Free online courseDiscrete Math

Course Description

Discrete mathematics is where careful thinking becomes a skill you can apply everywhere: in calculus-style reasoning, in computer science, in data and probability, and in any subject that depends on clear definitions and airtight arguments. This free online course is designed to help you move from intuitive math to rigorous math, building confidence with the language and tools used to write, read, and test mathematical claims.

You will start by learning how mathematicians describe collections and structure: sets, notation, the empty set, Cartesian products, and relations. From there, the course turns those building blocks into the idea of a function, showing how domain and range interact and how to decide whether a rule truly behaves like a function. Along the way, you will practice translating everyday statements into precise mathematical form, a key step toward stronger problem solving.

A major theme is logic. You will learn to analyze statements with truth tables, recognize equivalence, and work comfortably with conditionals, contrapositives, and biconditionals. You will also develop fluency with quantifiers and predicates, including how to negate complex claims correctly. These tools prepare you to judge arguments for validity and to avoid common traps such as confusing a statement with its converse or mishandling vacuous truth.

Once the logic is in place, the focus shifts to proof. You will see how definitions drive reasoning and how different strategies fit different problems: direct proof, counterexamples, proof by cases, contradiction, and contrapositive. Topics like parity, divisibility, rational numbers, modular arithmetic, and classic results about primes provide concrete practice so that proof writing becomes structured rather than mysterious.

The course then broadens into sequences and induction, including strong induction and recursion, with memorable examples that connect symbolic rules to patterns over time. Finally, you will build counting and probability intuition through permutations, combinations, conditional probability, Bayes’ theorem, and an introduction to Markov chains. You will also get a first look at graph theory and linear programming, tying discrete thinking to real decision-making and network-style problems.

By the end, you will be able to define objects precisely, translate words into symbols, test logical forms, and construct proofs that stand up to scrutiny—skills that strengthen performance in higher math and open doors to more advanced topics in computing and quantitative fields.