Study guides
Discrete Math Guides
Free, in-depth walkthroughs of the topics that trip up computer science students most: writing proofs, mathematical induction, truth tables, and counting. Every guide is worked example first, jargon second, and always free to read.
How to Write Your First Proof
A beginner-friendly walkthrough of what a proof is, how to structure a direct proof, and a fully worked example you can imitate.
Proof by Induction, Step by Step
Learn mathematical induction the reliable way: the base case, the inductive hypothesis, the inductive step, and a fully worked summation example.
Truth Tables Explained
Understand logical connectives, build truth tables row by row, and use them to test tautologies, contradictions, equivalence, and De Morgan's laws.
Combinatorics Counting Rules
Master the sum and product rules, tell permutations from combinations, decide when order matters, and apply the pigeonhole principle with worked examples.
Discrete Math for CS Students: A Study Plan
A practical module order, weekly plan, and exam-prep routine for getting through a discrete mathematics course without falling behind.
Proof by Contradiction Explained
The logic behind indirect proof, the classic proof that the square root of 2 is irrational, and guidance on when to reach for contradiction.
Set Theory Basics
Membership, subsets, union, intersection and complement, Venn diagram intuition, and cardinality, explained from the ground up for CS students.
Modular Arithmetic Explained
Congruence, the mod operation, the arithmetic properties that make it work, and applications from clock time to hashing and cryptography.
Graph Theory Basics
Vertices and edges, degree and the handshaking lemma, walks, paths and cycles, connectivity, and trees, explained from the ground up.
Logic Connectives and Quantifiers
The five connectives and their truth conditions, precedence rules, the universal and existential quantifiers, and how to negate them.
Recurrence Relations Explained
Define, unroll, and solve recurrence relations, including linear homogeneous ones with constant coefficients via the characteristic equation.
Pigeonhole Principle Applications
The basic and generalized pigeonhole principle, how to name your pigeons and holes, and airtight proofs that a repeat or collision must occur.
Big-O Notation for Discrete Math
Asymptotic growth from the formal definition: big-O, big-Omega and big-Theta, the common growth classes, and how to compare two functions.
Number Bases and Binary Conversion
Positional notation, binary, octal and hexadecimal, the conversion algorithms in both directions, and the basics of two's complement.