From Mathematics to Generic Programming (EPUB)


From Mathematics to Generic Programming

Summary ↠ PDF, DOC, TXT or eBook ✓ Alexander A. Stepanov

Enting that algorithm in SymPy then analyzing it This Is What I Recommend You what I recommend you with this book don t simply copy his examples and expect to get some kind of understanding through wrought memorization but explore what he s talking about with your own work s much rewarding and in line with what I think the author was trying to get across much rewarding and in line with what I think the author was trying to get across by the examples to begin withPursue what you re interested in keep working hard pay attention to what s going on around you and be lexible these are the rules Sometimes it works sometimes it doesn t Nathan Seiberg I expected this book to be written in a bit popular 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 Not the best to learn Number Theory and Algebra Sleep with the Fishes from really reuires you to have some knowledge of these in theirst place I wonder what s up with C Concepts these days Well explained material with engaging history and C code. D year old algorithm demonstrating indispensable lessons about clarity and efficiencyAncient paradoxes beautiful theorems and the productive tension between continuous and discreteA simple algorithm The Apache Wars: The Hunt for Geronimo, the Apache Kid, and the Captive Boy Who Started theLongest War in American History forinding 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 techniues to organize knowledge about your algorithms and data structuresSurprising subtleties of simple programming tasks and what you can learn rom themHow practical implementations can exploit theoretical knowled. .
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Along The Euclidean algorithmgreatest common denominator is the main tool of Stepanov of this book may be used too much Algorithms have existed as he says or as long as we ve been doing math The A World on Fire fact that computers use them is historically new not the norm Turns out that mathematicians have developed great methodsor analyzing such algorithms and the Euclidean algorithm is used exhaustively in a variety of ways to illustrate both the axiomatic nature of algorithm reuse but also how we might do analysis on such algorithmsIf you ve read my review or Dijkstra s A Discipline of Programming you might remember the line I said abstraction is not a Programming you might remember the line I said abstraction is not a idea BUT HOW WE RE ABSOLUTELY PRECISE how we re absolutely precise s what what Stepanov like Dijkstra is trying to get across here Just because we are reorienting our thinking does not mean we lose rigorousness in act it s how we ensure it I m taking a lot of Calculus in "my undergrad so an algorithm I use daily is the Hessian "undergrad so an algorithm I use daily is the Hessian or second derivative test I ollowed along with Stepanov s writing by implem. 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 or 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 our thousan. As long as algebra "And Geometry Have Been "geometry have been their progress have been slow and Their Uses Limited But When uses limited but when two sciences have been united they have lent each mutual orces 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
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to the 1960 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 but crucially is a way to ensure rigorousness Mathematics is a game played according to certain simple rules with meaningless marks on paper David HilbertIn many ways this book is just Stepanov removing the paper The The Oxford New Greek Dictionary fact that he uses C code is irrelevant I used Python and Java without having used C in years and it was sufficiently trivial that I couldollow. 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 The Cello Suites : J.S. Bach, Pablo Casals, and the search for a Baroque masterpiece first needed to solve and then show how these mathematical solutions translate to generic programming and the creation.