The Algebra of Code, Volume 1

A hands-on, exercise-driven guide that teaches functional programming and real mathematics — set theory, abstract algebra, and category theory — together, using more than 500 short coding exercises in F#.

Category theory, abstract algebra, and set theory aren't just academic abstractions — they're the mathematical backbone of functional programming patterns that working developers use every day. The Algebra of Code makes those connections explicit, using the F# language and more than 500 short exercises to build fluency in both the math and the code simultaneously.

Paul Orland — an F# Software Foundation–recognized expert and author of Math for Programmers — starts with core functional programming concepts (functions, types, recursion, composition) and introduces the mathematical structures behind them: sets, groups, monoids, functors, and eventually categories. Each concept arrives with code you can run, exercises you can solve, and explanations that connect the abstraction to concrete software design decisions. The result is a book where the math makes you a better programmer and the programming makes you a better mathematical thinker.