Rating: 
Summary: Simply Amazing
Review: This book is a rare achievement. It is a survey of mathematics that both broad in scope yet concise in its explanations. It isn't simply a history of the development of mathemeatics and yet it takes us through the its development in a very wonderful way.It is delightful to just read through from left to right and yet each chapter acts as an introdcution the reader can use as a springboard to very deep study of an amazing range of mathematical topics. In the foreward, Prof. Hilton of SUNY says it very well: "The unstated premise of this book - a premise that virtually all mathematicians would agree to - is that mathematics, like music, is worth doing for its own sake." After reading this book, even a non-mathematician can agree.
Rating: 
Summary: Broad coverage of high school topics
Review: This book is a wonderful supplement to the standard high school curriculum, beginning with algebra and extending through Euclidean geometry, analytic geometry, to differential and integral calculus, and including brief introductions to other "back of the book" topics like probability, determinants, and so on. It is full of hard-to-find details left behind by most texts, such as explicit solutions to third- and fourth- degree polynomials in one variable. It's fun to browse this book in search of such tidbits to fill in your mathematical knowledge. "Mathematics..." is written at a level just right for someone who has progressed as far as calculus or college engineering math but no further. It is also nice that the myriad (albeit brief) historical references help connect the material with its initial development. Unfortunately, the lack of any contextual information (brief biographies would be welcome) make these references rather dry and unrevealing: authors, dates, and titles of publications is frequently all we get. I have to agree, too, with the Willingboro reviewer: although this text covers a wide variety of traditional high school and early college topics, at the same time it clearly exhausts its author's knowledge of the subject and therefore cannot provide a foundation for proceeding further. It is akin to a travelogue that directs the reader along completed, well-worn paths, visiting all the conventional landmarks, without pointing out the existence of other paths, other points of interest, or taking the readers to lookout points and vistas suggesting territory remaining to be explored. Almost all the topics covered are ancient, rarely extending beyond what was known by the middle of the 19th century. (A chapter on fractals is the only exception.) Many important and modern subjects are barely mentioned and certainly not developed beyond the limited introduction available in most high school texts: graph theory, number theory, complex analysis, algebraic geometry, functional analysis, group theory, Galois theory, differential geometry, category theory, ..., the list can go on and on. (For example, topology--a vast subject--gets less than three pages, whereas eight pages are devoted to illustrating the routine mechanics of solving euclidean triangles using trigonometry.) This is a shame, because the wealth of topics nevertheless discussed by this book provides an amazing foundation for introducing these modern ideas and pointing out their deeper implications and ramifications. As a result, mathematics comes out looking like a kind of beautiful fossil rather than an organic, evolving creature.
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