Discrete Mathematics
- Introduction to the course, preliminaries
- Fundamental principles of counting
- The principle of inclusion and exclusion
- Derangements, Rook polynomials, Arrangements with forbidden positions
- Generating functions
- Partitions of integers, the exponential generating function
- Basics of logic, logical equivalence
- Logical implication: rules of inference, quantifiers
- Mathematical induction, the well-ordering principle
- Relations, functions, Stirling numbers of second kind
- Composition and inverse of functions, complexity analysis
- Partial order relations, lattice
- Equivalence relations, partitioning
- Homogeneous recursive relations, first order, second order
- Non-homogeneous recursive relations, the method of generating functions
- Introduction to graph theory