- Paperback: 672 pages
- Publisher: Dover Books (1985)
- Language: English
- ISBN-10: 0486248232
- ISBN-13: 978-0486248233
- Product Dimensions: 5.4 x 1.3 x 8.5 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 4.2 out of 5 stars See all reviews (134 customer reviews)
- Amazon Best Sellers Rank: #32,827 in Books (See Top 100 in Books)
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Mathematics for the Nonmathematician
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About the Author
Morris Kline: Mathematics for the Masses
Morris Kline (1908–1992) had a strong and forceful personality which he brought both to his position as Professor at New York University from 1952 until his retirement in 1975, and to his role as the driving force behind Dover's mathematics reprint program for even longer, from the 1950s until just a few years before his death. Professor Kline was the main reviewer of books in mathematics during those years, filling many file drawers with incisive, perceptive, and always handwritten comments and recommendations, pro or con. It was inevitable that he would imbue the Dover math program ― which he did so much to launch ― with his personal point of view that what mattered most was the quality of the books that were selected for reprinting and the point of view that stressed the importance of applications and the usefulness of mathematics. He urged that books should concentrate on demonstrating how mathematics could be used to solve problems in the real world, not solely for the creation of intellectual structures of theoretical interest to mathematicians only.
Morris Kline was the author or editor of more than a dozen books, including Mathematics in Western Culture (Oxford, 1953), Mathematics: The Loss of Certainty (Oxford, 1980), and Mathematics and the Search for Knowledge (Oxford, 1985). His Calculus, An Intuitive and Physical Approach, first published in 1967 and reprinted by Dover in 1998, remains a widely used text, especially by readers interested in taking on the sometimes daunting task of studying the subject on their own. His 1985 Dover book, Mathematics for the Nonmathematician could reasonably be regarded as the ultimate math for liberal arts text and may have reached more readers over its long life than any other similarly directed text.
In the Author's Own Words:
"Mathematics is the key to understanding and mastering our physical, social and biological worlds."
"Logic is the art of going wrong with confidence."
"Statistics: the mathematical theory of ignorance."
"A proof tells us where to concentrate our doubts." ― Morris Kline
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Top Customer Reviews
Before I get into the positive qualities of this book, I should note its flaws. As another reviewer pointed out, Kline's beginning chapter on history is inept, even offensive. He heaps praise upon praise when describing the accomplishments of the Greeks, and dismisses the contributions of the Arabs, Babylonians, Egyptians, and Indians with a wave of the hand. He even relays the story of the Arabs destroying the library, which historians have seen fit to doubt as far back as Edward Gibbon. For Kline, mathematics made a brilliant beginning with the Greeks, and then stayed more or less the same until the Enlightenment. The extent to which that is true, I know not; but it at least seems unlikely to me.
Thankfully, the book gets markedly better after that. (One shouldn't judge a book by the cover, or even the first chapter, apparently.) For, whatever Kline lacks as a historian, he makes up as a pedagogue. Kline doesn't simply move from arithmetic to geometry to algebra to trigonometry, but instead situates every subject within a specific historical period and practical problem. For example, he teaches trigonometry by using the kind of problems that the Alexandrian Greeks, such as Ptolemy and Eratosthenes, were tackling: the distance from the earth to the moon, the radius of the earth, the establishment of longitude and latitude. Every chapter comes with biographical sketches of the major thinkers involves, as well as some practical problem that the mathematical theory would solve.
Following this procedure, Kline manages to take the most abstract of all abstract subjects, and to make it exquisitely human. In school, we are taught trigonometry by showing us how to plug numbers into a calculator. Kline shows us that trigonometry allows us to chart the earth, and measure the heavens. We encounter Newton measuring the refraction of light, and Galileo plotting the course of cannonballs. We learn how sinusoidal motion allows us to measure time, and how the Renaissance painters invented projective geometry in their attempt to create realistic perspective.
In sum, Kline shows mathematics for what it is: a tremendously exciting intellectual endeavor--one that has expanded our knowledge of the universe immeasurably. Math is not born of the dreams of philosophers (at least, not exclusively), but has been, and continues to be, integral to the solution of everyday problems. It's curious that something only accessible to the mind allows us to make sense of our senses. In short, Kline has given me the greatest gift a teacher can give--not knowledge, but wonder.
What is the basis of algebraic thinking? How did geometry develop? Why was trigonometry insufficient for measuring moving celestial objects? What was in the air that prompted Newton and Leibniz to create the basis of calculus? How and who improved on their mathematical innovations? This book has all –and much more.
It is unfortunate that the title of the book has been changed, since the target audience is less clear now. The book probably succeeds admirably at delivering a captivating account of mathematics to a reader completely, or at least largely, unfamiliar with the topic - and I am going to rate it highly for that. Only a word of warning, take good heed of the target audience, if you have not slept through your high school mathematics lessons, there is nothing new for you in this book mathematics-wise (save perhaps for the chapter on non-Euclidead geometries), and at best, the only new thing you will end up learning will be the historical background - but there are much better resources for that.