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Algebra and analytical geometry

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-2010/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
MOR74Mgr. Zuzana Morávková, Ph.D.
KRC76Mgr. Jiří Krček
Summary
The topic is the part of basic three-semester mathematical course in bachelor degree.
The first part introduces grounding of the linear algebra - linear spaces and mapping, properties of these, matrix calculus and systems of linear equations. The second part summarizes the analytical geometry of linear and quadratic objects.
Learning Outcomes of the Course Unit
The main goal is to build compact system of basic knowledge in algebraic equations and its systems in the frame of finite-dimensional linear spaces. Obtained knowledge will be applied in connected themes as vector algebra and analytical geometry.
Course Contents
1. Complex numbers.
2. Polynomials and algebraic equations.
3. Linear spaces – part 1.: linear independence, dimension, basis.
4. Matrix algebra.
5. Rank of matrix, systems of linear equations.
6. Determinants, inverse matrix, matrix equations.
7. Linear spaces – part 2: linear mapping, fundaments of spectral theory.
8. Linear, bilinear and quadratic forms.
9. Spaces with scalar product.
10. Vector algebra.
11. Analytical geometry of linear objects.
12. Classification of conics.
13. Quadric surfaces.
Recommended or Required Reading
Required Reading:
Doležalová, J.: Mathematics I, VŠB-TUO, Ostrava, 2005
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company, 1990
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaI/m1.pdf
Burda, P., Havelek, R., Hradecká, R.: Algebra a analytická geometrie (Matematika I),1997, ISBN 80-7078-479-2.
Recommended Reading:
Leon, S. J.: Linear Algebra with Applications. MACMILLAN New York, 1980,
ISBN 0-02-369810
http://mi21.vsb.cz/modul/linearni-algebra
Škrášek, J., Tichý, Z.: Základy aplikované matematiky I. SNTL Praha, 1989,
ISBN 04-0544-89
Planned learning activities and teaching methods
Lectures, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 10
        ExaminationExamination70 21