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### Terms for 2017

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#### September, 14

Open Day

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# Mathematical Methods 2

The aim of this subject is to teach students to use mathematical tools for their further study.  This subject is focussed on the various ways of working with ordered n-tuples.

## What are you going to learn

1. Mathematical logic - Tautology, derivation rules (modus ponens, generalization rule), a mathematical proof.
2. Theory of relations - Binary relation, (partial) order, equivalence, equivalence classes.
3. Graph and its representation - Basic concepts (node, edge, subgraph, sequence, circle, path, …), (un)directed graph, graph isomorphism.
4. Eulerian graph and trees - Eulerian graph, eulerian cycle, threes.
5. Vector space - Vector, operations with vectors, linear independence, basis, rank space.
6. Matrices - Matrix (introduced as a rectangular table of cells), rank of a matrix, transpose matrix, operations with matrices.
7. System of linear equatios - General theorems on solvability, using matrices to solve systems of linear equations.
8. Determinant of a matrix - Square matrix, inverse matrix, determinant of a matrix.
9. Linear programming - Types of problems, formulation of a mathematical model, basic concepts, graphical solution, the possibility of termination, interpretation.
10. Simplex method - Single-phase and two-phase simplex method, the interpretation of single-phase methods (using simplex table), test optimization; relationship between simplex method and matrix numbers.
11. Analytic geometry - Geometric interpretation of algebraic concepts and their use in practice.
12. Applications - Examples of the use in practice.

## How the course is organized

### Full time study

The course consists of 12 lectures and 12 workshops, each lasting 1,5 hours.

### Part time study

The course consists of 4 tutorials, each lasting 3 hours.

## Recommended literature

• MATOUŠEK, J., NEŠETŘIL, J.: Invitation to discrete mathematics, Ofxord Univerzity Press, 2009.
• DIESTEL, R.: Graph Theory, 4th edition, Springer, 2012.
• CHENEY, W., KINCAID, D.: Linear Algebra: Theory and Applications, Jones & Bartlett Publishers, 2010.
• MATOUŠEK, J., GÄRTNER, B.: Understanding and Using Linear Programming, Springer, 2007.