Algebra and Calculus in Applications

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

We illustrate methods based on combination of (CONtinuous) calculus and discrete (disCRETE) structures, so

calles concrete mathematics. Theorems are motivated by problems from informatics and they are illustrated on problems

from informatics.

Requirements:

Syllabus of lectures:

1. Difference calculus on sequences

2. Matrix calculus for solving of systems of linear difference equations

3. Words without forbidden subchains

4. Generating functions: ordinary, exponential, Dirichlet’s function

5. Methods of use of generating functions

6. Applications of generating functions to difference equations

7. Hilbert’s metric and its applications to linear maps

8. Joint spectral radius

9. Nonlinear recurrence relations

10. Asymptotic growth of solutions of recurrence relations

Syllabus of tutorials:

Study Objective:

Study materials:

Povinná literatura:

[1] P. Cull, M. Flahive, R. Robson, Difference Equations: From Rabbits to Chaos, Springer Verlag (2005)

[2] R. L. Graham; D. E. Knuth; O. Patashnik, Concrete Mathematics. A foundation for computer science, 27. dotisk

(2013)

Doporučená literatura:

[3] J. Jungers: The Joint Spectral Radius: Theory and Applications, Springer Verlag (2009)

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Matematické inženýrství - Matematická informatika (PS)