Blog
Occasional Random thoughts from us.
Why Clock Arithmetic Is Actually Mathematics
When you say 9 o'clock plus 5 hours is 2 o'clock, you're doing the same arithmetic mathematicians study as cyclic groups. Here is how clocks, calendars, angles and music all wrap around.
Alan Turing and the Turing Machine: A Cornerstone of Computer Science
Alan Turing, a name synonymous with the birth of computer science, left an indelible mark on the 20th century. His conceptualization of the Turing…
The Mathematics of Modular Arithmetic
What is the last digit of 3^100? You can find it in your head with modular arithmetic. Here are the rules of congruences, inverses and the Chinese remainder theorem, plus where they protect your data.
The Mathematics Every Software Engineer Actually Needs
Not calculus proofs. Logarithms, modular arithmetic, Boolean logic, probability and percentiles show up in everyday engineering. Here are the eight areas that pay off most, with the numbers to prove it.
The Mathematics Behind Search Algorithms
Binary search finds one item among a billion in 30 steps, yet a bug in it went unnoticed in Java for about nine years. Here is the math of linear search, binary search, hashing, B-trees and text search.
Mastering Truth Tables: The bedrock of logical arguments
In the realm of mathematics, logic serves as the backbone of reasoning and deduction. Among the fundamental tools in logic, truth tables stand out as a…
The Mathematics of Algorithms
Algorithms are named after a 9th-century mathematician, and their study is pure math: invariants prove them correct, recurrences measure their speed, and P vs NP asks what they can never do efficiently.
Why Every Programmer Should Understand Big-O Notation
Sorting a million items takes 0.02 seconds with one algorithm and about 17 minutes with another. Here is what Big-O notation measures, how to read it, and the real bug that made a hit game load for minutes.
Random Numbers Aren't Really Random
Computers can't flip coins, so most "random" numbers are calculated. That's why one company photographs a wall of lava lamps, and why a two-line code change once left thousands of encryption keys guessable.
Pseudo-Random Numbers Explained
A one-line formula with a remainder can produce millions of random-looking numbers. Here is how linear congruential generators, the Mersenne Twister and modern PRNGs work, and the famous generator whose numbers fell into 15 planes.
How Computers Calculate Trigonometric Functions
There's no sine table inside your calculator. Instead, it uses polynomials, angle symmetries, or a clever shift-and-add trick invented for a 1950s bomber. Here is how sin, cos and tan are really computed.
How Computers Actually Calculate Square Roots
A Babylonian method from nearly 4,000 years ago doubles the correct digits with every step, and it's still at the heart of how software computes √x. Here is how it works, plus the digit-by-digit method chips use.