Discrete Mathematics
- Counting Principles: Principles of sum a and product, arrangement, permutation, combination, combination with repetition, the reflection principle
- Inclusion and Exclusion: Theorem of the principle of inclusion and exclusion, applications in counting, generalization of the principle
- Generating Functions: The generating function of a given sequence, the application of generating functions in counting problems, the convolution of sequences
- Logic: Introduction, propositional logic, semantics and model theory, proof theory
- First-Order Logic: Open statements, quantifiers, model theory, proof theory, soundness, completeness
- Properties of Integers: The axiomatic system of integers, mathematical induction, generalizations, inductive definitions, applications
- Elementary Number Theory: Divisibility, greatest common divisor, division algorithm, the fundamental theorem of arithmetics
- Residues: The complete system of residues, the residues system of residues, Eulers phi function, Lagranges theorem, Euler-Fermats theorem, Chinese residues
- Relations and Functions: One-to-one functions, images, onto functions, restriction
- Partially Ordered Sets: Reflexive, symmetric, anti-symmetric, and transitive relations, equivalence relations, commutative and associative relations, minimal and maximal, lower and upper bounds, supremums, infimums, lattice
- Recurrences: Recursive equations, solving linear homogeneous recursive equations
- Nonhomogeneous Recursive Equations: Solution, using generating functions, system of equations
- Graph Theory: Undirected and directed graphs, walks, paths, circuits, cycles, Eulerian graphs
- Hamiltonian and Planar Graphs: Definitions, Theorems
- Graph coloring: Chromatic polynomials, chromatic numbers, decomposition theorem