Objectives and outcomes
Students acquire a basic knowledge of discrete mathematics. Gaining a significant knowledge of discrete mathematics will be beneficial for their further education.
Lectures
Introduction to mathematical logic. The concept of statement, operations over statements, truth tables. Introduction to set theory. Set operations, power set. Methods of proof. Relations and graphs. Functions and cardinality of sets. Types of functions. Symbols and formulas concept, the concept of tautology and decidability. Predicate calculus. Symbols, notion of terms and formulas, valid formula. Combinatorics. Basic principles of enumeration, the inclusion-exclusion principle, permutations, combinations, partitions and compositions. Algorithms and recursion. Recurrent equations. The theory of numbers. Theorem about sharing, Euclidean algorithm, prime factorisation, modular numbers, congruencies, Chinese remainder theorem.
Practical classes
Solving problems from the units covered in the lectures.