Discrete Math for CS

by Mizel Cluett

A complete 30-class course bridging discrete mathematics, formal proof, and Java programming. Every concept is presented with rigorous proofs and runnable Java code.

Course Modules

Module 1

Integers, Definitions & Proofs

Parity, divisibility, primes, GCD, direct proof and counterexample.

Module 2

Remainders & Modular Arithmetic

Quotient-remainder theorem, congruences, CRT, prime factorization.

Module 3

Logic, Quantifiers & Programs

Propositional logic, implication, quantifiers, Design by Contract.

Module 4

Sets & Data Collections

Set operations, power sets, partitions, De Morgan's laws for sets.

Module 5

Functions, Relations & Mappings

Domains, composition, injection, surjection, equivalence relations.

Module 6

Induction & Recursion

Weak, strong, and structural induction. Recursive definitions.

Module 7

Counting & Finite Reasoning

Counting principles, binomial coefficients, pigeonhole, probability.

Module 8

Algorithms & Correctness

Specifications, loop invariants, Hoare logic, termination proofs.

Module 9

Trees, Complexity & Verification

BSTs, heaps, Big-O, structural induction on trees, formal verification.