Learn Mathematics
Original tutorials with fully solved examples, key formulas and practice questions. Each one links to the calculators that let you check your own working.
Gaussian Elimination and RREF: A Step-by-Step Guide
Learn Gaussian elimination, row echelon form and reduced row echelon form with a fully solved example, the rank connection and practice questions.
The Extended Euclidean Algorithm Explained
Understand the Euclidean algorithm, Bezout coefficients and modular inverses with a full back-substitution example, formulas and practice questions.
How RSA Works: A Step-by-Step Worked Example
A clear walk-through of RSA key generation, encryption and decryption with small numbers, the maths behind why it works, and practice questions.
Modular Arithmetic for Beginners
A beginner guide to congruences, remainders, modular inverses and solving ax = b (mod m), with a worked example and practice questions.
The Rank–Nullity Theorem and the Four Fundamental Subspaces
Understand column space, row space, null space and the rank-nullity theorem with a fully worked 3x4 example and practice questions.
The Chinese Remainder Theorem Explained with Examples
Learn how the Chinese Remainder Theorem solves systems of congruences, how to merge equations step by step, and when no solution exists.
How to use these tutorials
Read the explanation, then work through the solved example with pen and paper before looking at the steps. Attempt the practice questions, and check your answers with the matching calculator: it shows every intermediate step, so you can find exactly where a hand calculation went wrong.