Course detail

Mathematics IV

FSI-4M-AAcad. year: 2025/2026

The course makes students familiar with descriptive statistics, random events, probability, random variables and vectors, probability distributions, random sample, parameters estimation, tests of hypotheses, and linear regression analysis. Seminars include solving problems and applications related to mechanical engineering. PC support is dealt with in the course entitled Statistical Software, which is optional.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Libor Žák, Ph.D.

Department

Institute of Mathematics (ÚM)

Offered to foreign students

Of all faculties

Entry knowledge

Rudiments of the differential and integral calculus.

Rules for evaluation and completion of the course

Seminar credit conditions:

  • active attendance in practices
  • sufficient or better of written exam
  • admission of semester assignment.

Examination (written form) consists of two parts:

  • a practical part – tasks from the covered topics. Total 0 to 80 points (with own summary of formulas)
  • a theoretical part - 4 tasks related to basic notions, (their properties, sense and practical use); each theoretical question 0 to 5 points.

Evaluation: each task 0 to 20 points evaluation according to the total number of points from practical and theoretical part: excellent (90 - 100 points), very good (80 - 89 points), good (70 - 79 points), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).

Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Aims

The course objective is to make students acquainted with basic notions, methods and progresses of probability theory, descriptive statistics and mathematical statistics as well as with the development of students` stochastic way of thinking for modelling a real phenomenon and processes in engineering branches.
Students obtain the needed knowledge of the probability theory, descriptive statistics and mathematical statistics, which will enable them to understand and apply stochastic models of technical phenomena based upon these methods.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Anděl, J.: Základy matematické statistiky. Praha : Matfyzpress, 2005.
Hahn, G. J. - Shapiro, S. S.: Statistical Models in Engineering.New York : John Wiley & Sons, 1994.
Montgomery, D. C. - Renger, G.: Applied Statistics and Probability for Engineers. New York : John Wiley & Sons, 2003.

Recommended reading

Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2003.
Meloun, M. - Militký, J.: Statistické zpracování experimentálních dat. Praha : Plus, 1994.
Seger, J. - Hindls, R.: Statistické metody v tržním hospodářství. Praha : Victoria Publishing, 1995.

Classification of course in study plans

  • Programme B-STI-A Bachelor's 2 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

1. Random events, probability, conditional probability, independent events. 2. Random variable, functional characteristics. 3. Numerical characteristics of random variables. Introduction to basic distributions. 4. Basic distributions – continuation (properties and application). 5. Random vector, types, functional and numerical characteristics. 6. Random sample, sample characteristics (properties, sample from N). 7. Parameters estimation (point and interval estimates of parameters N and Bi). 8. Testing statistical hypotheses (types, basic concepts) – one-samle tests. 9. Testing statistical hypotheses – two-samle tests. 10. Testing statistical hypotheses – multi-samle tests, goodness of fit tests. 11. Elements of regression analysis. – introduction, point estimates 12. Regression analysis – interval estimates, hypotheses testing. 13. Regression analysis – diagnostics, other regression models, Summary of covered topics.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

1. Descriptive statistics (one-dimensional sample). 2. Descriptive statistics (two-dimensional sample). Combinatorics. Semester work assignment. 3. Probability, conditional probability, independent events. 4. System reliability, random variables - functional and numerical characteristics. 5. Random variables – continuation. 6. Basic probability distributions (Minitab – reliability diagrams). 7. Two-dimensional discrete random vector, functional and numerical characteristics. CLT illustration 8. Written exam. Interval estimates. 9. Testing hypotheses of one-dimensional parameters, power of tests. 10. Testing hypotheses of parameters in two samples. 11. ANOVA, chisquare tests (equality of probabilities of more categories), goodnes of fit tests. 12. Regression analysis - regression line. 13. Regression analysis – model, assignment submition.

Computer-assisted exercise

13 hod., compulsory

Teacher / Lecturer

doc. RNDr. Libor Žák, Ph.D.

Syllabus

Computer seminars follow up the topics covered in seminars using statistical software (Excel, Minitab).