Product Description
“Ask a mechanical, structural, or electrical engineer how far they would get without a heavy reliance on a firm mathematical foundation, and they will tell you, ‘not far.’ Yet so-called software engineers often practice their art with little or no idea of the mathematical underpinnings of what they are doing. And then we wonder why software is notorious for being delivered late and full of bugs, while other engineers routinely deliver finished bridges, automobiles, electrical appliances, etc., on time and with only minor defects. This book sets out to redress this imbalance. Members of my advanced development team at Adobe who took the course based on the same material all benefited greatly from the time invested. It may appear as a highly technical text intended only for computer scientists, but it should be required reading for all practicing software engineers.”
—Martin Newell, Adobe Fellow
“The book contains some of the most beautiful code I have ever seen.”
—Bjarne Stroustrup, Designer of C++
“I am happy to see the content of Alex’s course, the development and teaching of which I strongly supported as the CTO of Silicon Graphics, now available to all programmers in this elegant little book.”
—Forest Baskett, General Partner, New Enterprise Associates
“Paul’s patience and architectural experience helped to organize Alex’s mathematical approach into a tightly-structured edifice—an impressive feat!”
—Robert W. Taylor, Founder of Xerox PARC CSL and DEC Systems Research Center
Elements of Programming provides a different understanding of programming than is presented elsewhere. Its major premise is that practical programming, like other areas of science and engineering,must be based on a solid mathematical foundation. The book shows that algorithms implemented in a real programming language, such as C++, can operate in the most general mathematical setting. For example, the fast exponentiation algorithm is defined to work with any associative operation. Using abstract algorithms leads to efficient, reliable, secure, and economical software.
This is not an easy book. Nor is it a compilation of tips and tricks for incremental improvements in your programming skills. The book’s value is more fundamental and, ultimately, more critical for insight into programming. To benefit fully, you will need to work through it from beginning to end, reading the code, proving the lemmas, and doing the exercises. When finished, you will see how the application of the deductive method to your programs assures that your system’s software components will work together and behave as they must.
The book presents a number of algorithms and requirements for types on which they are defined. The code for these descriptions—also available on the Web—is written in a small subset of C++ meant to be accessible to any experienced programmer. This subset is defined in a special language appendix coauthored by Sean Parent and Bjarne Stroustrup.
Whether you are a software developer, or any other professional for whom programming is an important activity, or a committed student, you will come to understand what the book’s experienced authors have been teaching and demonstrating for years—that mathematics is good for programming, and that theory is good for practice.
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This book defines lots of usual STL algorithms and uses with algebra. This makes a comprehensive writing process for algorithms and concepts. This book is a must read for anybody that wants or is a programmer. This book also shows how regular types are the core of rationing in imperative programming, and the value of value-based programming, no pun intended.
Amazon User Rating: 5 / 5
I wanted to find a book that would give a very formal and mathematical perspective on computer programming and that is what I got. I found this book very difficult to read. The concepts were often foreign, abstract and often described in a very terse manor. However, after reading and re-reading sections of the book it started to slowly make sense. Once I started understanding a little bit it made more and more sense and I really started to appreciate what the book was doing.
I have never come across problem solving presented in this manor before. The algorithms initially appear quite cryptic but once I read and desk-checked the algorithms they came across as quite clever – who would have thought there was so much to be said about ‘power algorithm’. I would recommend this book to anyone who is up for a challenge – who can appreciate code that doesn’t have an immediate application to business application development. It is certainly not an easy read and is suited to mathematically minded programmer.
That being said, I do have some complaints. Sometimes the book comes across as overly terse, they give one explanation that’s it. It could have used diagrams to better communicate an idea. It lacks an explicit overarching theme and direction.
There is one warning I will give to the prospectus buyer: “The book does not have worked examples, solutions to the exercises, nor does it give proofs for all of the lemmas.” This is not a real problem but it breaks the flow of the book as you have to stop and convince yourself that the information presented is correct.
All and all it is a stimulating, interesting and challenging book.
Amazon User Rating: 4 / 5
This little book is quite unusual among current publications on programming. It
supplies a mathematical definition of the various components of a programming language, working up from the simplest constructs. The book then works up to algorithms based on the mathematical rules that have been constructed, and asks the programmer to step back and think about why tasks are performed in a certain way. The preface makes the point of mentioning that no mechanical or electrical engineer would go about solving problems in the same haphazard way that many computer programmers solve problems, and this book’s purpose is to apply mathematical reasoning to program construction.
The book does not stay in the realm of the theoretical, however. Algorithms are implemented in a real programming language – C++ – a language with which most all programmers are familiar. There are numerous open-ended projects for the reader to test his/her knowledge of the principles applied.
I see that the table of contents is already supplied in the product description so I’ll just briefly summarize the chapter contents as mentioned in the preface: Chapter 1 describes values, objects, types, procedures, and concepts. Chapters 2-5 describe algorithms on algebraic structures, such as semigroups and totally ordered sets. Chapters 6-11 describe algorithms on abstractions of memory. Chapter 12 describes objects containing other objects. The afterword presents the authors’ reflections on the approach presented by the book.
The authors also specifically outlines the prerequisite knowledge for the reader of this book. They assume a basic knowledge of algebra and a knowledge equivalent with an undergraduate course on discrete mathematics. They also programming maturity and hopefully familiarity with C++ as well as an understanding of computer architecture and fundamental algorithms and data structures.
If you are just looking for a book from which to extract some useful algorithms you should look elsewhere. If you are looking for a book that teaches you how to quantify, define, and evaluate a useful algorithm, this would be one of the newest books on that subject.
Amazon User Rating: 5 / 5
Stepanov and McJones have created an excellent description of the mappings from mathematics to computer science, and I recommend this book should be in the library of every programmer, software architect and software engineer. I especially appreciated the building of concepts from first principles, which helps in the logical understanding of the concepts in programming. In today’s software, there is more than the traditional serial, digraph mappings, and I wish this had been given more explicit treatment – especially in the non-deterministic aspects of parallel computation. With that one small caveat, this is an excellent reference and wonderful treatment of the mathematics underlying computer software.
Amazon User Rating: 4 / 5
This book is heavy on math and in-depth, intricate concepts. It’s somewhat low on applicability for me in my line of work – but I’m sure lots of other folks will find it very useful. Lots of concise, in-depth discussion of foundational knowledge, and plenty of exercises to help evolve your skills.
The tone’s exceedingly dry and academic, and I got very tired of the authors repeated assertions that you need to be using a “real programming language such as C++.” Guess all the value-providing projects I’ve helped roll out in Perl, Java, C#, and other languages haven’t counted.
That said, this is a wonderful book for those interested in raising their skills in hardcore algorithms and low-level software engineering.
Amazon User Rating: 4 / 5