Discrete structures are a core subject presenting the necessary mathematical topics that are needed to build on in computer science and engineering. It is highly probable that most of the topics will be new to a typical high school graduate, and also the familiar concepts will be studied in a new setting.
Topics include:
- Propositional logic: reasoning, formal proofs.
- Predicate logic: basics.
- Set theory: naive approach, basics of counting.
- Functions: composition of functions.
- Relations: equivalence relations, ordered structures.
- Number theory: basics, Diophantine equations, Euler function, congruence relations and modular arithmetic.
- Permutations: a primer of an algebraic structure.
- Graph theory: basics, walks, paths and connectedness, bipartite graphs, trees, Euler and Hamilton graphs, coloring.
Coursework consists of homework assignments, midterms and a final exam. Homeworks are distributed on a weekly basis and their load is uniform throughout the course.
