Abstract algebra

Notes on the structures that underlie modern mathematics — groups, rings, fields, and beyond. Covers foundational concepts like homomorphisms, quotient groups, ideals, and Galois theory, with an emphasis on building intuition alongside rigor. Each note breaks down one idea at a time, connecting abstract definitions to concrete examples. Written for anyone willing to think carefully about why the math works, not just how to apply it.

Curry’s Paradox and Löb’s Theorem: When Logic Becomes Magic

Imagine a statement: "If this statement is true, then mermaids exist."

Groups, Rings, and Fields: The Building Blocks of Abstract Algebra

Group Theory Fundamentals: The Hidden Structure Behind All of Mathematics

The idea of a group is surprisingly simple. A group is a set of objects and an operation with four…

Homotopy Type Theory (HoTT): The Mathematics of Paths and Types

Back when the GenAI hype was just getting started, I ran an experiment: an entire video script written by ChatGPT,…

1 2