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ČESKÉ VYSOKÉ UČENÍ TECHNICKÉ V PRAZE
STUDIJNÍ PLÁNY
2022/2023

Mathematics for Informatics

Přihlášení do KOSu pro zápis předmětu Zobrazit rozvrh
Kód Zakončení Kredity Rozsah Jazyk výuky
NIE-MPI Z,ZK 7 3P+2C anglicky
Přednášející:
Francesco Dolce
Cvičící:
Francesco Dolce
Předmět zajišťuje:
katedra aplikované matematiky
Anotace:

The course focuses on selected topics from general algebra with emphasis 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 the demonstration of applications in computer science. The course focuses on clear presentation and argumentation.

Požadavky:

linear algebra, elements of discrete mathematics, elements of calculus

Osnova přednášek:

1. Basic notions of abstract algebra: groupoid, 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. Geometrical interpretation of partial derivatives, tangent spaces.

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

9. Constrained multivariable optimization.

10. Integration of multivariable functions.

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

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

13. Error estimation in numerical algorithms. Numerical differentiation.

Osnova cvičení:

1. Functions, 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.

Cíle studia:

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.

Studijní materiály:

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

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

3. Cheney, E. W. - Kincaid, D. R. Numerical Mathematics and Computing. Cengage Learning, 2007. ISBN 978-0495114758.

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

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

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

Poznámka:

Předmět je ekvivalentní s MI-MPI. Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/MI-MPI/

Další informace:
https://courses.fit.cvut.cz/NIE-MPI
Rozvrh na zimní semestr 2022/2023:
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
Po
místnost TH:A-942
Dolce F.
12:45–15:15
(přednášková par. 1)
Thákurova 7 (FSv-budova A)
místnost TH:A-942
Dolce F.
15:15–17:00
(přednášková par. 1
paralelka 101)

Thákurova 7 (FSv-budova A)
Út
St
Čt

Rozvrh na letní semestr 2022/2023:
Rozvrh není připraven
Předmět je součástí následujících studijních plánů:
Platnost dat k 29. 1. 2023
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/cs/predmet6623906.html