Product Description
Erudite and entertaining overview follows development of mathematics from ancient Greeks, through Middle Ages and Renaissance to the present. Chapters focus on Logic and Mathematics, the Number, the Fundamental Concept, Differential Calculus, the Theory of Probability and much more. Exercises and problems.

CUSTOMER REVIEWS (Average Customer Rating: 4.5 based on 25 reviews)

Fair. by Austin Somlo (Vincentown, NJ)

3 Stars
July 07, 2009
Mathematics for the Nonmathematician is a fair read. Somehow, it feels a lot more a suitable book for anyone wishing to become a mathematician but isn't sure what it is like. There is some good stuff to learn from, and sometimes, there are worked out solutions to problems in almost every chapter. All in all, you can't go wrong with Mathematics for the Nonmathematician.

Mathematics For The Mathematical Junkie by Daniel Myers (Greenville, SC USA)

4 Stars
May 16, 2009
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." The abstruse insights in which this book abounds can only be reached by a competent grasp of mathematical methodology. That being said, Kline is a whimsical and almost lyrical writer - a bit of a shocker for a book on mathematics! He has a wry wit which he gives full rein to herein. In describing the Greeks and their obsession with astronomy, he observes, "The problem of finding the design of planetary motions continued to engage the minds of the Greeks, possibly because they were not distracted by the `heavenly' stars of stage, screen, and radio with whom many modern minds seem preoccupied." His prose is rich in such quips. The book is actually a lark to read at points. But the heart of the book is unvarnished mathematics - with which I have a slight problem. He covers the derivation of trigonometric functions splendidly, as well as their uses, as well as the kinetics, or mathematics of motion. But his account of the calculus is rather sparse for my taste. Any treatment of derivatives and integrals without mention, account or derivation of the fundamental theorem is, to my mind, lacking. Further, his derivation of the quadratic formula is absurdly complex and takes pages. It is true, as one reviewer noted, that most students are only presented with the equation and not given its derivation. But the derivation is - comparatively - simple. I worked it out on my own when I was in school, and it need only cover one page, at maximum. The book is really quite an achievement. But I'm only giving it four stars because it is extremely uneven: No fundamental theorem of the calculus but reams about projectile motion etc. As a bonus, I'll tack on as a comment, once the review is posted, Kline's mischievous proof that 2=1 for the prospective reader to see if he can suss out the flaw in it. If the mathematics leaves you stymied this is not the book for you. On the other hand, if you follow the mathematics quite easily, but are left baffled and staring at the page, determined to suss out the mathematical solecism embedded in it, then you poseess just the sort of questing mind that will delight in this tome!

All Asians, not only mathematicians or scientists should read this book by Lee Hong Kyu (Seoul Korea)

5 Stars
March 03, 2009
Asians did not develop science or mathematics as Greeks did. People here in Korea are still talking about ancient things while Galilleo and Newton solved problem hundred years ago. When a friend of mine read this book he cried, because of his long term ignorance of wisdom western tradition made and written in this book. Zhu Si asked his student study nature, exactly the kind of works Galilleo did, but they repeated those teaching without doing experiment. Cofucians are still teaching what Zhu Si said.

A Good friend you should keep with you and give to your children by Elmann (Newton, New Jersey United States)

5 Stars
January 01, 2009
From Kenneth Ellman, ke@kennethellman.com Morris Kline the prolific author of "Mathematics for the Nonmathematician" (previously known as "Mathematics for the Liberal Arts" ) was one of those rare teachers who not only knew their subject throughly and intimately but also loved the manner and way mathematics integrated with all aspects of human life and activity. I have owned his books and given away copies, for many years. This is an "old" book having been published in 1967, so you would think it is far better known that it actually is. Kline bridged the gap for so many people who felt or feel somewhat estranged from the language of math. His books are wonderful, warm and comfortable as they take the "Nonmathematician" into the world of symbols and numbers and equations and they kind of hold your hand during this excursion into the world of the language and culture of math. You may find yourself learning this math without even realizing it as the ideas are so intertwined with the culture and history of man. The current Dover edition contains the Instructors Manuel with answer keys; a very valuable resource. This particular book successfully integrates human history and scientific accomplishments with mathematics. A thread runs through the Kline book keeping the connection of the basic human search for knowledge and adaptation with the development of mathematics as a language and expression. As a survey course and introduction it leaves little to be desired. Any work will be subject to criticism, but if you measure the book by the standard of what the student will have learned after completion of a course with this as the textbook, you will be very, very, pleased. Particularly the extensive "Recommended Reading". Unfortunately this text is not normally used in high school nor college and so many students who could truly benefit will not get exposure to Professor Kline. Perhaps some of the instructors find it difficult to teach as this book does, but then that is the fault of the instructor not the book. It is my opinion that books such as this greatly aid the interest in math and will keep many students of any age attached to the use of math as a language and a part of the culture in which they live. Inevitably death came to Kline in 1992 so the time has long passed to take his classes at New York University where he was a Professor of Mathematics. However he is well known and left an extensive legacy of articles and books to allow this deceased Professor to continue teaching. If only the Teaching Company has made a video with him! As reported in the New York Times Obituary for Morris Kline he wrote a 1986 editorial in Focus, a Journal of the Mathematical Association of America and is quoted: "On all levels primary, and secondary and undergraduate - mathematics is taught as an isolated subject with few, if any, ties to the real world. To students, mathematics appears to deal almost entirely with things which are of no concern at all to man". He is also quoted as stating: "the greatest contribution mathematics has made and should continue to make was to help man understand the world about him." This Kline book can teach math, science, history, and civilization from this unusual prospective. It would be quite refreshing for students to be able to grab onto this type of portrayal and learn about history with numbers while learning how numbers were used, needed and applied in history. The text consists of 24 chapters with everything from the Classical Greek Period, Arithmetics, Logic, Algebra, Geometry, Gravitation, Calculus and etc. This is a book for continual enjoyment and review. If you children learn what is in this book you will be happy. Kenneth Ellman, ke@kennethellman.com

Really good textbook. A tad dry, though. by Mike (NYC)

4 Stars
December 10, 2008
As far as math textbooks go, this is one of the best written. If you want a one volume refresher on arithmetic, geometry, etc., this is your book. Of course, as far as that goes, there's not much comparison. Aside from Quine, Russell, Whitehead and Einstein, most modern mathematicians simply cannot write. Textbooks as a genre do not tend to be spectacularly interesting either. For what it is, this book is great. I used it to refresh my math knowledge before tackling some mathematical philosophy. It was up to the task. The author has a splendid grasp of math and an above average knowledge of history (though he does make some fairly large oversights and generalizations, esp with the Greeks) which he blends in a refereshing way. On the downside, the examples are a bit too abstract for an intro book, but they're less abstract than most other textbooks. Additionally, some of the example problems are very hard to follow. Lastly, for long stretches, the book is ungodly dry. If you can afford it, I'd opt for Newman's 4 volume "World of Mathematics", also available from Dover instead. It's about $50 for the set. In addition to being a better introduction, it has a variety of primary sources written by mathematicians themselves selected for their relevance to particular topics. It's actually, dare I say, fun to read.

SIMILAR PRODUCTS

	Mathematics and the Physical World (Dover books explaining science) by Morris Kline (Author) Stimulating account of development of basic mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations and non-Euclidean geometries. Also describes how math is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, other phenomena.
	Calculus: An Intuitive and Physical Approach (Second Edition) by Morris Kline (Author) Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967...
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	The Language of Mathematics: Making the Invisible Visible by Keith Devlin (Author) "The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life—patterns that exist in the physical,...
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