Overview

This book is going to teach you how to intercept a missile. Not in the abstract, sanitized way of a textbook-though we'll cover the mathematics rigorously. You're going to learn these concepts the way you would if you were actually there: under pressure, with stakes, and with the growing realization that every equation has consequences. What you'll need: - Basic algebra (variables, equations, letters representing numbers) - A willingness to think in three dimensions - Rusty trigonometry (we'll review what we need) - Curiosity about calculus (no prior experience required) What you'll get: - Vectors that actually point at things you care about - The rocket equation that haunts every spacecraft designer's dreams - Trajectories that arc across continents in thirty minutes - Guidance laws stolen from nature (dragonflies figured this out millions of years ago) - Probability theory that decides how many interceptors to launch-and where - The Kalman filter, the algorithm that guided Apollo astronauts to the Moon and now lives in your smartphone Each chapter advances both the math and the story. You'll meet Captain Sarah Chen, your guide through the technical labyrinth of interception theory. You'll work through 37 problems-some straightforward, some that will make you stare at the ceiling. And by the end, you'll understand-really understand-how to thread a needle moving at fifteen thousand miles per hour with another needle moving just as fast. The mathematics of interception is beautiful. It weaves together geometry, physics, probability, and optimization into an elegant framework for solving what seems impossible. Along the way, you'll encounter ideas dating back to ancient Greece, techniques developed in secret during the Cold War, and approaches that remain classified to this day. We'll stick to the public stuff. Naturally. This isn't a book about war. It's a book about mathematics-the kind that works under pressure, the kind where being wrong isn't just a red mark on a test. Whether you're a student wondering when you'll ever use this stuff, an engineer brushing up on fundamentals, or just someone who wants to understand how the impossible becomes possible, this book is for you. But let's not get ahead of ourselves. Right now, there's a black sedan waiting outside your apartment. The driver won't say who sent him. Your phone is buzzing with a number you don't recognize. The clock is ticking. Are you ready?

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