This is the Safari online edition of the printed book.

 “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 Alex’s course, development and teaching of which I strongly supported as the CTO of Silicon Graphics, to be 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, 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.

Following key definitions, the book describes a number of algorithms and requirements for types on which they are defined that exemplify its abstract mathematical approach. 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, that theory is good for practice.

Amazon.com® Reader Reviews (Ranked by Helpfulness)

Average Amazon.com® Rating:  Based on 7 Ratings

A great book - 2009-07-23
Reviewer Rating:
I have been wondering what to say about this book and now Peter G. Neumann said it better (see previous review). However, I can still say this: There are many good books, but few great ones. "Elements" is a great book in that it can change the way you think about programming in fundamental ways: If you "get it" programming will never be the same again for you.

Reading "Elements" requires maturity both with mathematics and with software development. Even then it is so different from most books on programming that it can be hard going. The frequent comparisons of "Elements" to Knuth's "The Art of Programming" is well earned.

From ACM Risks Forum, vol 25 no 74 - 2009-07-23
Reviewer Rating:
What could be one of the most important books for developers of low-risk
systems has come to my attention, and deserves your consideration if you are
serious about understanding the mathematical foundations of programming and
applying them sensibly to your practice. It is not an easy read, but it is
a very compelling approach. To support its mathematically oriented
crispness, the book includes the definition of a small but elegant C++
subset that has been crafted by Sean Parent and Bjarne Stroustrup for
illustrative use in the book. I believe this material should be taught
within all computer science curricula.

A long quote and a short one on the back jacket give an idea of what is
involved:

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

The bottom of the inside cover suggests that through this book you will come
to understand that mathematics is good for programming, and theory is good
for practice. I applaud that sentiment.

Excellent mathematical foundation - 2009-08-15
Reviewer Rating:
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.

Must read for all computer scientists - 2009-11-10
Reviewer Rating:
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.

Rigorous and essential - 2009-10-18
Reviewer Rating:
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.

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