Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Mathematics - OPDM1M101A

Title:	Matematika
Guaranteed by:	Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty:	Faculty of Education
Actual:	from 2020
Semester:	both
E-Credits:	0
Hours per week, examination:	0/0, other [HS]
Capacity:	winter:unknown / unknown (10) summer:unknown / unknown (10)
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Note:	course is intended for doctoral students only enabled for web enrollment can be fulfilled in the future you can enroll for the course in winter and in summer semester

Guarantor:	prof. RNDr. Ladislav Kvasz, DSc., Dr.
Teacher(s):	prof. RNDr. Ladislav Kvasz, DSc., Dr.

Opinion survey results Examination dates WS schedule SS schedule Noticeboard

Annotation -

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (08.10.2020)

The goal of the course is mastering a certain field of scientific mathematics according to the topic of the PhD student's work. The field is chosen from the offer by the PhD Board and after consultations with the supervisor. The topic will be the basis for the topic examined in the state doctoral exam.

Literature - Czech

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (08.10.2020)

KLINE, M. Mathematical Thought from Ancient to Modern Times. Oxford University Press, 1990.

GRATTAN-GUINNESS, I. (ed.). The Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Routledge, 1994.

PETERSON, A. a BOHNER, M. Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, 2001.

CULL, P., FLAHIVE, M. a ROBSON, R. Difference Equations: From Rabbits to Chaos, Springer-Verlag, 2005.

COXETER, H.S.M. Introduction to Geometry. Wiley, 1989.

HILBERT, D. Foundations of Geometry. Open Court, 1999.

STEWART, I. Galois theory. London: Chapman and Hall, 1989.

ALEKSEEV, V. B. Abel’s Theorem in Problems and Solutions. Kluwer, 2004.

ARNOLD, V. I. Ordinary Differential Equations. Berlin: Springer, 1992.

PALIS, J. a de MELO, W. Geometric Theory of Dynamical Systems. Berlin: Springer, 2012.

PEITGEN, H.-O., JURGENS, H. a SAUPE, D. Chaos and Fractals. Springer, 2004.

MANDELBROT, B. Fractal Geometry of Nature. Times Books, 1982.

Requirements to the exam -

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (08.10.2020)

Examination from the given literature, and/or solutions to assigned problems.

Syllabus -

Last update: prof. RNDr. Naďa Vondrová, Ph.D. (08.10.2020)

We present some topics with selected basic literature. It will be supplemented according to the agreement between the teacher and the student.

A. Analysis of classical mathematical texts (the student is required to master the mathematical discipline from which the relevant classical text will be selected, to the extent sufficient for understanding and interpretation of the text)

B. Differential calculus and difference equations

C. Axiomatic construction of geometry

D. Galois theory

E. Geometric theory of dynamical systems

F. Fractal geometry