c601 Basics of mathematics

Faculty of Sports Studies
Autumn 2010
Extent and Intensity
0/8. 1 credit(s). Type of Completion: z (credit).
Teacher(s)
Mgr. Martin Sebera, Ph.D. (lecturer)
Guaranteed by
Mgr. Martin Sebera, Ph.D.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
At the end of this course, students should be able to:
* understand and be able to explain matrix and matrix operations;
* formulate a reasoned differential diagnosis for solving problems (equation systems, inverse matrix, determinants);
* use basic formulas for derivation
Syllabus
  • Chapter 1: Set Theory – basic constructs
  • Module 1.1 Set operations
  • Module 1.2 Notations
  • Chapter 2: VECTOR SPACE
  • Module 2.1 Conception of vector space
  • Module 2.2 Arithmetic vector space
  • Module 2.3 Subspace of vector space
  • Module 2.4 Linear dependence and independence
  • Module 2.5 Base a dimension of vector space
  • Chapter 3: MATRIX
  • Module 3.1 Conception of matrix
  • Module 3.2 Basic operations with matrixes
  • Module 3.3 Rank of matrix
  • Module 3.4 Multiplication of matrix
  • Chapter 4: DETERMINANTS
  • Module 4.1 Conception of determinant
  • Module 4.2 Properties of determinant
  • Module 4.3 Condensing method of calculation of determinant
  • Chapter 5: EQUATION SYSTEM
  • Module 5.1 Basis concepts
  • Module 5.2 Solving of equation system
  • Module 5.3 Methods of solving equation system
  • Chapter 6: MATRIX ALGEBRA
  • Module 6.1 Inversion matrix
  • Module 6.2 Matrix equations
  • Chapter 7: DERIVATION
Literature
  • REKTORYS, Karel. Přehled užité matematiky. I [Rektorys, 2000]. 7. vyd. Praha: Prometheus, 2000, 720 s. ISBN 80-7196-180-91. info
  • REKTORYS, Karel. Přehled užité matematiky. II [Rektorys, 2000]. 7. vyd. Praha: Prometheus, 2000, 874 s. ISBN 80-7196-181-72. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1990, 853 s. ISBN 80-03-00111-0. info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1986, 896 s. URL info
  • ŠKRÁŠEK, Josef and Zdeněk TICHÝ. Základy aplikované matematiky. 1. vyd. Praha: Nakladatelství technické literatury, 1983, 876 s. info
Teaching methods
lectures and class exercises
Assessment methods
Writing test, 5 examples, for pass minimally 4 examples must be done
Language of instruction
Czech
The course is also listed under the following terms Autumn 2008, Autumn 2009.
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