Fred Akalin

Notes on math, tech, and everything in between

I sometimes get inspired to write about things I learn. When I do, I put it here.

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The Fundamental Theorem of Algebra via Connectedness January 3, 2021
A topological proof.
Curvature computations with moving frames March 22, 2018
With examples from general relativity.
A Gentle Introduction to Erasure Codes November 30, 2017
A nice application of linear and abstract algebra.
Why is the Quintic Unsolvable? September 26, 2016
An explanation that doesn’t require a semester’s worth of abstract algebra.
Computing Integer Roots January 10, 2016
Generalizing the integer square root algorithm.
Sampling the Visible Sphere August 26, 2015
As cited in Physically Based Rendering, Third Edition.
Computing the Integer Square Root December 9, 2014
A proof of correctness and a run-time bound.
Finding the Most Significant Set Bit of a Word in Constant Time July 3, 2014
That is, using a constant number of word operations.
Primality Testing in Polynomial Time (Ⅱ) December 29, 2012
Implementing the AKS algorithm.
Primality Testing in Polynomial Time (Ⅰ) August 6, 2012
A guide to understanding the AKS primality test.
An Introduction to Primality Testing July 8, 2012
With a detailed explanation of the Fermat and Miller-Rabin primality tests.
A Pair of Counterexamples in Vector Calculus November 27, 2011
One for Green's theorem and the other for Fubini's theorem.
Understanding Evlis Tail Recursion October 28, 2011
Proper tail recursion's kissing cousin.
An Elementary Way to Calculate the Gaussian Integral January 6, 2011
Expressed as exercises for a calculus class.
Parallelizing FLAC Encoding May 5, 2008
With example code.
bfpp April 23, 2008
Embed Brainfuck in C++.
Finding the Longest Palindromic Substring in Linear Time November 28, 2007
With a reference Python implementation.
A Foray into Number Theory with Haskell July 6, 2007
How to solve Pell's equation.