- The Fundamental Theorem of Algebra via Connectedness
A topological proof

- Curvature computations with moving frames
With examples from general relativity.

- A Gentle Introduction to Erasure Codes
A nice application of linear and abstract algebra.

- Why is the Quintic Unsolvable?
An explanation that doesn’t require a semester’s worth of abstract algebra.

- Computing Integer Roots
Generalizing the integer square root algorithm.

- Sampling the Visible Sphere
As cited in *Physically Based Rendering*, Third Edition.

- Computing the Integer Square Root
A proof of correctness and a run-time bound.

- Finding the Most Significant Set Bit of a Word in Constant Time
That is, using a constant number of word operations.

- Primality Testing in Polynomial Time (Ⅱ)
Implementing the AKS algorithm.

- Primality Testing in Polynomial Time (Ⅰ)
A guide to understanding the AKS primality test.

- An Introduction to Primality Testing
With a detailed explanation of the Fermat and Miller-Rabin primality tests.

- A Pair of Counterexamples in Vector Calculus
One for Green's theorem and the other for Fubini's theorem.

- Understanding Evlis Tail Recursion
Proper tail recursion's kissing cousin.

- An Elementary Way to Calculate the Gaussian Integral
Expressed as exercises for a calculus class.

- Parallelizing FLAC Encoding
With example code.

- bfpp
Embed Brainfuck in C++.

- Finding the Longest Palindromic Substring in Linear Time
With a reference Python implementation.

- A Foray into Number Theory with Haskell
How to solve Pell's equation.