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From Mathematics to Generic Programming

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4.85
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From Mathematics to Generic Programming

4.85 30,765 Ratings
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Editor's Note:
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 aboutHow 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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Length N/A Pages
Released October 3, 2014
Identifier (ISBN) 23498372
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Alexander A. Stepanov
The Mind Behind the Work
Alexander A. Stepanov

Alexander A. Stepanov is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Alexander A. Stepanov can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Jessica Campbell
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"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
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Brian Wilson
Brian Wilson October 22, 2025
"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
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"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
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Mary Campbell October 31, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
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"Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
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Karen Adams April 16, 2024
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
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Kevin Brown
Kevin Brown March 07, 2025
"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
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Joshua Brown March 11, 2025
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George Turner
George Turner July 24, 2024
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend."
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"I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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Daniel Campbell
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"Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
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Kenneth Turner August 12, 2024
"Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
Ashley Edwards
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"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
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Kimberly Roberts May 01, 2024
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Cynthia Gomez
Cynthia Gomez August 24, 2025
"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Carol Martinez
Carol Martinez July 27, 2024
"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers."
Thomas Williams
Thomas Williams October 12, 2024
"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend."
Kenneth Mitchell
Kenneth Mitchell November 02, 2025
"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece."
William Moore
William Moore January 14, 2024
"It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes."
Ashley Jackson
Ashley Jackson June 21, 2025
"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
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Christopher Carter
Christopher Carter July 08, 2025
"I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers."
Margaret Phillips
Margaret Phillips April 30, 2025
"Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
Steven Scott
Steven Scott May 02, 2024
"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
Rebecca Williams
Rebecca Williams October 17, 2024
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
Rebecca Ramirez
Rebecca Ramirez January 06, 2025
"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
Cynthia Gomez
Cynthia Gomez November 20, 2025
"A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes."
Daniel Reyes
Daniel Reyes February 18, 2024
"Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author."
George Anderson
George Anderson May 21, 2024
"An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty."
Gary Williams
Gary Williams June 24, 2024
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author."
Steven Clark
Steven Clark January 20, 2024
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
Richard Cruz
Richard Cruz July 06, 2024
"Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
Patricia Campbell
Patricia Campbell July 15, 2025
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
Michael Robinson
Michael Robinson August 15, 2025
"Not entirely to my refined tastes. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars."
John Turner
John Turner September 16, 2025
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
Brian Green
Brian Green June 22, 2025
"I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall."
Gary Taylor
Gary Taylor August 12, 2025
"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel."
Emily  Davis
Emily Davis August 08, 2025
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Kenneth Mitchell
Kenneth Mitchell February 08, 2025
"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
James Sanchez
James Sanchez December 20, 2024
"I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel."
Jennifer Rivera
Jennifer Rivera April 29, 2025
"I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time."
Donna Mitchell
Donna Mitchell May 20, 2025
"Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Charles Flores
Charles Flores March 12, 2024
"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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Michael Jones April 23, 2025
"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem."
Andrew Allen
Andrew Allen September 02, 2024
"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Emily Rodriguez
Emily Rodriguez August 28, 2024
"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me."
Patricia Cruz
Patricia Cruz November 08, 2025
"Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
Donna White
Donna White April 14, 2025
"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Patricia Campbell
Patricia Campbell January 02, 2024
"Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
Ashley Nelson
Ashley Nelson August 05, 2025
"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend."
Gary Campbell
Gary Campbell March 04, 2025
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
Anthony Cruz
Anthony Cruz December 22, 2024
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
Margaret Carter
Margaret Carter August 08, 2024
"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me."
Mary Anderson
Mary Anderson October 23, 2024
"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel."
Eric Rivera
Eric Rivera December 15, 2024
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Joshua Robinson
Joshua Robinson December 12, 2025
"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Gary Campbell
Gary Campbell March 16, 2025
"Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me."
Sarah Cruz
Sarah Cruz February 24, 2024
"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend."
Ryan Walker
Ryan Walker June 11, 2024
"An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty."
Donna Sanchez
Donna Sanchez January 11, 2025
"Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall."
Kenneth Scott
Kenneth Scott February 27, 2024
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Karen Green
Karen Green July 08, 2024
"Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
George Campbell
George Campbell March 30, 2024
"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Sharon Green
Sharon Green July 14, 2024
"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
Jacob Miller
Jacob Miller November 21, 2025
"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
Michael Rivera
Michael Rivera February 09, 2024
"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre."
Karen Adams
Karen Adams November 11, 2024
"Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Joshua Nguyen
Joshua Nguyen September 22, 2025
"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
Michael Sanchez
Michael Sanchez May 02, 2024
"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
Melissa Nguyen
Melissa Nguyen September 21, 2024
"Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
Brian Jones
Brian Jones December 25, 2025
"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Matthew Wright
Matthew Wright October 15, 2024
"A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me."
Mary Thomas
Mary Thomas May 29, 2025
"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall."
Lisa Gonzalez
Lisa Gonzalez July 31, 2025
"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
Amanda Miller
Amanda Miller August 05, 2025
"Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
Brian Wilson
Brian Wilson November 14, 2024
"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
Christopher  Davis
Christopher Davis August 19, 2025
"A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me."
Amanda Martin
Amanda Martin March 12, 2024
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
Elizabeth Scott
Elizabeth Scott May 18, 2024
"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
Sandra Cruz
Sandra Cruz December 18, 2024
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
Nicholas White
Nicholas White January 28, 2024
"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
Sandra Lee
Sandra Lee August 29, 2024
"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
Margaret Roberts
Margaret Roberts December 07, 2024
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
Thomas Reyes
Thomas Reyes February 06, 2024
"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Sandra Rodriguez
Sandra Rodriguez March 22, 2025
"Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
Rebecca Williams
Rebecca Williams August 18, 2025
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
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