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

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorMgr. Jiří KrčekSubject version guarantorMgr. Zuzana Morávková, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation2022/2023
Intended for the facultiesFMTIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
MOR74 Mgr. Zuzana Morávková, Ph.D.
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 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

Full-time form (validity from: 2019/2020 Winter semester, validity until: 2022/2023 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21 3
Mandatory attendence participation: The mandatory participation is 80 %. To complete the credit, students must elaborate the home-project and pass the credit tests.

Show history

Conditions for subject completion and attendance at the exercises within ISP: To complete the credit, students must elaborate the home-project and pass the credit tests. On the basis of a successfully completed credit, they can take an exam, which consists of a practical and a theoretical part.

Show history

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (B0719A270001) Nanotechnology P Czech Ostrava 1 Compulsory study plan
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

Assessment of instruction



2022/2023 Winter
2021/2022 Winter
2020/2021 Winter
2019/2020 Winter