From Mathematics to Generic Programming

Posted on 02 January 2017 by Alexander A. Stepanov

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 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 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 New Read [ From Mathematics to Generic Programming ] author [ Alexander A. Stepanov ] For Kindle ePUB or eBook – kino-fada.fr As long as algebra and geometry have been separated, their progress have been slow and their uses limited, but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection Joseph Louis LagrangeWhat does geometry, abstract algebra, number theory and generic programming have in common This book attempts to answer that by starting at the early stages of organized mathematics and going all the way forward to the 1960 s The way I tho As long as algebra and geometry have been separated, their progress have been slow and their uses limited, but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection Joseph Louis LagrangeWhat does geometry, abstract algebra, number theory and generic programming have in common This book attempts to answer that by starting at the early stages of organized mathematics and going all the way forward to the 1960 s The way I thought about Stepanov s approach is that he attempts to generalize algorithms and shows how algorithms in many respects can be used as axioms In other words, generalization is not just merely a time saver, butcrucially is a way to ensure rigorousness Mathematics is a game played...Not the best to learn Number Theory and Algebra from, really requires you to have some knowledge of these in the first place.A worthy follow up to Elements of Programming Where Elements was terse, like an old math book, this book isconversational and it includes short biographies about some of the mathematicians mentioned in the text Includesby way of proofs than Elements Includes a handful of programming laws such as the law of useful return if you ve gone through the trouble of calculating something, consider returning it even if your current callers will ignore the return value.In an interview A worthy follow up to Elements of Programming Where Elements was terse, like an old math book, this book isconversational and it includes short biographies about some of the mathematicians mentioned in the text Includesby way of proofs than Elements Includes a handful of programming laws such as the law of useful return...This is a short dense book packed with historical information about mathematics All the template code examples given are short and well explained.While the title implies a mathematical derivation for the use of generic programming, it rather uses varied mathematical algorithms to illustrate its use.The cover blurb states If you re a reasonably proficient programmer who can think logically, you have all the background you ll need while the Prerequisites given in chapter 1 state we don t assum This is a short dense book packed with historical information about mathematics All the template code examples given are short and well explained.While the title implies a mathematical derivation for the use of generic programming, it rather uses varied mathematical algorithms to illustrate its use.The cover blurb states If you re a reasonably proficient programmer who can think logical...If you are really interested in the mathematical discipline of abstract algebra, and you are really interested writing code that is both efficient and has the widest possible application, and you can read C , then this is the book for you.Depends on what you expectI was very enthusiastic about this book when it was first announced My expectation was that author will give some introduction to mathematical constructs related to program composition that comes from category theory and functional programming, like monads, applicatives, traversables and so on Instead I found all familiar view on algebra, things ike groups, rings, some number theory and cryptography However despite my own dissatisfaction I can t avoid mentioning that Depends on what you expectI was very enthusiastic about this book when it was first announced My expectation was that author will give some introduction to mathematical constructs related to program composition that comes from cat...Very good book has really inspired me on many levels by its mathematical depth which was set just about as far down as I can go as well its breadth with the historical interludes were fascinating and stimulating I wasn...It takes a special author to seamlessly jump between ancient Babylonian astronomers using positional sexagesimal 60 based system and C generics Lucky for reader, both authors are doing it with ease Read this exceptionally well written book packed with historical inf...I expected this book to be written in a bitpopular science way Instead chapters were burdened with mathematics and hardcore algorithm optimization Sometimes the author s obsession with nice and sleek programs was getting in the way of clearer explanation.This is a book of mathematics for computer programming or a book of computer programming for mathematics Simply perfect If I have to wrote a book, I liked wrote this

02 January 2017

Alexander A. Stepanov