear model.
13. Coefficient of correlation. Partial coefficient of correlation.
14. Statistics modelling. Monte Carlo method.
Literature - fundamental:
1. J. Anděl: Matematická statistika, SNTL/ALFA, Praha 1978
2. F. Egermayer, M. Boháč: Statistika pro techniky, SNTL, Praha 1984
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
D-IME-K combined study --- no specialisation -- DrEx 0 Recommended course 3 1 W
D-IME-P full-time study --- no specialisation -- DrEx 0 Recommended course 3 1 W