Course details

Selected Chapters on Mathematics

MAD Acad. year 2020/2021 Summer semester

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The course extends undergrad mathematical courses. Mathematical thinking is demonstrated together with broadening and deepening knowledge of the areas of mathematics and their connection to applications in computer science is shown. The particular areas are, e.g., logics, proof techniques, decision procedures, formal model theory, lattices, probability, and statistics.

Doctoral state exam topics:

  1. Advanced finite automata methods. 
  2. Automata techniques in decision procedures and verification. 
  3. SAT and SMT techniques.
  4. Proof techniques in predicate and first-order logic.
  5. Logical decision procedures.
  6. Galois connection, abstract interpretation, and applications.
  7. Modal and temporal logics.
  8. Advanced probability theory.
  9. Stochastic process and their analysis.
  10. Probabilistic programming and inference.
  11. Advanced graph algorithms. 
  12. Randomized algorithms.
  13. Process algebras.

Guarantor

Deputy Guarantor

Language of instruction

Czech

Completion

Examination (written+oral)

Time span

26 hrs lectures

Assessment points

100 exam

Department

Lecturer

Subject specific learning outcomes and competences

The ability to formalize and solve problems using mathematical apparatus, in particular proving of theorems, deepening and practicing basic mathematical terms, overview of areas of mathematics with important applications in computer science, especially in those related to the topic of the dissertation.

Generic learning outcomes and competences

Broadening the ability to precisely formalize concepts and use the mathematical apparatus.

Learning objectives

  • Provide PhD students with better knowledge of mathematical methods used in computer science, especially in formal methods, with the focus on the particular topic of the dissertation,
  • Deepen the skills of application of the mathematical apparatus in general.

Prerequisite kwnowledge and skills

Basic notions of relations, sets, propositional and first-order logic, algebra, finite automata.

Syllabus of lectures

  1. Advanced finite automata methods. 
  2. Automata techniques in decision procedures and verification. 
  3. SAT and SMT techniques.
  4. Proof techniques in predicate and first-order logic.
  5. Logical decision procedures.
  6. Galois connection, abstract interpretation, and applications.
  7. Modal and temporal logics.
  8. Advanced probability theory.
  9. Stochastic process and their analysis.
  10. Probabilistic programming and inference.
  11. Advanced graph algorithms. 
  12. Randomized algorithms.
  13. Process algebras.

Progress assessment

An exam at the end of the semester.

Course inclusion in study plans

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