714-0761/04 – Algebra and analytical geometry (AAG)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | doc. RNDr. Jaroslav Vlček, CSc. | Subject version guarantor | doc. RNDr. Jaroslav Vlček, CSc. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FMT, FEI, USP, HGF | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods.
Students should learn how to
analyze problems,
distinguish between important and unimportant,
suggest a method of solution and verify each step of an algorithm,
generalize achieved results,
analyze correctness of results with respect to given conditions,
apply these methods while solving technical problems.
Teaching methods
Lectures
Tutorials
Project work
Summary
The topic is the middle part of basic three-semester mathematical course in bachelor degree. s the main goal, there 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.
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.
14. Reserve.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.