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Mathematics for the Nonmathematician (Dover books explaining science) – Review by Kenneth Ellman

A Good friend you should keep with you and give to your children

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,