Mathematics for the Nonmathematician Author: Visit Amazon's Morris Kline Page | Language: English | ISBN:
048646329X | Format: EPUB
Mathematics for the Nonmathematician Description
- Hardcover: 641 pages
- Publisher: Dover (2007)
- Language: English
- ISBN-10: 048646329X
- ISBN-13: 978-0486463292
- Product Dimensions: 8.9 x 5.7 x 1.7 inches
- Shipping Weight: 1.8 pounds
This is the classic text (available in Dover hardbound and paperback editions) for a college course on mathematics for those who are not science majors and probably hated math in high school. Making math interesting for such a group is a tall order, but one that Professor Kline fills admirably. This book is well written, quite informative and a great choice for the target audience and for many who are much more well versed in mathematics. The book starts with numbers and goes through Euclidian geometry, algebra, calculus, statistics, probability theory and some topics in non-Euclidian geometry and advanced algebra. All this is all done from the prospective of the historical development of mathematics and why it is useful to everyone. This is all done in somewhat simplified manner and in a non-condescending tone. I found that this approach enriched my understanding of many mathematical concepts. For instance, I learned the general solution for a quadratic equation as just a formula to be memorized. Professor Kline derives it. He does this by first solving quadratic equations by factoring them. He then shows how an equation that cannot be factored can be solved by a transformation of variables and that the general solution to the quadratic equation is nothing more than a generalized form of this latter approach. In school I learned about the ellipse and parabola from the standpoint of Cartesian geometry. This book first introduces these curves from the standpoint of how they would be drawn with string and a straight edge. This approach eliminates algebraic notation and I think more clearly shows the nature of these curves. There are many other gems in this book.
A spectrum exists in the books written by or about mathematicians and mathematics, and this spectrum is heavily weighted at the extremes. At one end, we have books purely verbal, descriptive and, more often than not, hagiographic in their descriptions of great mathematicians and their discoveries. - I suppose one could denominate these as mathematics groupie books. At the other end of the spectrum, we have straightforward mathematics textbooks, rather dry and boring, which roll off the presses with the regularity of the academic terms. To split the difference, to write a literate, narrative book on mathematics, is to attempt something akin to the labours of Hercules and, in the end, impossible to do perfectly, rather like trisecting an angle. Kline, however, does a bang-up job here, and approaches the limit - so to speak - of what is possible. Good show, Morris! But, as many other reviewers have made clear, this book should have printed across its cover the words above the entrance to Plato's Academy: "Let no man ignorant of mathematics enter here." It is a bit of a catch-22 for someone who wants to learn mathematics but is put off by textbooks; you really have to already possess a fluency in the mathematical tongue, to possess a flair for the subject, in order to appreciate the sweep of this really quite grand book. Some pages of the book are simply equation followed by equation leading to a satisfying simplification or representing a derivation. If you can't follow these steps - sometimes quite involved - then you simply won't arrive at the "Aha!" moments which are the chief delight of this book. To quote Kline, "In his wisdom, Thales perceived what we shall perceive as we follow the story of mathematics, that the obvious is far more suspect than the abstruse.
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