A History of Mathematics: An Introduction (2nd Edition) [Paperback]

Victor J. Katz (Author)

Book Description

ISBN-10: 0321016181 | ISBN-13: 978-0321016188 | Publication Date: March 6, 1998 | Edition: 2

Provides a world view of mathematics, balancing ancient, early modern and modern history. Problems are taken from their original sources, enabling students to understand how mathematicians in various times and places solved mathematical problems. In this new edition a more global perspective is taken, integrating more non-Western coverage including contributions from Chinese/Indian, and Islamic mathematics and mathematicians. An additional chapter covers mathematical techniques from other cultures. *Up to date, uses the results of very recent scholarship in the history of mathematics. *Provides summaries of the arguments of all important ideas in the field.

Product Details

• Paperback: 880 pages
• Publisher: Addison Wesley; 2 edition (March 6, 1998)
• Language: English
• ISBN-10: 0321016181
• ISBN-13: 978-0321016188
• Product Dimensions: 9.2 x 8.1 x 1.8 inches
• Shipping Weight: 3.2 pounds
• Average Customer Review: 4.0 out of 5 stars  See all reviews (11 customer reviews)
• Amazon Best Sellers Rank: #743,551 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

27 of 28 people found the following review helpful:

5.0 out of 5 stars A super reference!, May 1, 2004

By 

"jayjina" - See all my reviews

This review is from: A History of Mathematics: An Introduction (2nd Edition) (Paperback)

Katz's book is one of the best general works on the history of Mathematics around!

Its over-riding feature is that it is a TEXTBOOK - one that can be used for systematic study of the subject. Though tilted in favour of the mathematically inclined reader, the author has managed to connect the Maths to the History. The book has numerous topical exercises, sidebars and focus essays, which makes the subject easily accessible to the student. Yet, the structure and presentation are such that they also allow the book to be used simply as a reference or one that can be read purely for interest. Each chapter is followed by Exercises to assist the student to assess their learning and copious references that can be followed up for more details.

As with most good books of this genre, Mathematical developments from the last four centuries or so are most comprehensively presented. All the material is here: the "tussle" between Algebra and Geometry, the formal beginnings of the Calculus, the growth of Analysis, the development of new Mathematical techniques to tackle problems in Physics, and Probability mathematics.

The book places these developments within the socio-political context. Each chapter and main section starts with a preamble setting out the environment, the stimuli for the mathematical development to be discussed, etc. So, important events like the Renaissance, the French Revolution, etc. are discussed. In this regard, the use of Biography boxes for the main characters in the story of Mathematics helps to render the book more accessible to readers who may not be Mathematical. For instance, the chapter on Differential Equations would be inaccessible to the non-Mathematical reader were it not for such boxes retelling the lives and times of people like Bernoulli, Euler, Lagrange, and Laplace.

The early chapters deal with Babylonian and Greek developments, the latter with well presented biographies of Aristotle, Plato, and Euclid, among others. The chapters on the mathematics of the Arabs is well balanced, whilst that on India and China is possibly the best I have seen in a "mainstream" work of this type.

Where other authors like Morris Kline have almost totally ignored the contributions of these cultures to the subject, Katz has done a fine job. To note a couple of examples:

(1) India as the rightful source of the decimal place value system;
(2) Bhramagupta's research into what it usually known as Pell's equation, some 1000 years before Pell, and,
(3) Madhava's derivation of the power series for the arcsine and his appreciation of convergence over 200 years before Gregory.

Overall, a very good book that, like Edna Kramer's work, adds to the accessibility of a stimulating subject that is at the heart of the intellectual development of mankind.

22 of 23 people found the following review helpful:

5.0 out of 5 stars Maybe the best general history of math available, August 7, 2002

By A Customer

This review is from: A History of Mathematics: An Introduction (2nd Edition) (Paperback)

This book is excellent. It provides a general view of mathematics evolution that both discusses the mathematical formulation of the problems and the historic details. It is organized as a textbook, but it is interesting to read or to use as reference. For me, one of the most gratifying features was the cross cultural details that went beyond the so common vague and politically correct lip service and actually referred the content of often-forgotten important contributors.
It is interesting, for instance, to see correct and detailed references to Pedro Nunes and other mathematicians of the Discoveries time, and the relation between geometric developments and navigation problems.

13 of 15 people found the following review helpful:

5.0 out of 5 stars That's because it's a HISTORY book (and good one!), November 30, 2006

By 

Navigator (Los Gatos, California) - See all my reviews

Amazon Verified Purchase

This review is from: A History of Mathematics: An Introduction (2nd Edition) (Paperback)

It's probably bad form to write a review of a review, but I was a little chapped at reading a previous reader's complaint that this book wasn't well suited for teaching mathematics. That's sort of like complaining that your microwave oven doesn't also play DVD's; it wasn't INTENDED to do that, and this book wasn't intended to be a math text - it's a HISTORY of mathematics, just like the title says (duh).

The many fine points of the text have already been discussed in previous reviews. The single drawback of the book is its price, which might put it beyond reach of some who would like to own it. However, it certainly is worth the bucks, as it's probably the best historical overview of mathematics to be found.