Mathematics for Informatics
| Kód | Zakončení | Kredity | Rozsah | Jazyk výuky |
|---|---|---|---|---|
| MIE-MPI | Z,ZK | 7 | 3+2 |
- Přednášející:
- Martin Holeňa (gar.), Jitka Hanousková, Karel Klouda
- Cvičící:
- Jitka Hanousková, Karel Klouda
- Předmět zajišťuje:
- katedra teoretické informatiky
- Anotace:
-
Students will master advanced topics from various fields of mathematics and learn mathematical methods that are useful in applications in modern informatics.
- Požadavky:
- Osnova přednášek:
-
1. [2] Universal algebra: groups, finite groups, Cayley tables, group types, permutation, alternating, cyclic, and symmetry groups, normal subgroups.
2. Finite fields, prime order of field, rings and their properties, integral domain, ideal. Lattices.
3. Introduction to category theory, classes of objects, classes of morphisms and its properties, examples of categories: grupoid, category of all lattices, category of all commutative groups, category of all integral domains, category of all relations. Homomorphisms.
4. Selected problems of graph theory, types of Hamiltonian problems. Algebraic solutions of combinatorial problems, Polya enumeration theorem.
5. Algebra and algorithms (Algorithms for calculations of polynom roots - Newton' method, Lehmer-Schur's method, etc.).
6. Convex sets, convex hull, pure convex set, theorem on partition of convex sets, Minkowski theorem on projection.
7. Selected problems of number theory, quadratic congruence, Gauss algorithms. Special primes - factorial, palindromic, cyclic, Gauss', Eisenstein's primes. Examples of applications.
8. Properties of Fermat primes, Little Fermat Theorem, primality tests, Pépin test, number theory and geometry, constructability of polygons.
9. Selected numerical methods, Lagrange and Hermite interpolation, numerical integration, numerical solution of ordinary differential equations, calculating of eigenvalues of matrices, methods of solving of linear equations systems.
10. Fast algorithms: multiplication, numerical searching of square roots, Fourier transformation, Fermat transformation.
11. Axiomatic systems and their properties, recursive functions, proofs in the axiomatic system, examples of axiomatic systems, Peano's arithmetics, von Neumann's model of numbers.
12. Special logics, multi-valued logics, modal logics, fuzzy logics.
- Osnova cvičení:
- Cíle studia:
-
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.
- Studijní materiály:
-
1. Schroeder, R. M.: ''Number Theory in Science and Communication'', Springer, Berlin, 2006.
2. Křížek, M., Luca, F., Somer, L.: ''17 Lectures on Fermat Numbers: From Number Theory to Geometry'', Springer, New York, 2001.
3. Graham, R., Knuth, D., Patashnik, O.: ''Concrete Mathematics: A Foundation for Computer Science'', Addison-Wesley, Reading, Mass., 1989.
4. Lovász, L.: ''Combinatorial Problems and Exercises'', 2nd Ed., Akademiai Kiadó Budapest and North- Holland, Amsterdam, 1993.
- Poznámka:
-
Rozsah=prednasky+proseminare+cviceni3p+1r+1c, Prednasejici: doc. RNDr. Alena Šolcová Ph.D.
- Rozvrh na zimní semestr 2011/2012:
- Rozvrh není připraven
- Rozvrh na letní semestr 2011/2012:
-
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 Út St Čt Pá - Předmět je součástí následujících studijních plánů:
-
- Computer Security, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Design of Digital Systems, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Computer Systems and Networks, Presented in English, for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- System Programming, in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Computer Science, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Information Systems and Management, in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Software Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Web Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Knowledge Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (povinný předmět programu)
- Master Informatics, Presented in English - Version for Students who Enrolled in 2010 (povinný předmět programu)
- Master Informatics, Presented in English - Version for Students who Enrolled in 2011 (povinný předmět programu)
- Master Informatics, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Computer Security, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- System Programming, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Computer Science, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Information Systems and Management, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Software Engineering, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Web Engineering, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Knowledge Engineering, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Design of Digital Systems, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)
- Computer Systems and Networks, Presented in English - Version for Students who Enrolled in 2012 (povinný předmět programu)