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Mathematics for the Nonmathematician (Dover Books on Mathematics), by Morris Kline
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Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen.
Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts.
In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.
- Sales Rank: #18552 in Books
- Published on: 1985-02-01
- Released on: 1985-02-01
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x 1.28" w x 5.43" l, 1.46 pounds
- Binding: Paperback
- 672 pages
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
Most helpful customer reviews
145 of 145 people found the following review helpful.
This is a classic and a great book.
By Metallurgist
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 had previously 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. For instance, there is a chapter on oscillatory motion that describes the motion of a spring-weighted bob, leading to the development of mechanical watches and clocks.
While I thought that I had a reasonably good mathematical education, I found that I was largely ignorant of topics such as non-Euclidian geometry and advanced algebra (for instance symbolic logic and set theory). While this book provides only a fragmentary introduction to these topics, it was enough to let me get a glimpse of the boarder world of mathematics. The breadth of topics that are covered should not put off potential readers. The aim is to survey mathematics, rather than provide an in-depth presentation of any of the topics that are covered. As such, it is not a substitute for a good geometry, algebra or any other text on a specific mathematical subject. For the most part, nothing beyond high school mathematics is required and those more advanced topics such as calculus are covered in chapters that were prepared so that they can be skipped without destroying the subsequent continuity of the book. The presentation is clear and focuses on the readers understanding, rather than on being as rigorous as possible. Much of the treatment is based on simple geometrical arguments and straightforward high school algebra. The book concentrates more on how the mathematics was developed than on calculating for its own sake, but there are many numerical problems, whose solutions are provided in the 1967 Dover edition, which contains the Instructors Manual. The previous edition, published under the title of Mathematics for Liberal Arts, contains only the solutions to selected problems.
I purchased this book because it had good discussions of many of the classical problems that had concerned man for millennia. For instance, what is the diameter of the earth, how far away from the earth are the moon and sun, how does one measure distance on the spherical earth? Most books discussing Newton mention that he developed this theory of gravity in part based upon knowledge of the size of the moon and its distance from the earth. In some books this is just stated as a fact, in others it is stated as something worked out by Greek mathematicians more than 1500 years previously. Professor Kline goes through these calculations, showing that they are very simple and straightforward. The book also goes into some topics that are not even touched on in freshmen physics courses. For instance, there is an excellent discussion of how the weight of an object varies with latitude. This book correctly accounts for the rotation of the earth and how the force that this produces varies with latitude (an approach developed by Christian Huygens) and shows that this is much more important than the effect due non spherical nature of the earth (i.e., the earth being slightly flattened at the poles means that the distance to the center of the earth is smaller at the poles, thereby slightly increasing the force of gravity there.)
The book includes some special topics of interest to liberal arts majors. There is a nice description of the development of prospective geometry and the influence of renaissance painters on the development of mathematics. There is also a discussion of sound waves and the mathematics of music. There is also a good discussion of the influence of classical Greek philosophy and how this shaped the development of mathematics and how modern mathematics has overturned the idea that there is such a thing as absolute truth in mathematics (i.e., there are many different geometries and algebras beyond that envisioned by the Greek and renaissance mathematicians).
The historical development of mathematics is included in the discussion of individual mathematical topics and in a few special chapters devoted entirely to historical development. I found that these latter chapters were the weakest part of the book. They present an entirely Euro-centric approach, largely leaving out the contributions of the Babylonians, Indians and Chinese. I recommend Derbyshire's "Unknown Quantity" for a more modern and more balanced approach. This is a small quibble that I do not feel measurably detracts from the very high quality of the rest of the book.
All in all, this is a great book for those who are interested in how mathematics was developed and for those who want a general survey of mathematics, be it for a course, for a review, or for a deeper understanding of the subject. I found that it greatly enriched my understanding of math fundamentals and the thought process leading to the development of mathematical concepts.
115 of 123 people found the following review helpful.
A big book about math
By Steve and/or Jodene
This book was originally written as a textbook (for a math-for-the-non-mathematician type course). It can be used as one (though as a textbook it's a bit dated), read cover-to-cover for edification and pleasure (the style is a bit more instructional than the average popular math book), or dipped into here and there for the topics the reader personally finds interesting. With well over 500 pages of fairly small print, there's a lot here, covering a wide variety of topics, with (it seems to me) particular emphasis on history, geometry (of various kinds), and applications of math to physics. If you leaf through the book, you'll find some pages of nothing but text, some pages full of geometrical diagrams, some of equations and formulas, and even a few Renaissance paintings (in the discussion on mathematical perspective). With so much here, readers will probably find some parts more interesting than others--though which parts are the interesting ones may be a matter of personal opinion.
0 of 0 people found the following review helpful.
Math Need Not Frighten You
By Jonathon York
As someone who has a background in the humanities who also happens to love "stinky math books", this book is absolutely fantastic. I encourage anyone who has been intimidated by mathematics at some point to pick up this book. It was originally titled "Mathematics for the Liberal Arts" but perhaps someone pointed out that "Mathematic" and "Geometric" are part of the classical Liberal Arts Quadrivium. Kline's explanation of derivatives is especially worthwhile.
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