Concrete Math Companion

This book is written as a companion to Concrete Mathematics (Graham, Knuth, and Patashnik); following it closely in its choice of topics and order of treatment and making frequent explicit references to it. Because this book is written in an executable notation, any expression can be entered directly into a computer for experimentation.

This ability to experiment with mathematical ideas complements the treatment in GKP. Although this text can be used independently, it is recommended that the texts be used together, sometimes reading a section from GKP first, and sometimes reversing the order.

Conventional mathematical notation is analytic in the sense that it permits meaningful manipulation of sentences according to relatively strict and simple rules. The use of notation that is both analytic and immediately executable on a computer permits quick and reliable experimentation that can make abstract mathematical ideas more accessible, and their study more enjoyable.

The notation J used in this text possesses these properties and is readily available on a wide variety of computers.

In order to minimize digressions from the mathematical development, a notation will be introduced together with brief commentary sufficient to interpret the particular sentence. To achieve a broader understanding of the notation a reader may:

a) Experiment by entering related sentences on the computer.

b) Consult the final section of each chapter for a discussion of the notation introduced.

c) Consult J Introduction and Dictionary (Iverson).

This style of development will be illustrated by introducing a few of the basic elements of the notation, using a fixed-width font for dialogue with the computer, and Times Roman for commentary: