The Nature and Growth of Modern Mathematics

By Edna E. Kramer

Book Overview

Now available in a one-volume paperback, this 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; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.

• Format: Paperback
• Language: English
• ISBN: 0691023727
• ISBN13: 9780691023724
• Release Date: February 1983
• Publisher: Princeton University Press
• Length: 784 Pages
• Weight: 1.78 lbs.
• Dimensions: 1.4" x 5.5" x 8.5"

Customer Reviews

A great history book!

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!

Thirty Years and Still the Best

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.

The best of the Math History books

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.

Excellent text for those interested in advanced mathematics

This book gives a detailed view of the who and why in the world of mathematics. Included are the actual concepts and proofs on a simplified level. I have taken advanced courses in math but only after I read this book did I understand the reasons for the way mathematics developed and the way mathematicians answered their critics, which is never covered in formal college cources. Highly recomended, easy to read.

The Best Documented History of Mathematics Ever

MS Kramer's THE NATURE AND GROWTH OF MODERN MATHEMATICS is the best book ever written on the subject of mathematics development. It gives an anthology of the history of modern mathematics and some antiquity items that are the root of mathematical development. It is a true history of mathematics because it gives not only the WHO did it but What they did (the mathematics piece that was added in the big puzzle). It presents equations, formulas, and their relationships with pure mathematics and scientific discovery in an easy followed nonthreating manner. This is a mathematical science book that should be read by every mathematician, scientist, engineer, and even lay persons with an interest in the history and development of human knowledge