In this substantive yet accessible book‎,‎ pioneering software designer alexander stepanov and his colleague daniel rose illuminate the principles of generic programming and the mathematical concept of abstraction on which it is based‎,‎ helping you write code that is both simpler and more powerful‎.‎ If you‎'‎re a reasonably proficient programmer who can think logically‎,‎ you have all the background you‎'‎ll need‎.‎ Stepanov and rose introduce the relevant abstract algebra and number theory with exceptional clarity‎.‎ They carefully explain the problems mathematicians first needed to solve‎,‎ and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code‎.‎ To demonstrate the crucial role these mathematical principles play in many modern applications‎,‎ the authors show how to use these results and generalized algorithms to implement a real‎-world public‎-key cryptosystem‎.‎ As you read this book‎,‎ you‎'‎ll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency‎.‎ You‎'‎ll also gain deep insight into the value of mathematics to programming‎-insight that will prove invaluable no matter what programming languages and paradigms you use‎.‎ You will learn about * how to generalize a four thousand‎-year‎-old algorithm‎,‎ demonstrating indispensable lessons about clarity and efficiency * ancient paradoxes‎,‎ beautiful theorems‎,‎ and the productive tension between continuous and discrete * a simple algorithm for finding greatest common divisor ‎(‎gcd‎)‎ and modern abstractions that build on it * powerful mathematical approaches to abstraction * how abstract algebra provides the idea at the heart of generic programming * axioms‎,‎ proofs‎,‎ theories‎,‎ and models‎:‎ using mathematical techniques to organize knowledge about your algorithms and data structures * surprising subtleties of simple programming tasks and what you can learn from them * how practical implementations can exploit theoretical knowledge