The Nature and Growth of Modern Mathematics [Paperback]

Edna Ernestine Kramer (Author)

Book Description

ISBN-10: 0691023727 | ISBN-13: 978-0691023724 | Publication Date: February 1, 1983

The book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story - ultimately linked to modern digital computers - the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; erogodic theorems; epsilon-delta arithmetization; integral equations.

Product Details

• Paperback: 784 pages
• Publisher: Princeton University Press (February 1, 1983)
• Language: English
• ISBN-10: 0691023727
• ISBN-13: 978-0691023724
• Product Dimensions: 8.3 x 5.5 x 2 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #1,167,728 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

5.0 out of 5 stars A great history book!, November 11, 2003

By 

"jayjina" - See all my reviews

This review is from: Nature and Growth of Modern Mathematics (Hardcover)

Edna Kramer's is perhaps the best of the genre of books on the History of Mathematics.

The most pleasing feature about this book is that it is a fine balance between the mathematical ideas and the lives of the mathematicians. Best of all, it paints a sympathetic history of the times in which the discoveries were made. The use of anecdotes and "little" events in the lives of the men and women really brings to life both the subjects and their work.

Although my particular favourite sections are on the achievements of Euler, Gauss, Lagrange, d'Alambert, Ricci, Levi Civita, and Riemann, the book is truly an expansive landscape - there is coverage of virtually all the greats from the 16th century onwards. There are numerous examples from which to learn the basics of the mathematics. For instance, the sections on the history of the calculus are interwoven with simple, yet lucid examples. Equally, the more complex ideas like integral equations and partial differential equations are illustrated by examples drawn from the physical world.

All this makes the book worthwhile - it DOES NOT skirt over the Mathematics, but rather, makes an active attempt at imparting knowledge and understanding. This makes the book ideal for both the Maths specialist who is interested in history and for the generalist seeking a broad understanding without being daunted by the Maths. Kramer has done a marvellous job in meeting this tough challenge.

If this book has one failing, it is the way it skims over mathematical contributions from non-western societies, but it balances this somewhat by not overplaying the "Greek card". Some books do go on about Euclid as if he was the Newton of the ancients! Having said this, it can be excused since the book is quite old and much new knowledge has been gained on contributions from India and China in the last couple of decades. The interested reader may also wish to look up George Joseph's book, "The flight of the Peacock" for this.

An ideal book for both history and mathematics. I have had my copy for 20 years and it keeps my interest, still. Thoroughly recommended!

7 of 7 people found the following review helpful:

5.0 out of 5 stars Thirty Years and Still the Best, August 29, 2000

By 

Tim R. Niles "Nomad" (Silicon Valley) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: The Nature and Growth of Modern Mathematics (Paperback)

I first read "The Nature and Growth of Modern Mathematics" in 1970 as an engineering student with minors in math and physics. This book, over the course of a summer, provided me with the history of mathematical development at the same time leaving me with the elementals of math areas in which I had not submerged myself. The effect was a tremendous weaving together of mathematical knowledge - both the rudiments of theory and simple examples of applications - which has served me well in the decades since.

There is a great deal of power in the present era from being able to recognize the appropriate techniques from a more wide knowledge base, at times, yes, to synthesize two or more techniques to solve a potent problem or develop an application. Edna Kramers book gave me a great deal, and it is written in a way that could assist people in all occupations and with all interests.

It is a fascinating and at times awe inspring overview of math.

7 of 7 people found the following review helpful:

5.0 out of 5 stars The best of the Math History books, November 15, 1999

By A Customer

This review is from: The Nature and Growth of Modern Mathematics (Paperback)

Edna Kramer's book has 30 chapters. Each one starts with an odd bit of history. Then Edna explains the critical impact this nugget had. After that, she does an excellent write up of the mathematics involved, complete with formulas and proofs. Each chapter is then rounded out with more facts, more history, and more math. Every chapter is superbly structured. I would recommend this book for anyone who enjoys mathematics.