310-2010/02 – Algebra and analytical geometry (AAG)
Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
Subject guarantor | Mgr. Jiří Krček | Subject version guarantor | Mgr. Jiří Krček |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | winter |
| | Study language | English |
Year of introduction | 2019/2020 | Year of cancellation | |
Intended for the faculties | FMT | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Lectures
Tutorials
Project work
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.
Compulsory literature:
Doležalová, J.: Mathematics I, VŠB-TUO, Ostrava, 2005
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company, 1990
Recommended literature:
Leon, S. J.: Linear Algebra with Applications. MACMILLAN New York, 1980,
ISBN 0-02-369810
Way of continuous check of knowledge in the course of semester
Course-credit (10-30 points):
- participation on tutorials is obligatory, 20% of absence can be apologized
- pass two written tests ... 10 + 10 p.
- semestral project ... 10 p.
Exam (0-70 p.):
- praktical part ... 50 p.
- theoretical part ... 20 p.
E-learning
Other requirements
Absolving two tests (0-10 p.).
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.