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Top algebra books mentioned on stackoverflow.com

Hacker's Delight

Henry S. Warren

" "This is the first book that promises to tell the deep, dark secrets of computer arithmetic, and it delivers in spades. It contains every trick I knew plus many, many more. A godsend for library developers, compiler writers, and lovers of elegant hacks, it deserves a spot on your shelf right next to Knuth.""--Josh Bloch" "When I first saw the title, I figured that the book must be either a cookbook for breaking into computers (unlikely) or some sort of compendium of little programming tricks. It's the latter, but it's thorough, almost encyclopedic, in its coverage." "--Guy Steele These are the timesaving techniques relished by computer hackers--those devoted and persistent code developers who seek elegant and efficient ways to build better software. The truth is that much of the computer programmer's job involves a healthy mix of arithmetic and logic. In "Hacker's Delight," veteran programmer Hank Warren shares the tricks he has collected from his considerable experience in the worlds of application and system programming. Most of these techniques are eminently practical, but a few are included just because they are interesting and unexpected. The resulting work is an irresistible collection that will help even the most seasoned programmers better their craft. Topics covered include: A broad collection of useful programming tricks Small algorithms for common tasksPower-of-2 boundaries and bounds checkingRearranging bits and bytesInteger division and division by constantsSome elementary functions on integersGray codeHilbert's space-filling curveAnd even formulas for prime numbers! This book is for anyone who wants to create efficient code. "Hacker's Delight" will help you learn to program at a higher level--well beyond what is generally taught in schools and training courses--and will advance you substantially further than is possible through ordinary self-study alone. 0201914654B06272002

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Code

Charles Petzold

A discussion of the history and future of coding theory celebrates the ingenuity of language systems and their uses from Braille and Morse code through binary codes to 32-bit operating systems.

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Concrete Mathematics

Ronald L. Graham, Donald Ervin Knuth, Oren Patashnik

This book, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills--the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every discipline.

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Elements of Programming

Alexander A. Stepanov, Paul McJones

New techniques for building more secure, reliable, high-performance software, from the renowned creator of the C++ STL • • A truly foundational book on the discipline of generic programming: how to write better software by mastering the development of abstract components. • Based on Alexander Stepanov's breakthrough lectures to programmers at Adobe and throughout Silicon Valley. • For serious software developers, architects, and engineers, the perfect complement to Knuth's theory and Stoustrup's practice. Elements of Programming is the next breakthrough book for serious practitioners seeking ways to write better software. In this book, Alexander Stepanov - the legendary architect and creator of the C++ Standard Template Libraries - focuses on the discipline that offers the greatest potential for improving contemporary software: the proper development of abstract components. Drawing on his enormously popular lectures to programmers at Adobe and throughout Silicon Valley, Stepanov illuminates crucial techniques of generic programming, specifically focusing on abstraction as the key to secure, reliable, and high-performance software. Together with co-author and ACM Fellow Paul McJones, Stepanov shows programmers how to use mathematics to compose reliable algorithms from components, and to design effective interfaces between algorithms and data structures. Topics covered in Elements of Programming include: transformations, associative operations, linear orderings, ordered algebraic structures, iterators, coordinates and coordinate structures, copying algorithms, rearrangement, sorting, and much more. This book requires an understanding of mathematics, but is consistently focused on identifying superior solutions to practical programming problems. Stepanov and McJones illuminate their concepts and techniques with C++ code, but the techniques are equally applicable to a wide range of contemporary object-oriented languages.

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From Mathematics to Generic Programming

Alexander A. Stepanov, Daniel E. Rose

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 Alexander A. Stepanov has been programming since 1972-first in the Soviet Union and, since emigrating in 1977, in the United States. He has programmed operating systems, programming tools, compilers, and libraries. His work on the foundations of programming has been supported by GE, Polytechnic University, Bell Labs, HP, SGI, Adobe, and, since 2009, A9.com, Amazon's search subsidiary. In 1995, he received the Dr. Dobb's Journal Excellence in Programming Award for the design of the C++ Standard Template Library. Daniel E. Rose is a research scientist who has held management positions at Apple, AltaVista, Xigo, Yahoo, and A9.com. His research focuses on all aspects of search, ranging from low-level algorithms for index compression to human--computer interaction. Rose led the Apple team that created desktop search for the Mac. He holds a Ph.D. in cognitive science and computer science from the University of California, San Diego, and a B.A. in philosophy from Harvard.

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Tricks of the 3D Game Programming Gurus

André LaMothe

Focusing on 3D game programming, this book provides advance coverage for the intermediate and advanced game programmer. We now have the technology to create games that look real, but, all this technology isn't easy or trivial to understand. This book will give readers the knowledge to create a full 3D, texture-mapped, lit video game for the PC with a software rasterizer they can write themselves. They could also understand the underlying principles of 3D graphics and be able to better understand and utilize 3D hardware today and in the future.

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Mathematics for Computer Graphics Applications

Michael E. Mortenson

This completely revised Second Edition of "Computer Graphics" includes valuable information on major organizational changes within the last few years. This edition brings to the fore the basic mathematical tools of computer graphics, including vectors, matrices, and transformations. Additionally, it provides a strong, comprehensive base in exploring math, computer science, physics, engineering, and in special subjects such as algebraic and computational geometry, geometric modeling, and CAD/CAM. A highly diversified book that can be utilized as a primary textbook, supplemental teaching resource, individual tutorial, or key reference text. Includes new chapters on symmetry, limit and continuity, constructive solid geometry, and the Bezier curve. Provides many new figures and exercises. Contains an annotated suggested reading list with exercises and answers in each chapter. Appeals to both academics and professionals. Offers a new solutions manual for instructors.

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All the Mathematics You Missed

Thomas A. Garrity

An essential resource for advanced undergraduate and beginning graduate students in quantitative subjects who need to quickly learn some serious mathematics.

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Introduction to Parallel Computing

Ananth Grama

A complete source of information on almost all aspects of parallel computing from introduction, to architectures, to programming paradigms, to algorithms, to programming standards. It covers traditional Computer Science algorithms, scientific computing algorithms and data intensive algorithms.

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