Discretica

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.

6 min read

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.

7 min read

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.

6 min read

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.

7 min read

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.

7 min read

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.

6 min read

Set Theory Basics

Membership, subsets, union, intersection and complement, Venn diagram intuition, and cardinality, explained from the ground up for CS students.

6 min read

Modular Arithmetic Explained

Congruence, the mod operation, the arithmetic properties that make it work, and applications from clock time to hashing and cryptography.

7 min read

Graph Theory Basics

Vertices and edges, degree and the handshaking lemma, walks, paths and cycles, connectivity, and trees, explained from the ground up.

7 min read

Logic Connectives and Quantifiers

The five connectives and their truth conditions, precedence rules, the universal and existential quantifiers, and how to negate them.

7 min read

Recurrence Relations Explained

Define, unroll, and solve recurrence relations, including linear homogeneous ones with constant coefficients via the characteristic equation.

6 min read

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.

6 min read

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.

6 min read

Number Bases and Binary Conversion

Positional notation, binary, octal and hexadecimal, the conversion algorithms in both directions, and the basics of two's complement.

6 min read