Mathematics for Informatics

Garant předmětu:

Přednášející:

Cvičící:

Předmět zajišťuje:

katedra aplikované matematiky

Anotace:

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.

Požadavky:

linear algebra, elements of discrete mathematics, elements of calculus

Osnova přednášek:

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.

Osnova cvičení:

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

Cíle studia:

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

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

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

mathematics.

Studijní materiály:

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.

Poznámka:

Information about the course and courseware are available at https://courses.fit.cvut.cz/MIE-MPI/

Další informace:

https://courses.fit.cvut.cz/MIE-MPI/

Pro tento předmět se rozvrh nepřipravuje

Předmět je součástí následujících studijních plánů: