Discrete Mathematics

Most K-12 mathematics education in school is focused on continuous mathematics, with geometrical shapes that form perfectly connected curves and functions that can be applied all across the real numbers. But what about phenomena that are fundamentally discrete, that involve counting distinct objects with separate numbers rather than on a continuum? Discrete mathematics is a one-semester survey course that investigates these phenomena.

Students will learn about sets, logic, number theory and the proof techniques of modern mathematics, including divisibility and modular arithmetic. We will study combinatorics in detail, including combinatorial proofs, the pigeonhole principle, in the inclusion-exclusion principle, Latin squares, Sterling numbers, and an analysis of finite geometric structures. We extensively study graph theory with a detour into polyhedra, and finish the class with an investigation of formal models of computation and formal grammars such as finite automata and pushdown automata.

Discrete Mathematics Unit Outline

Unit 1: Number Theory

Unit 2: Combinatorics

Unit 3: Occupancy and Fixed Point Property

Unit 4: Graph Theory

Unit 5: Models of Computation