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Course, academic year 2019/2020
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Bachelor seminar II - NMUM332
Title in English: Bakalářský seminář z matematiky II
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 2
Hours per week, examination: summer s.:0/2 C [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: http://www.karlin.mff.cuni.cz/~halas/BCsemin.htm
Guarantor: Mgr. Zdeněk Halas, DiS., Ph.D.
Class: M Bc. DGZV
M Bc. DGZV > Doporučené volitelné
M Bc. MZV
M Bc. MZV > Doporučené volitelné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Annotation -
Last update: T_KDM (04.05.2012)
This subject is continuation of Bachelor seminar I. It is intended for second-year students (accessible also for third-year students) of teaching of mathematics. The subject is based on needs of second-year students who went through appreciable part of their bachelor's degree study. Its content is determined by that what students consider problematic. On the basis of their questions we will go over the first and second year passages from mathematical analysis, linear algebra, geometry and algebra. In this way student manages to a considerable extent its own education and student is encouraged
Aim of the course -
Last update: T_KDM (04.05.2012)

This subject helps to see the whole picture as for the requirements of bachelor's exam. The aim is to complete, to consolidate and to organize key mathematical knowledge and skills, to develop discovering of relations between particular mathematical disciplines. Last but not least, student will be encouraged to creative approach to mathematics.

Course completion requirements - Czech
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (07.06.2019)

Nutnou a postačující podmínkou získání zápočtu je

  • v průběhu semestru soustavně prokazovat znalost postupně probírané látky

a zároveň

  • na konci semestru prokázat velmi dobrou znalost všech probíraných témat, přičemž u žádného z témat nesmí být zjištěna znalost odpovídající hodnocení nevyhověl(a). Tuto část student má možnost opakovat (1 řádný a dva opravné termíny).

Aktivní účast na semináři je "strongly recommended".

Literature -
Last update: T_KDM (04.05.2012)

Veselý, J. Matematická analýza pro učitele I. Matfyzpress, 1997.

Veselý, J. Matematická analýza pro učitele II. Matfyzpress, 1997.

Brabec, J. a kol. Matematická analýza I. SNTL, 1989.

Brabec, J., Hrůza, B. Matematická analýza II. SNTL, 1986.

Černý, I. Úvod do inteligentního kalkulu. Academia, 2002.

Černý, I. Úvod do inteligentního kalkulu 2. Academia, 2005.

Bečvář, J. Lineární algebra. Matfyzpress, 2002.

Sekanina, M. a kol. Geometrie I. SPN, 1986.

Sekanina, M. a kol. Geometrie II. SPN, 1988.

Janyška, J., Sekaninová, A. Analytická geometrie kuželoseček a kvadrik. Brno, 1996.

Blažek, J. a kol. Algebra a teoretická aritmetika I. SPN, 1983.

Blažek, J. a kol. Algebra a teoretická aritmetika II. SPN, 1985.

Děmidovič, B. P. Sbírka úloh a cvičení z matematické analýzy. Fragment, 2003.

Syllabus -
Last update: T_KDM (04.05.2012)

Actual topics will be established mainly on the basis of questions of students and on the monitoring of their needs. The set of all possible topics is determined by contents of bachelor exam:

1. Relations, mappings and their basic properties.

2. Construction and properties of number domains.

3. Groups and their homomorphisms.

4. Ring, integral domain, division ring and their basic properties.

5. Vector space, base, dimension, linear mapping. Vector space equipped with dot product, cross product.

6. Matrices and their properties, application for solution of systems of linear equations.

7. Determinants and their properties, Cramer's rule.

8. Basic concepts of divisibility in integral domains.

9. Differential calculus of functions of one real variable - limit, continuity, derivative, Taylor's theorem, behaviour of a function.

10. Elementary functions and their definition.

11. Primitive function. Integration by parts and substitution.

12. Riemann integral and its applications, improper integrals.

13. Sequences of real numbers, limits.

14. Infinite series and their sums. Basic theorems concerning absolute and nonabsolute convergence, criteria of convergence.

15. Differential equations, basic methods of their solution.

16. Affine and Euclidean space.

17. Groups of geometric projections.

We will prefer topics which were not discussed in the previous semester.

 
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