Math You Actually Need: A Practical Guide for Programmers
English | March 29, 2026 | ASIN: B0GHZC31KN | 505 pages | Epub | 13.25 MB
Your loop runs in 12 seconds. A single formula drops it to 0.003.This book shows you the exact math that makes code faster - no proofs, no chalkboard lectures, no "you'll need this someday." Every chapter starts with a real programming problem, solves it the obvious (slow) way, then reveals the mathematical insight that makes it 10x to 1,000,000x faster. Every claim is backed by a timed benchmark you can run yourself.What you'll learn:Why your nested loop is secretly O(n²) - and the closed-form formula that replaces it (Chapter 1: Arithmetic Series)How binary search cuts a million-item lookup from 1,000,000 steps to 20 (Chapter 2: Logarithms)The trick that lets databases, caches, and load balancers wrap around cleanly - modular arithmetic (Chapter 4)How to pack four values into a single integer using bitwise operations (Chapter 5)Why password strength is a math problem, not a length problem (Chapter 6: Combinatorics)How to estimate unique visitors in 12 KB of memory instead of gigabytes (Chapter 7: Probability & HyperLogLog)The set theory behind SQL JOINs - and why knowing it makes you write better queries (Chapter 9)How Dijkstra's algorithm finds the shortest path in a network (Chapter 11: Graph Theory)The linear algebra that powers image filters, 3D games, and recommendation engines (Chapter 13)How RSA encryption works - and why factoring large numbers keeps it secure (Chapter 14: Number Theory)Each of the 16 chapters follows the same structure:A real programming problemThe naive (slow) solution - working code you can runThe math insight, explained with intuition - not formulasThe better solution - working code you can runA benchmark proving the differenceAll 130 Python code examples are runnable as-is and available in a companion GitHub repository. The concepts are language-agnostic - if you code in JavaScript, Go, Rust, or Java, the math works the same way.This book is for working programmers, self-taught developers, bootcamp graduates, and anyone preparing for technical interviews. No math degree required. If you can write a for-loop, you can read this book.You don't need more math. You need the right math.
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