## Excerpt

The unusual nature of this book makes desirable some description in addition to the general remarks in the preface.

The first four chapters, presupposing only arithmetic, introduce algebra, plane geometry and trigonometry. The fifth chapter extends the natural number system to include irrational numbers, thus completing preparation for analytic geometry and calculus. Each of these seven chapters concludes with a list of exercises designed to further illustrate and to broaden the concepts which they have introduced.

Succeeding chapters are for the most part self-contained, except that they presuppose the first seven chapters or the same subjects studied elsewhere.

Puzzlement, manipulation and important routine drill have been kept at a minimum. These matters play important psychological roles in conventional text books but would be out of place in this book whose purpose is to present the principles of mathematics as clearly and briefly as possible -- to make mathematics easily understandable.

Teachers who use this book in introductory or general courses will want to supply exercises adapted to their classes. Those people who use it for home study will fix its discussions in mind by repetition and, or, dreaming about them.

Readers who desire to study further into any of the topics can find detailed treatments in text books on the classic courses and extensive references are supplied in the chapters on the newer courses, e.g. The Mathematical Theory of Games presents an extensive bibliography.

Finally, readers who do not care to go into the technical language of mathematics can make a brief survey of the field by readjust the introductions to the various chapters.

Glenn James . . .