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doc. RNDr. Petr Hliněný, Ph.D. (KTP FI MU)

lecture 2, class exercises 0, select another -,  cze čeština

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Course objectives. This course is focused on understanding basic mathematical concepts necessary for describing program semantics and formalization of the relationship between intuitive program constructs and their mathematical meaning. This is essential for building up a set of basic concepts and formalisms needed for other theoretical courses in computer science. At the end of this course the students should: know the basic notions of discrete mathematics and of propositional logic; understand the logical structure of mathematical statements and mathematical proofs; be able to precisely formulate their claims, algorithms, and relevant proofs; and apply acquired knowledge in other CS courses as well as in practice later on.

doc. RNDr. Petr Hliněný, Ph.D. (KTP FI MU)

lecture 2, class exercises 1, select another -,  eng angličtina

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Course objectives. This is a standard course in graph theory. Basic concepts, graph properties (with simplified proofs), formulations of usual graph problems, and abstract-level algorithms for their solving, are presented. Although the content of this course is targetted at CS students, it is accessible also to others.
At the end of the course, successful students shall understand in depth and tell all the basic terms of graph theory; be able to reproduce the proofs of some fundamental statements on graphs; be able to solve new simple problems; and be ready to apply this knowledge in (especially) computer science applications.

Prerequisites. Basic mathematics, sets, relations, induction (roughly corresponding to the mathematical parts of IB000).

doc. RNDr. Petr Hliněný, Ph.D. (KTP FI MU)

lecture 2, class exercises 1, select another -,  eng angličtina

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Course objectives. The purpose of this subject is to introduce students to the area of structural graph theory and its applications. Basic principles underlying this theory and algorithmic applications are surveyed. A prominent role is given to "width" parameters of graphs, like tree-width or branch-width or rank-width.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of structural graph theory and of graph minors including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.

Prerequisites. Graph theory MA010. Some knowledge of algorithmic complexity and of predicate logic is welcome.

doc. RNDr. Petr Hliněný, Ph.D. (KTP FI MU)

lecture 2, class exercises 1, select another -,  eng angličtina

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Course objectives. This subject presents students with basic types of optimization tasks (e.g., combinatorial, linear, and integer optimization), and teaches the most common solution methods. The main focus is on explaining and understanding (not memorizing!) the presented solution methods, including their thorough mathematical background, so that the students would be able to combine these methods with other approaches in solving nonstandard optimization problems. At the end of the course students should be able to: understand and explain the network-flow algorithm, the simplex method, and the branch-and-bound algorithm; formulate suitable and sound mathematical models of practical optimization problems; and use available tools to solve these problems.

Prerequisites. Mathematical knowledge on course levels of basic linear algebra (vectors, matrices, linear equations) and discrete mathematics (relations, graphs). Introductory knowledge of topology is also welcome.

doc. RNDr. Petr Hliněný, Ph.D. (KTP FI MU)

lecture 2, class exercises 1, select another -,  eng angličtina

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Course objectives. This subject introduces a mathematician or a theoretical computer scientist into the beauties of the topological graph theory. The lectures survey important results in this area, starting from classical ones like the Kuratowski theorem, through the Four Colour theorem, till recent structural results connected with the Graph Minor project, and the crossing number problem.
In this course the students will learn about some cutting-edge recent development in graph theory. At the end, they should: understand the basic principles of topological graph theory and of graph crossing numbers including algorithmic applications; and be able to continue with some scientific work in this area if they choose to.

Prerequisites. Teorie grafu MA010 (Graph theory). Introductory knowledge of topology is also welcome.

doc. RNDr. Petr Hliněný, Ph.D. (KTP FI MU)

lecture 2, class exercises 1, select another -,  eng angličtina

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Course objectives. The aim of this advanced subject is to introduce students to basics of matroid theory and its connections to combinatorial optimization. Roughly saying, matroids present an algebraic/geometric generalization of graphs, and everybody should know their connection with the greedy algorithm...

Prerequisites. Graph theory MA010, Linear algebra (ANY).