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 aboutHow to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiencyAncient paradoxes, beautiful theorems, and the productive tension between continuous and discreteA simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on itPowerful mathematical approaches to abstractionHow abstract algebra provides the idea at the heart of generic programmingAxioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structuresSurprising subtleties of simple programming tasks and what you can learn from themHow practical implementations can exploit theoretical knowledge

    The rapid maturation of PHP has created a skeptical population of users from more traditional enterprise languages who question the readiness and ability of PHP to scale, as well as a large population of PHP developers without formal computer science backgrounds who have learned through the hands-on experimentation while developing small and midsize applications in PHP. While there are many books on learning PHP and developing small applications with it, there is a serious lack of information on scaling PHP for large-scale, business-critical systems. Schlossnagle's Advanced PHP Programming fills that void, demonstrating that PHP is ready for enterprise Web applications by showing the reader how to develop PHP-based applications for maximum performance, stability, and extensibility.