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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Mathematics for Informatics

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Code Completion Credits Range Language
MIE-MPI Z,ZK 7 3+2
Lecturer:
Štěpán Starosta (guarantor), Maria Saumell Mendiola
Tutor:
Štěpán Starosta (guarantor), Maria Saumell Mendiola
Supervisor:
Department of Applied Mathematics
Synopsis:

The course focuses on selected topics from general algebra, number theory, numerical mathematics, multivariate calculus and continuous optimization. The topics are selected to emphasize the connection with computer science. Some examples of applications of mathematics to computer sciences are given: cryptography, discrete Fourier transform and fuzzy control.

Requirements:
Syllabus of lectures:

1. Basic notions of abstract algebra: grupoid, monoid, group, homomorphism.

2. Cyclic and finite groups and their properties.

3. Discrete logarithm problem in various groups and its applications in cryptography.

4. Rings and fields and their properties.

5. Modular arithmetics and equations in finite fields.

6. Representing numbers in computers, floating point arithmetics.

7. Solving systems of linear equations, finding eigenvalues and stability of numerical algorithms.

8. Multivariable calculus: partial derivative and gradient.

9. Continuous optimization methods. Selected optimization problems in informatics.

10. Constrained multivariable optimization.

11. Integration of multivariable functions.

12. Discrete Fourier transform.

13. Mathematics of uncertainty: fuzzy set theory

Syllabus of tutorials:

1. Fucntions, derivative, polynomials

2. Grupoid, semigroup, monoid, group

3. Cyclic group, generators

4. Homomorphism, discrete logarithm, fields and rings

5. Finite fields

6. Discrete exponenciation, CRT, discrete logarithm

7. Machine numbers.

8. Multivariable functions, partial derivatives

9. Multivariable optimization

10. Multivariable optimization with constraints

11. Multivariable integration

12. Fuzzy sets

Study Objective:

Mathematics as a language for description of the world is a key discipline for an informatics engineer. The aim of this module is introduce students to the relevant parts of modern mathematics that form the theoretical background of many informatics disciplines and to develop students in general problem solving.

Study materials:

1. Schroeder, R. M.: ''Number Theory in Science and Communication'', Springer, Berlin, 2006.

2. Graham, R., Knuth, D., Patashnik, O.: ''Concrete Mathematics: A Foundation for Computer Science'', Addison-Wesley, Reading, Mass., 1989.

Note:
Further information:
https://courses.fit.cvut.cz/MIE-MPI/
Time-table for winter semester 2018/2019:
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
roomTH:A-1242
Saumell Mendiola M.
07:30–10:00
(lecture parallel1)
Thákurova 7 (FSv-budova A)
roomTH:A-1242
Saumell Mendiola M.
10:00–11:45
(lecture parallel1
parallel nr.101)

Thákurova 7 (FSv-budova A)
Thu
Fri
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-04-18
For updated information see http://bilakniha.cvut.cz/en/predmet1439806.html