"The desire to explore thus marks out the mathematician. This is one of the forces making for the growth of mathematics. The mathematician enjoys what he already knows; he is eager for more knowledge."
[Quotations XIV: The joy of mathematics -- 8/8/07]

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Product Description

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Product Details

• Amazon Sales Rank: #175369 in Books
• Published on: 1982-12-01
• Original language: English
• Number of items: 1
• Binding: Paperback
• 224 pages

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Customer Reviews

Projective Geometry, Matrices, Groups, Transformations and More
W. W. Sawyer argues that the pleasure given by a unifying discovery is greatest when a person has struggled with masses of undigested information in an old form. In support of this thesis he reveals unexpected relationships and interdepencies between various topics that might at first seem entirely independent and unrelated.

Despite the wide range of mathematical topics, Prelude to Mathematics only assumes that the reader remembers some basic algebra, geometry, and trigonometry. Calculus is not required. The reader is generally free to skip around; Sawyer has indicated where two chapters are more closely linked and should be read in sequence.

This short book consists of two largely independent sections. The first five chapters (about 60 pages) - On Beauty and Power, What are the Qualities of a Mathematician, Pattern in Elementary Mathematics, Generalization in Elementary Mathematics, and On Unification - provide a general overview of mathematics and mathematical thought.

Chapters 6 through 14 examine more advanced topics often not encountered in lower level mathematics courses.

I especially enjoyed Sawyer's overview of Projective Geometry and its companion chapter, Apparent Impossibilities. Sawyer's discussion of matrices from the perspective of coordinate transformations (rotations, reflections, and stretches) was surprisingly effective. Determinants are traditionally taught before matrices; Sawyer deliberately reverses the order.

Also, the chapters titled On Transformations and On Groups were quite good. The three chapters titled Non-Euclidian Geometries, Algebra without Arithmetic, and Finite Arithmetics and Geometries are good, but perhaps a little dated.

Prelude to Mathematics was first published in 1955 and reprinted as an inexpensive soft cover Dover edition in 1982.

Looking beyond Prelude to Mathematics, I highly recommend Foundations and Fundamental Concepts in Mathematics by Howard Eves for the chapters on non-Euclidian geometries and abstract algebras. Richard Courant's classic text, What is Mathematics? - An Elementary Approach to Ideas and Methods, is another good choice, however, it is a little more advanced.

For the reader intrigued with Sawyer's discussions of matrices, transformations, and groups, I suggest two inexpensive Dover editions: Matrices and Transformations by Anthony Pettofrezzo and An Introduction to Matrices, Sets, and Groups for Science Students by G. Stephenson.

I MUST HAVE COME ACROSS THIS YEARS AGO WHEN
the material in it was over my head, but I had forgotten about it. What a treasure!! MATHEMATICIAN'S DELIGHT is more famous, I believe, but this book is filled with wisdom. Sawyer introduces finite geometries and group theory in simple prose. He figures out where Hall and Knight came up with the ideas for some of their exercises in their (famous) HIGHER ALGEBRA text. He introduces the hypergeometric function as a generalization of power series expressions of functions (something I feel I should certainly have heard of before reading about it here.) I can't imagine anyone with an interest in mathematics not finding something in this book to make him or her say "Hmmm..." or even make him or her pick up a pen and do some figuring.
Highly recommended.

The best introductory math book!
This is the book that really got me interested in mathematics. I had never thought that a math book could be so engrossing. I finished reading it in a couple days and i immediately seeked out the author's other books. And the quality of the other book are of the same level as this one. It is a shame that the author's other books are mostly out of print. What i appreciate most about the book is that the math concepts are always are related to where it came from. The part on series is a small gem, and the book is full of ones like that. Without having met the author, he is in my mind certainly one of the best math teachers ever. (George Polya is another). Thank you, Mr Sawyer.