- 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.
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