Mathematics for Cybernetics - Selected Topics

Lecturer:

Pavel Pták (gar.)

Tutor:

Pavel Pták (gar.)

Supervisor:

Department of Cybernetics

Synopsis:

Overview of modern mathematics. Ordering, lattices, Boolean algebras,

representations. Topological spaces. Metric spaces, completeness,

fixed-point theorem with applications, fractals. Linear spaces,

constructions with linear spaces. Systems of linear equations, spectral

theory. Matrix calculus, matrix inequalities. Least squares and singular

value decomposition. Tensor product. Elementary theory of Hilbert spaces.

Introduction to category theory.

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

E. Artin Geometric Algebra Paperback, Wiley-Interscience; Reprint edition

(February 1988)

Walter Rudin Real and Complex Analysis (Higher Mathematics Series) ,

McGraw-Hill Science/Engineering/Math; 3 edition (May 1, 1986)

Note:

Time-table for winter semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri
Thu	roomKN:G-205 Pták P. 14:30–16:00 (lecture parallel1) Karlovo nám. Laboratoř PC
Fri

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)
• Doctoral studies, structured daily studies (compulsory elective course)
• Doctoral studies, structured combined studies (compulsory elective course)