Mathematics for Informatics
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
MIE-MPI | Z,ZK | 7 | 3+2 |
- Lecturer:
- Martin Holeňa (gar.), Jitka Hanousková, Karel Klouda
- Tutor:
- Jitka Hanousková, Karel Klouda
- Supervisor:
- Department of Computer Science
- Synopsis:
-
Students will master advanced topics from various fields of mathematics and learn mathematical methods that are useful in applications in modern informatics.
- Requirements:
- Syllabus of lectures:
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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.
- Syllabus of tutorials:
- Study Objective:
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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.
- Study materials:
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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.
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
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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
Mon Tue Fri Thu Fri - The course is a part of the following study plans:
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- Computer Security, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (compulsory course in the program)
- Design of Digital Systems, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (compulsory course in the program)
- Computer Security, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (compulsory course in the program)
- System Programming, in English, Version for Students, who Enrolled in 2010 and 2011 (compulsory course in the program)
- Computer Science, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (compulsory course in the program)
- Information Systems and Management, in English, Version for Students, Succeeding in 2010 and 2011 (compulsory course in the program)
- Software Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (compulsory course in the program)
- Web Engineering, Presented in English, Version for Students, who Enrolled in 2010 and 2011 (compulsory course in the program)
- Knowledge Engineering, Presented in English, Version for Students, Succeeding in 2010 and 2011 (compulsory course in the program)
- Master Informatics, Presented in English - Version for Students who Enrolled in 2010 (compulsory course in the program)
- Master Informatics, Presented in English - Version for Students who Enrolled in 2011 (compulsory course in the program)
- Master Informatics, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Computer Security, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- System Programming, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Computer Science, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Information Systems and Management, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Software Engineering, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Web Engineering, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Knowledge Engineering, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Design of Digital Systems, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)
- Computer Systems and Networks, Presented in English - Version for Students who Enrolled in 2012 (compulsory course in the program)