Art of Computer Programming, The: Volume 1: Fundamental Algorithms, 3rd Edition

Chapter One. Basic Concepts

Practice yourself, for heaven’s sake, in little things;

and thence proceed to greater.

— EPICTETUS, Discourses IV.i (C. A.D. 110)

Many persons who are not conversant with mathematical studiesimagine that because the business of [Babbage’s Analytical Engine] is togive its results in numerical notation, the nature of its processes mustconsequently be arithmetical and numerical, rather than algebraical andanalytical. This is an error. The engine can arrange and combine itsnumerical quantities exactly as if they were letters or any other generalsymbols; and in fact it might bring out its results in algebraical notation,were provisions made accordingly.

— AUGUSTA ADA, Countess of Lovelace (1843)

1.1. Algorithms

THE NOTION ...