White Water lTh abstract algebra and number theory Or if you want some good time reading about history of mathematics Not the best toearn Number Theory and Algebra from really reuires you to have some knowledge of these in the first place I think the overall concept is interesting but it didn t feel revolutionizing to me As The Slave Dancer long as algebra and geometry have been separated their progress have been slow and their usesimited but when these two sciences have been united they have ent 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 attempt For those of us who need a refresher and a bit Computer those of us who need a refresher and a bit Computer is a wholly mathematical pursuit Although many computer science departments are housed in engineering the heart and soul is abstract mathematics This book reminds us that a computer only does what it is told to do and told in a proper fashion While the present tends fall towards AI this book takes a decidedly different tact It gives us the rudimentary basics of computer secur. 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 "**cryptosystem As you read this book you'll master the thought processes necessary for effective programming As you read this book you'll master the thought processes necessary for effective programming earn how to generalize narrowly conceived algorithms to widen their usefulness without Sleep with the Fishes losing efficiency You'll also gain deep insight into the value of mathematics to programming insight that will prove invaluable no matter what programminganguages and paradigms you use You will earn aboutHow to generalize a four thousan. ,

## Alexander A. Stepanov ☆ 7 Summary

,Ity whose fundamentals rest in Abstract Algebra It

**#Is A Joy To Read #**a joy to read wonder what s up with C Concepts these days A worthy follow up to Elements of Programming Where Elements was terse ike an old math book this book is conversational and it includes short biographies about some of the mathematicians mentioned in the text Includes by way of proofs than Elements Includes a handful of programming aws such as the aw 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 valueIn it even if your current callers will ignore the return valueIn interview Stepanov said It is as if mathematicians would start with axioms You do not start with axioms you start with proofs Only when you have found a bunch of related proofs can

__you come up with axioms You end with axioms Since all math textbooks__come up with axioms You end with axioms Since all math textbooks ve ever used started with axioms I was curious to see how things could be different This book stands as a great example of just that the authors don t point that out until near the end I am considering sending copies to some friends and relatives not all programmers or mathematicians. D year old algorithm demonstrating indispensable A World on Fire 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 techniues to organize knowledge about your algorithms and data structuresSurprising subtleties of simple programming tasks and what you canearn from themHow practical implementations can exploit theoretical knowled. .

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 Very cool book which builds a bridge between abstract algebra and template functions in C Well explained material with engaging history and C code 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 ike 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 and cryptography However despite my dissatisfaction I can t avoid mentioning that book is exceptionally well written Through historical view on mathematics development author achieved very whole and capturing story I spent some fun good time reading itBottom ine read it if you want to

get familiar wi.familiar wi. 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 ogically 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.