Mathematics for Informatics

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Code Completion Credits Range Language
NI-MPI Z,ZK 7 3P+2C Czech
Garant předmětu:
Štěpán Starosta
Jan Spěvák, Štěpán Starosta
Michal Kupsa, Pavel Paták, Jan Spěvák, Štěpán Starosta, Jakub Šístek
Department of Applied Mathematics

The course comprises topics from general algebra with focus on finite structures used in computer science. It includes topics from multi-variate analysis, smooth optimization and multi-variate integration. The third large topic is computer arithmetics and number representation in a computer along with error manipulation. The last topic includes selected numerical algorithm and their stability analysis. The topics are completed with demonstration of applications in computer science. The course focuses on clear presentation and argumentation.


linear algebra, elements of discrete mathematics, elements of calculus

Syllabus of lectures:

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

2. Cyclic and finite groups and their properties.

3. Rings and fields.

4. (2) Finite fields. Applications in cryptography.

5. Multivariate calculus: partial derivative, gradient, and Hessian.

6. Unconstrained extremas of multivariate functions.

7. (2) Constrained extremas of multivariate functions.

8. Mutlivariate integral.

9. Representing numbers in computers, floating point arithmetic and relevant errors.

10. (2) Solving systems of linear equations, finding eigenvalues and stability of numerical algorithms.

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. Constrained multivariable optimization

11. Constrained multivariable optimization with inequality constraints

12. Multivariable integration

Study Objective:

The course covers selected topics from general algebra and number theory with

emphasis on modular arithmetics and finite structures, computer arithmetics and representation of numbers,

multivariable calculus and continuous optimization. It provides some examples of informatics applications of


Study materials:

1. Dummit, D. S. - Foote, R. M. Abstract Algebra. Wiley, 2003. ISBN 978-0471433347.

2. Mareš, J. Algebra. Úvod do obecné algebry. Vydavatelství ČVUT, 1999. ISBN 978-8001019108.

3. Paar, Ch. - Pelzl, J. Understanding Cryptography. Springer, 2010. ISBN 978-3642041006.

4. Cheney, E. W. - Kincaid, D. R. Numerical Mathematics and Computing. Cengage Learning, 2007. ISBN


5. Higham, N. J. Accuracy and Stability of Numerical Algorithms. SIAM, 2002. ISBN 978-0898715217.

6. Marsden, J. - Weinstein, A. Calculus III. Springer, 1998. ISBN 978-0387909851.

Further information:
Time-table for winter semester 2024/2025:
Time-table is not available yet
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-04-23
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