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From Mathematics to Generic Programming

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From Mathematics to Generic Programming

4.85 77,781 ratings · 3,387 reviews
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Overview: 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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Book details & editions

ISBN
23498372
Publication date
October 3, 2014
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Alexander A. Stepanov
About the Author
Alexander A. Stepanov
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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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Margaret Taylor
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
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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 very distinguished novel.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Excellent, though slightly flawed. 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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Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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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. A wonderful companion for a quiet weekend.
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Sharon Jackson December 05, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Susan King
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Andrew Robinson
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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.
Eric Brown
Eric Brown November 07, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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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.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Ashley Turner
Ashley Turner February 09, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Jacob Adams
Jacob Adams February 21, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Ashley Turner
Ashley Turner August 17, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Rebecca Walker
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Mary Phillips
Mary Phillips June 30, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Sarah Moore
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Paul Edwards
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Jessica Martinez
Jessica Martinez August 21, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Brian Collins
Brian Collins January 11, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Elizabeth Williams
Elizabeth Williams June 11, 2025
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William Miller
William Miller August 08, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Carol Roberts
Carol Roberts July 03, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Cynthia Evans
Cynthia Evans November 16, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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David Baker December 11, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty.
Robert Thomas
Robert Thomas February 04, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Richard Green
Richard Green March 23, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Donald Clark
Donald Clark May 03, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Daniel King
Daniel King January 17, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Kevin Green
Kevin Green March 07, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Elizabeth Reyes
Elizabeth Reyes May 04, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Paul Walker
Paul Walker January 23, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Lisa Nguyen
Lisa Nguyen March 04, 2024
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Melissa Diaz
Melissa Diaz November 15, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Cynthia Gomez
Cynthia Gomez September 17, 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.
George Diaz
George Diaz December 10, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Joshua Baker
Joshua Baker January 08, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Melissa Robinson
Melissa Robinson January 10, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Amanda Miller
Amanda Miller November 11, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Mary Lewis
Mary Lewis January 02, 2024
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Robert Diaz
Robert Diaz January 14, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Robert Thomas
Robert Thomas December 13, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Charles Reyes
Charles Reyes June 15, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Stephanie Martin
Stephanie Martin January 27, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Kenneth Walker
Kenneth Walker September 02, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Sharon King
Sharon King July 16, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Patricia Wright
Patricia Wright March 07, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Amanda Williams
Amanda Williams July 12, 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 very distinguished novel.
Cynthia Young
Cynthia Young May 24, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Ashley Clark
Ashley Clark March 09, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Jacob Lee
Jacob Lee September 24, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Jessica Williams
Jessica Williams August 03, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Michael Anderson
Michael Anderson November 22, 2025
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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