Mathematics

• Shannon's Information Theory from First Principles: Entropy, Channel Capacity, and the Fundamental Limits of Communication · 2025-03-05

  Build Shannon's information theory from the ground up: entropy as a measure of uncertainty, source coding theorem, channel capacity, and the noisy-channel coding theorem that established the theoretical limits of reliable communication.

• Floating Point: How Computers Represent Real Numbers · 2023-02-08

  A deep exploration of IEEE 754 floating point representation, the mathematics behind binary fractions, precision limits, and the subtle bugs that can arise when working with real numbers in code.