 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Mathematics for Informatics

Code Completion Credits Range Language
MI-MPI Z,ZK 7 3P+2C Czech
Lecturer:
Štěpán Starosta (guarantor)
Tutor:
Štěpán Starosta (guarantor), Michal Kupsa, Jan Spěvák, František Štampach
Supervisor:
Department of Applied Mathematics
Synopsis:

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.

Requirements:

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. 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. Multivariable calculus: partial derivative and gradient.

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

8. Constrained multivariable optimization.

9. Integration of multivariable functions.

10. Representation of numbers in computers, floating point arithmetics and related errors.

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

12. Error estimation in numerical algorithms. Numerical differentiation.

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

mathematics.

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

978-0495114758.

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.

7. Ross, T. J. Fuzzy Logic with Engineering Applications (3rd Edition). Wiley, 2010. ISBN 978-0470743768.

Note:
Further information:
https://courses.fit.cvut.cz/MI-MPI/
Time-table for winter semester 2019/2020:
 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 roomTK:BSStarosta Š.14:30–16:00(lecture parallel1)DejviceNTK Ballingův sál roomTK:BSStarosta Š.14:30–16:00ODD WEEK(lecture parallel1)DejviceNTK Ballingův sálroomT9:302Starosta Š.16:15–17:45(lecture parallel1parallel nr.101)DejviceNBFIT učebna roomT9:301Štampach F.09:15–10:45(lecture parallel1parallel nr.102)DejviceNBFIT učebnaroomT9:301Štampach F.11:00–12:30(lecture parallel1parallel nr.103)DejviceNBFIT učebnaroomT9:343Kupsa M.12:45–14:15(lecture parallel1parallel nr.105)DejviceNBFIT učebnaroomTH:A-1342Spěvák J.14:30–16:00(lecture parallel1parallel nr.106)Thákurova 7 (FSv-budova A)roomTH:A-1342Spěvák J.16:15–17:45(lecture parallel1parallel nr.107)Thákurova 7 (FSv-budova A) roomT9:343Kupsa M.11:00–12:30(lecture parallel1parallel nr.104)DejviceNBFIT učebna roomTH:A-1242Štampach F.09:15–10:45(lecture parallel1parallel nr.108)Thákurova 7 (FSv-budova A)
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-04-04
For updated information see http://bilakniha.cvut.cz/en/predmet1434606.html