Customer Reviews

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

5 star:		(6)
4 star:		(2)
3 star:		(1)
2 star:		(1)
1 star:		(1)

 

 

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.

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.

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.

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+++!

Ok, the title probably sounds pretty dumb so let me explain. Trying to read the first 6 or so chapters was a nightmare. Maybe I haven't taken the right classes yet? I don't know but I could hardly get through any of the actual math. This book made me scared of Euclid! All I can see when I think about this book are random circles and angles and how it's all supposed to mean something. I also remember trying to learn about the Chinese Remainder Theorem from this book. Result: I still don't even have a clue what it's about.

Place my order on August 21, 2010 and receive @ Sept 2. the condition of my book fits the description you described.

While this subject may be very boring, this book is clear and concise and walks the reader through the development of modern mathematics. It isn't exactly chronological and instead chooses to follow a subject based time line. A solid purchase for those students who have utterly confusing professors.

It's a good comprehensive study of math's roots. My wife used it for her master's program.

there have been glowing reviews for this text but i do not think they accurately reflect the book in its entirety. that is to say, that yes, as a history book, this is a good reference book with a lot of information. however, as a book to teach students about mathematics, it falls far from even being decent. the text is poorly laid out, often fudging the exactness of crucial definitions, with the finer details being left to the reader to figure out in each chapters example problems. the chapter problems in general require a much greater of mathematics than the book is willing to give and do not build very well upon one another. good for reading about the history, but if you're trying to learn the math behind it, you may just wind up very, very frustrated.

I'll try not say anything too disruptive. (Nevertheless, an official range of love it to hate it seems to say it's more than okay to just let the emotions rip.) This is just the sort of technical history that William Berkson would call out as "a pack of lies." For a much more historically accurate and far less shallow take on this topic, i highly recommend A History of Mathematics: From Mesopotamia to Modernity (Also why in the world would Mathematical Review ever publish a review of Hodgkin's book by Katz?!?! When I read Katz's review of Hodgkin, I felt immediatly uncomfortable since there is the very real possibility of Katz having the motivation to do all in his power to rid the marketplace of any competitor.)