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Prelude to Mathematics (Dover Books on Mathematics) Paperback – January 20, 2011
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Top Customer Reviews
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.Read more ›
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.
Most Recent Customer Reviews
I read this book. Only opinion is that the books seems very biased on what the author believes a mathematician should be.Published 12 months ago by jjangcindy
Some of the topics presented were interesting, however I wish more topics had been covered rather than being so wordy and devoting whole chapters to one topic such as matrices. Read morePublished on April 1, 2006 by book reviewer
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. Read morePublished on August 2, 2005 by W. Watson
I got Sawyer's book used in a book store and for 15 years I have used it's wisdom in my work on non Euclidean geometry, fractals and group theory. Read morePublished on July 28, 2001 by Roger Bagula
Please also read Sawyer's Mathematician's Delight. My last review was more appropriate for that book, as it refers to the infinite series example. But this also a superb book. Read morePublished on December 14, 1999 by Nan Zhang