Prelude to Mathematics (Dover Books on Mathematics) by W. W. Sawyer (PDF)

Description

No mathematician can be a complete mathematician unless he is also something of a poet. — K. WeierstrassIn 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 apparently impossible — for example, an arithmetic 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.

User’s Reviews

Editorial Reviews: About the Author A prolific author who sought to make math interesting and accessible to all, W. W. Sawyer (1911-2008) was a professor at the University of Toronto for more than three decades. Dover has reprinted his The Mathematician’s Delight, which has been in print continuously since 1943 and has sold over 500,000 copies.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Well, this really is a terrific book. Lots of simple ideas very well explained. He spells out the notion of pattern quite well, and what it means in terms of mathematics. It seems many modern authors just state that math is about patterns and leave it at that. He seems to get to the point on many subjects that a reader has in the back of his mind as he reads about the material.I’m not sure this book is really intended for the layman. I’m sure many could handle it. Certainly the material is kept at a very introductory level, but he does seem to be talking to the teacher quite often, and some times to the budding mathematician.My Dover edition doesn’t have an index. Too bad. Hard to believe there wasn’t one, or should be one. A little bit of laziness on Dover’s part?I have one bone to pick about a short piece of material. He claims Del Square V is the most widely found pattern in nature,pp. 13-14. He mentions its applications in physics, magnetism, electrostatics, radiation, waves, etc. I’m sure he’s thinking of Del dot Del of V. Oddly, he never describes to the lay reader what it actually is. It seems out of place with the material in the rest of the book.) Anyway, he does provide a foot note, which in part says, “It expresses in symbols the law that the value of V at any point equals the average value of V on a sphere with its center at the point. That law treats all points and directions alike, and is the simplest law that does so.” Good luck to the layman on that one.–

⭐With an E reader, it was too difficult to flip back and forth among diagrams, new math rules, equations, and results. Being ab engineer, I had a hard time with seeing any value of the new maths beyond “you can” and there might br interesting patterns.

⭐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.

⭐I read this book. Only opinion is that the books seems very biased on what the author believes a mathematician should be.

⭐Most of material goes way over my head. You can still get a lot out of this books because it explains significance and importance of everything mentioned which is really the most interesting part. I think it’s good for giving yourself context for future maths reading.

⭐Every time I have picked up a W.W. Sawyer book, I have not been disappointed. I mostly regret not having read his books earlier (I started with the last book he wrote, on Functional Analysis in graduate school). Sawyer has a particular mathematical writing style that I find fresh, insightful, and understandable. He uses humor, lots of analogies and pictures, and well-motivated examples to get you to learn a concept. This book is no different, and I plan on going through the rest of the catalog of books written by Sawyer.This book covers a variety of mathematical topics, from groups to projective geometry, to determinants, and to matrices. You won’t be an expert, but you’ll have a flavor of what’s going on. Sawyer wrote it for people thinking about getting deeper into math, and I think it would work wonderfully there (though I’d like such people to read it and give me feedback), but I have a ton of mathematical experience, and the book shines for me as well. It explains connections between various branches of math, and helps you take a new look at old subjects and just reminds me of the “beauty” (or whatever you want to call it) of math, and learning a math truth for yourself. I particularly enjoyed that Sawyer doesn’t dumb anything down. He even talks about the hypergeometric functions (I have an interest in them, since they are basically every function you ever work with in physics) and he explains them without overly complicating things.There are just a lot of great insights, humorous statements, and wonderful analogies throughout. I am so sad that Sawyer didn’t write even more.

⭐I first met this excellent publication around 60 years ago as a Sixth Form maths student, doing Double Maths, and I found it immensely stimulating and entertaining and instructive. Indeed it further ignited my love for the subject. I have just bought this copy for my eldest honorary granddaughter, who is in Lower Sixth and also studying maths, and I have enjoyed browsing it before giving it to her; but after a gap of around sixty years I admit to now finding it hard work!In a few instances it is dated, insofar as it predates the invention of the electronic calculator, so occasional comments about numerical work (which is not what the book is primarily about) need to be read in that historical context.Irrespective of date, much of the text about the philosophy of mathematics, and adaptive and imaginative response to pattern, remains just as relevant today as when it was written; and the writer offers some superb ideas.The writer does have a tendency to make statements which are obvious to him, and may indeed be obvious to his intended audience, but which are not so immediately obvious to this lapsed mathematician. I then, after a period, realise “Yes, that is correct, because …”If the student (which is the intended audience) can respond to that, this is excellent; and if this septuagenarian takes longer to work it out that is life!Overall I still think this is a potentially stimulating and entertaining and informative book for the maths student; but whether it is within the reach of the single maths student at Lower Sixth level (rather than the Double Maths student, or the Single Maths student at Upper Sixth) is an open question.

⭐If you need to brush up on your maths or are helping someone else this book ,and it’s sister Mathematician’s Delight, are the best books you will find. His way of introducing complex ideas is ingenious and you will develop a better understanding than you ever did at school. I have had his books for nearly 40 years and I still refer to them all the time. I cannot recommend them highly enough

⭐On time, as expected, no hassles, Happy

⭐Got this for my ‘A’-level student grandaughter: and she is loving it. Got it for myself when I was a student in 1966. Awesome.

⭐I liked the ‘how to think like a mathematician’ approach. Some other books take a historical review approach which I also like and I found WW Sawyer’s approach refreshing.

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