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A History of Mathematics: An Introduction [Paperback]

Victor J. Katz
5.0 out of 5 stars  See all reviews (3 customer reviews)

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Book Description

1 Nov 1998 0321016181 978-0321016188 2

One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history.



Product details

  • Paperback: 856 pages
  • Publisher: Pearson; 2 edition (1 Nov 1998)
  • Language: English
  • ISBN-10: 0321016181
  • ISBN-13: 978-0321016188
  • Product Dimensions: 23.4 x 20.6 x 4.6 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: 1,202,608 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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12 of 13 people found the following review helpful
By A Customer
Format:Paperback
"A History of Mathematics" gives a profound review of the mathematical revolution strongly interwoven within human history. Each chapter contains a well organized overview of the mathematical developments with anecdotal episodes about the heroes. Although mathmatical knowledge is required to fully bask in this book, non-mathemticians could enjoy it very much.
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1 of 1 people found the following review helpful
5.0 out of 5 stars A super reference! 21 July 2011
Format: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.
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3 of 7 people found the following review helpful
5.0 out of 5 stars A work of art 4 Jan 2001
By A Customer
Format:Paperback
As a physicist and math lover, I enjoyed every line of this beautiful book.
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Amazon.com: 3.8 out of 5 stars  13 reviews
27 of 28 people found the following review helpful
5.0 out of 5 stars A super reference! 1 May 2004
By "jayjina" - Published on Amazon.com
Format: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 7 Aug 2002
By A Customer - Published on Amazon.com
Format: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!) 1 Dec 2006
By Navigator - Published on Amazon.com
Format:Paperback|Verified Purchase
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.
7 of 9 people found the following review helpful
5.0 out of 5 stars a brief opinion 12 Jan 2005
By Matthew Bolone - Published on Amazon.com
Format:Paperback
As a phd student in economics, the study of mathematics is more than a parallel, it is a symmetrical relationship. In the study of mathematics, further appreciation of its tools and meaning can be better appreciated in an understanding of its roots and the needs of such tools. This book offers that and more. It is thorough yet comprehendible to even the casual student of mathematics.

It should be considered the premier text on the subject of mathematical history as well as a wonderfully written text of reference. A+++!
5.0 out of 5 stars Great Math Book 6 Mar 2014
By Martin J. Mulder - Published on Amazon.com
Format:Paperback|Verified Purchase
Very easy to read and understand the History
of Math. I highly recommend this book as a resource
for Math teachers.
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