discrete-mathematics
4 free lessons tagged discrete-mathematics across Math. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
Modular Arithmetic: Doing Maths on a Clock
Wrap the number line into a circle and addition and multiplication survive intact while division mostly does not. This lesson builds congruences, shows why you can reduce early to avoid overflow, works through Euclid's algorithm and modular inverses, and explains how a million-digit exponent becomes twenty multiplications.
Graphs: A Language for Relationships
A graph is two sets and an incidence relation, and that austerity is why the same object models build dependencies, social networks, register allocation and road maps. This lesson covers the structural properties worth knowing, the special families that make hard problems easy, and the line where a small change to a question makes it intractable.
Proof and Induction: Covering Infinitely Many Cases
Testing checks the cases you thought of; a proof covers all of them at once, including the ones nobody will ever run. This lesson builds direct proof, contradiction and induction as working tools, shows the two ways induction fails, and connects it to the loop invariants that make a program correct rather than merely untested.
Counting Without Listing
Combinatorics answers how many arrangements exist without producing any of them, which is what makes password strength, hash collisions and search-space size computable at all. This lesson builds the product rule, permutations, combinations, inclusion-exclusion and the pigeonhole principle, then applies them to problems where intuition is reliably wrong.