310-2010/01 – Algebra and analytical geometry (AAG)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMT, FEI, HGF, USPIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Part-time Credit and Examination 18+0

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

Project work


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.


Other requirements

Absolving two tests (0-10 p.).


Subject has no prerequisities.


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

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation: 80 %

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2020/2021 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
2019/2020 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner