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on April 3, 2004
As an overview and introduction to the history and conceptual development of mathematics, this is a very interesting book. As a primer for anyone seeking to learn or brush up on these principles, it falls a bit short.
I enjoy the history and Mr. Kline's development of this subject but I was looking more for an instructional book that would teach me these basics as it developed the ideas and history.
While it's an interesting book, it falls short as a teaching device because:
1. Answers are not provided for all exercises and I had trouble confirming my understanding.
2. Important theorems and axioms that should be memorized are hidden in the text and should be marked in bold or marked out by a similar method so the reader can recognize and review them more quickly.
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TOP 50 REVIEWERon April 20, 2016
If you were expecting math theory without the math or an opportunity to replace algebra with arithmetic tricks then you will be sorely disappointed.

Like his earlier book "Mathematic s: a cultural approach) this is a sneaky way to introduce liberal arts students to the world of mathematics by showing them a practical approach. Don't by any means mistake this for what it is not; it is not a way to cut corners as by the time you finish this book you will been introduced to just about every phase of mathematics and geometry.

Although it can be a fun approach, you will need to be prepared to learn some stuff about things such as theory of gravity.

It starts off with the historical orientation to math and why math is important.

To give you an idea of the simplicity of this book here is a sample of the contents:

a historical orientation
logic and mathematics
number: the fundamental concept
algebra, the higher arithmetic
the nature and use of Euclidean geometry
charting the earth and the heavens
the mathematical order of nature
the awakening of Europe
mathematics and painting in the Renaissance
projective geometry
coordinate geometry
the simplest formulas in action
parametric equations and curvilinear motion
the application of formulas to gravitation
the differential calculus
the integral calculus
trigonometric functions and oscillatory motion
the trigonometric analysis of musical sounds
non-Euclidean geometries and their significance
arithmetic's and their algebras
the statistical approach to the social and biological sciences
the theory of probability
nature and the values of mathematics

As you can see you're in for a lot of fun especially if you liked mathematics for non-mathematicians. Ha!
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on August 29, 2003
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.
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on January 12, 2004
This book is truly an achievement. While not intended for true practitioners, the book is entertaining while though provoking at the same time. I take it with me to my favorite coffee shop sometimes just to open it randomly and read a few pages at a time. Not only does the author weave great historical moments with the progression of mathematical thought, he covers areas such as physics, art, music, and astronomy. He has also renewed my interest in taking the subject up again after many years. I have enrolled in a course in the Calculus based on this as well as other great math books.
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on August 25, 1999
Morris Kline is an excellent author, and he does a wonderful job of explaining how mathematics works and how to use it. The book is an easy read, and at the end you'll be all fired up to go back to college and take calculus all over again!
I wish I had had the opportunity to study under Mr. Kline, because if you read his other books, you can see that he was a very thoughtful and insightful man, who simply wanted to share his love of mathematics with other people.
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on April 9, 2000
I think the author not only knows mathematics, but also knows a lot about other fields, like physics, music, and painting. He is an expert in the history of mathematics and explains well how each important mathematics concept was developed over time. However, I would like to stress that Kline knows how to teach. The structure and the helpful hits in the books are valuble resources for any instructor who wishes to teach a course using this book as the main textbook.
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on August 27, 2001
A must have for the mathmatically curious. The subject seaquence is laid out in a logical order. Beginning with the premises of inductive vs. deductive reasoning, basic algebra, geometry, and the Calculus. This is not a good book for becoming proficient in sepcific areas of mathematics, but offered for me at least, a logical reference point for approaching the core sujects. I highly recommend this book for self-study.
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on March 8, 2003
Kline, a noted historian and educator of mathematics, wrote a book that stands the test of time. This isn't of much use to anyone with high-school math who doesn't care to know why math is the way it is. For everyone else, this is a good book. Solutions to problems at the end of the book are very handy. I recommend this book along with Timothy Gowers's "Mathematics: A Very Short Introduction".
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on September 24, 1996
A Fantastic piece of literature. It is a guide to an amazing
new world for those of us, who will never become the next
Fermat or Gauss. Kline writes in such a way that you are
drawn into the whole mathematic principle, from history to
thought processes all of the time keeping the reader aware
of the implication of this new concept on our reality.
Brillant!!!!
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on July 11, 2003
This book is great but it does get pretty technical at some points. Don't let that discourage you though, just skip the parts that are too technical, they won't distract you from getting the major points.
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