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Prelude to Mathematics (Dover Books on Mathematics) Paperback – January 20, 2011


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Prelude to Mathematics (Dover Books on Mathematics) + Mathematician's Delight (Dover Books on Mathematics) + A First Look at Numerical Functional Analysis (Dover Books on Mathematics)
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 224 pages
  • Publisher: Dover Publications; Revised edition (January 20, 2011)
  • Language: English
  • ISBN-10: 0486244016
  • ISBN-13: 978-0486244013
  • Product Dimensions: 8.4 x 5.3 x 0.6 inches
  • Shipping Weight: 8.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #1,193,237 in Books (See Top 100 in Books)

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Customer Reviews

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Well, this really is a terrific book.
W. Watson
Most Modern mathematics is written by people who can't communicate... Sawyer is a guide for writers of mathematics... how to do it well!
Roger Bagula
I finished reading it in a couple days and i immediately seeked out the author's other books.
Nan Zhang

Most Helpful Customer Reviews

22 of 22 people found the following review helpful By Michael Wischmeyer on August 10, 2005
Format: Paperback
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.
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14 of 15 people found the following review helpful By Nan Zhang on November 3, 1999
Format: Paperback
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.
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13 of 14 people found the following review helpful By William Meisel on November 1, 2004
Format: Paperback Verified Purchase
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.
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3 of 3 people found the following review helpful By Patrick Regan VINE VOICE on November 11, 2006
Format: Paperback
Prelude To Mathematics covers many aspects of the field of mathematics including modular arithmetic, non euclidean geometry, projective geometry, matrices and determinants. In addition the author discusses common themes in mathematics including pattern, generalization and unification. Although the types of mathematics are introduced in different chapters the author draws them together several times in the book making for a unified approach. I learned a lot from this book. It is the type of book you want to reread because there is so much information in it.
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2 of 2 people found the following review helpful By AC on February 24, 2012
Format: Paperback
Wow, Wow, Wow.

After reading these reviews, I couldn't resist 'seeing for myself', & purchased a copy of this book. I am utterly struck by Sawyer's brilliance. His expository style & its effectiveness are truly exceptional. And it amazes me that in a brief foray to a latter section of the book, & in under 10 minutes of my time, he had connected aspects of relatedness crucial to my understanding the 'why' of a branch of mathematics for which all encounters I'd had previously had failed to even *hint* at -- & that he conveyed it in such an uncluttered & straightforward manner, with excellent (& minimal) use of accompanying material (e.g. diagrams, symbols, etc.), was remarkable, & overall, resulted in some part of my mind 'exhaling', & my feeling a kind of gratitude seemingly reserved for the rare, magical educator whose talent 'lifts' us, & makes some previously inaccessible or otherwise 'cloudy' realm a new arena in which we can 'play'.

I find myself struggling to convey just how remarkable this work (of true art) is. Ironically, this reminds me (it reverberated in my mind) of the sentence which begins the third paragraph of the book -- "It is very difficult to communicate the things that are really worth communicating." -- all I can say is that Sawyer mastered that difficulty, & accompanying his analytical gifts was a creative style, passion, & flair for presentation which result in an educational force to be reckoned with.

It's one thing for someone to have penetrating insight, but to have been blessed with the gift of being a true teacher, & then to couple those talents & channel them through an exceptional facility with language (let alone an economical use thereof), is a wonder to behold, & a priceless gift to those with a desire to learn.

I'm grateful that this book exists.
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