Book Title: "Prelude to Mathematics" by W.W. Sawyer

Title Prelude to Mathematics
Author(s) W.W. Sawyer
Description [FRONT] An account of some of the more stimulating and surprising branches of mathematics, introduced by an analysis of the mathematical mind, and the aims of the mathematician.

[BACK] In this lively and stimulating account, noted mathematician and educator W.W. Sawyer (Professor Emeritus, University of Toronto) defines mathematics as "the classification and study of all possible patterns." It is a broad definition, but one that seems appropriate to the great scope and depth of the topic. Indeed, mathematics seems to have few boundaries, either in applications to practical matters or in its mind-stretching excursions into realms of pure abstraction.

Gearing his approach to the layman whose grasp of things mathematical may be a bit precarious, Professor Sawyer offers a lucid, accessible introduction to the mathematician's cast of mind. Five well-written preliminary chapters explore the beauty, power and mysticism of mathematics; the role of math as an adjunct in utilitarian matters; and the concepts of pattern, generalization and unification as both tools and goals of mathematical thought.

After developing this conceptual groundwork, the author goes on to treat of more advanced topics: non-Euclidean Geometry, matrices, projective geometry, determinants, transformations and group theory. The emphasis here is not on mathematics with great practical utility, but on those branches which are exciting in themselves—mathematics which offers the strange, the novel, the appraently impossible—for example, an arthmetic in which no number is larger than four.

Mathematicians will appreciate the author's grasp of a wide range of important mathematical topics, and his ability to illuminate the complex issues involved; laymen, especially those with a minimal math background, will appreciate the accessibility of much of the book, which affords not only a portrait of mathematics as a matchless tool for probing the nature of the universe, but a revealing glimpse of that mysterious entity called "the mathematical mind." Professor Sawyer has further enhanced this new Dover edition with updated material on group theory, appearing here in English for the first time.
Dedication --
ISBN 978-0-486-24401-3
Book Dimensions Width: 5.5″ (5 ½″)
Height: 8.5″ (8½″)
Depth: 0.44″ (7/16;″)
Page Count 244
Contents On Beauty and Power, What are the Qualities of a Mathematician?, Pattern in Elementary Mathematics, Generalization in Elementary Mathematics, On Unification, Geometries other than Euclid's, Algebra without Arithmetic, Matrix Algebra, Determinants, Projective Geometry, On Apparent Impossibilities, On Transformations, Finite Arithmetics and Geometries, On Groups
Cover Design Paul E. Kennedy
Published 1982 (originally published in 1955)
Publisher Dover Publications ( Originally published by Penguin Books, Ltd, Harmondsworth, Middlesex.
Copyright © 1955, 1982 by W.W. Sawyer. All Rights Reserved.
Manufactured / Printed in United States of America by Courier Corporation
Book Format Hardcover, Paperback, Mass Market Paperback, Kindle, eBook
Quoted Reviews "No mathematician can be a complete mathematician unless he is also something of a poet." — K. Weierstrass
Best Seller's List --
Other Revised and enlarged republication of the edition published by Penguin Books Ltd., Harmondsworth, Middlesex, England, 1955.
Library of Congress Cataloging-in-Publication Data 1. Mathematics—1961—
I. Title.
CIP Number 82-4567
LC Control Number ????
LC Call Number QC39.2.S27  1982
DDC Call Number ????


Prelude To Mathematics by W.W. Sawyer

Book Review (Posted on 10-15-2017)

These introductory books to Mathematics really come in handy—books that school professors ought to recommend to their students to spark curiosity and inspiration of everything, including the hows and whys of, Math. Why most professors don't do so is beyond me, as our society continues to be mathematically illiterate (you don't have to like Math but come on, you at least should do Arithmetic in your sleep).

Author and professor W.W. Sawyer wrote a unique take on Math, talking about what the mathematician sees and what s/he interprets in the world around them. Sawyer mentions about seeking patterns and symmetry which are key components to doing good math and being a good mathematician. Along the first part of the book comes some advice when diving into the world of problem solving, along with what to expect (nothing too overwhelming). What I found interesting was Sawyer's claim that advanced mathematics is very much easier to do and study than elementary mathematics. That struck me a bit because even though I personally am a whiz at Arithmetic and Algebra, I still have yet to venture into the advanced disciplines (I'll be studying and getting there so stay tuned). Well, I have, and am, self-studying in Mathematical Logic and got a grasp of Statistics, but I still have yet to know about Topos and Tensor Calculus so we'll see if Sawyer's claim holds.

The rest of the book covers the advanced disciplines of mathematics such as Determinants, Matrix Algebra Projective Geometry and Group Theory to name a few. While these coverages are great, this parts of the book began getting drier and drier. It was hard to read and keep up because the attention from author to reader drifted, and felt like I was reading an average textbook. The fact that there's no Appendix or Index led me that this was an account just placed to spread the word and a simple message to those wanting to pick up a book about Math. While that's fine, the meat slowly got rotten and became hard to read after the introductory chapters from the first part of the book. That's pretty tough since the book started off quite well.

Having said that, the rest of the book are just overviews to solidify the author's claim as to how easy advanced mathematical disciplines are much easier than the math we all learned in elementary school. It's like eating a delicious scratch-made tacos eventually tasting that the rest of the tacos you're about to finish eating became stale and bland, making it difficult to finish but not wanting to throw away.

Not a bad book, but I wish Sawyer kept up this thesis from the first parts of the books onto the very end. Better yet, he could've introduced the topics while gently discussing about the "artistry" or functions of the topics. I felt that passed half way through the book, he removed his attention to the reader and turned into a textbook author. Definitely a book that could've had potential.

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