Seminar of Contemporary Mathematics 1

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

This seminar provides a different approach to those fields of mathematics that are included in curriculum but also to those that are not part of basic courses of mathematics.

Requirements:

Knowledge of mathematical analysis, linear and general algebra in the scope of bachelor's degree programme Mathematical Modelling at FNSPE, CTU in Prague.

Syllabus of lectures:

1. Definition of Eudox' real numbers, 2. Kurzweil integral, 3. Non-standard analysis, 4. Probabilistic methods in combinatorics, 5. Distributional properties of sequences, 6. Groebner basis, 7. Solving differential equations using symmetry methods, 8. On simplicial partitions. This seminar is partially covered by hosting collaborators of Dept of Mathematics.

Syllabus of tutorials:

The subject is a seminar.

This seminar provides a different approach to those fields of mathematics that are included in curriculum but also to those that are not part of basic courses of mathematics.

Study Objective:

Knowledge:

Overview in modern trends in mathematics.

Skills: During working on simple problems and recherche on selected topic, students get acquianted with basis of scientific work.

Study materials:

Presentations of lecturers which are published on web pages of the subject and other study materials are recommended on individual basis according to the selected to pick for home work.

Obligatory:

[1] P.J. Davis, R. Hersh, The mathematical experience, Birkhauser Boston, 1981

Recommended:

[2] M. Aigner, G. M. Ziegler, Proofs from THE BOOK, Springer-Verlag, 2004

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (elective course)
• Aplikované matematicko-stochastické metody (elective course)
• Matematické inženýrství - Matematická fyzika (elective course)
• Matematické inženýrství - Matematická informatika (elective course)
• Matematické inženýrství - Matematické modelování (elective course)
• Mathematical Engineering - Mathematical Physics (elective course)