Elements of Programming

Engineers in mechanical, structural, and electrical fields rely heavily on solid mathematics, so they would struggle without it. Many software engineers, by contrast, work without much grasp of the mathematics behind their craft. That gap may help explain why software so often ships late and riddled with defects, while bridges, cars, and appliances are typically finished on schedule with only minor flaws. This book aims to close that gap.

The authors argue that practical programming, like other scientific and engineering disciplines, should rest on a rigorous mathematical base. Their algorithms are written in a real language, C++, but they are framed for the most general mathematical setting possible. Fast exponentiation, for instance, is defined for any associative operation. The authors contend that abstract algorithms of this kind lead to software that is efficient, dependable, secure, and economical. This is not a collection of quick programming tricks. Its value lies in deeper insight, and readers get the most from it by working through every chapter in order, studying the code, proving the lemmas, and completing the exercises. Along the way, readers learn how a deductive approach helps ensure that software components fit together and behave as intended.

The text presents a series of algorithms along with the requirements each one places on the types it operates on. The code, available online, uses a small subset of C++ that an experienced programmer should be able to follow. That subset is specified in an appendix co-written by Sean Parent and Bjarne Stroustrup. The book suits software developers, other professionals for whom programming is central, and committed students who want to see how mathematics and theory can directly improve everyday practice.