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Programming is the art of transforming thought into code to accomplish a desired goal. This book seeks to improve that process by exploring the mathematics often present under the surface, if not out in the open. The topics discussed in this book are a condensed version of the mathematics required of most undergraduate computer science majors. They span foundational notions from set theory through discrete mathematics to linear algebra (essential for modern AI) to calculus. At all times, the book presents a balance between the math and the way programmers use it via examples in Python, C, and other languages where appropriate. Often, the code examples are directly relevant to everyday coding problems. While it’s possible to be a good coder without a solid knowledge of mathematics, I argue that such knowledge will make you an even better coder. Mathematics is the second system devised by humans for encoding and manipulating patterns. Language is the first. Programming is yet another such system, arguably the third. Mathematics and programming are interdependent; skills learned in one domain transfer to the other. Logical thinking, problem-solving, and abstract reasoning are fundamental to both. As a coder, you will eventually encounter algorithms and data structures requiring you to have a solid mathematical foundation in order to understand them well. Indeed, for many decades, computer science was part of the mathematics department. Theoretical computer science remains to this day a thoroughly mathematical enterprise. It has never been my experience that knowledge gained is wasted. Everything I’ve learned, academically speaking, has been of use to me at some point, even if years or decades later, when suddenly applicable in a domain perhaps far removed from where I first learned it. But of all those concepts, the mathematical ones have proven the most helpful. By the end of the book, I hope you’ll agree.