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Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition (Mathematical Association of America Textbooks) 2nd Edition

3.8 out of 5 stars 18 customer reviews
ISBN-13: 978-0883857366
ISBN-10: 0883857367
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Due Date: Dec 18, 2016 Rental Details
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Editorial Reviews


'This is a beautiful and important book, a pleasure to read, in which the history recounted fully illuminates the mathematical ideas, and the ideas themselves are superbly explained: a wonderful accomplishment.' Barry Mazur, Harvard University

Book Description

Where did maths come from? Who thought up all those symbols, and why? What's the story behind negative numbers? The sketches here answer these questions and many others in an informal, easygoing style that's accessible to teachers, students, and anyone who is curious about the history of mathematical ideas.

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Product Details

  • Series: Mathematical Association of America Textbooks
  • Hardcover: 288 pages
  • Publisher: The Mathematical Association of America: Oxton House Publishing; 2 edition (December 2003)
  • Language: English
  • ISBN-10: 0883857367
  • ISBN-13: 978-0883857366
  • Product Dimensions: 6 x 1 x 9 inches
  • Shipping Weight: 12.8 ounces
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #48,814 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Juliann Davison on January 23, 2010
Format: Hardcover
As a college senior majoring in Mathematics Education, I needed to take a Math History class. I read two books that focus on the history of mathematics; one of those books was Math Through the Ages. I found this book, especially in comparison with the other book, Journey Through Genius, to be disjointed, redundant and vague. The first part of the book reads like a typical math history book and the second part repeats the information given in the first part but reads more like a textbook, including questions and projects that pertain, loosely, to the information offered in each section. I found that the questions were often irrelevant for anyone not specifically majoring in Math history, which is fine for a history book... unless that book claims to be great for students of math education. Also, I felt that the questions and projects asked more from the student than the book gave to the student. It is one thing for the projects to expect extra research, but the point of a book is to give you the knowledge you need, especially to answer its end-of-section questions, not just pose more questions than it answers. Really, if you want a better understanding of Mathematics and its history, check out Journey Through Genius. It reads better and offers more detail in explaining concepts that pertain to today's mathematicians.
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Format: Hardcover
This is a superficial history pandering to future teachers. The insights that history can bring to the classroom are desperately needed to improve mathematics education, but this book is too vapid and uncritical to serve the cause well. Consider for example the following piece of pseudo-history.

We are told that "it was a truly revolutionary step forward at the time" when Harriot "proposed a simple but powerful technique for solving algebraic equations: Move all the terms of the equation to one side of the equal sign" (p. 81). An equation in such a form can of course be solved by factoring, and, according to the authors, "a lot was known about factoring polynomials, even in Harriot's time, so this principle was a major advance in the theory of equations" (p. 82).

One can only hope that the reader will recognise the tell-tale signs of hot-air pop-history in this baloney. How could such an utterly trivial idea have been "a truly revolutionary step"? And how come previous mathematicians knew "a lot" about factoring polynomials yet somehow failed to see how to apply it to equation solving? Did they sit around and factor polynomials all day just for fun? It doesn't make any sense.

A very different picture emerges if one studies actual history instead of this unsubstantiated sensationalism. In Harriot's book, the "truly revolutionary" idea of moving the terms to one side is never even mentioned but rather taken for granted as the triviality that it is. Instead, the book is a long tabulation of expansions of expressions of a variety of forms such as (x+a)(x+b)(x+c), (x-a)(x+b)^2, etc. The resulting catalogue of "canonical forms", as he calls them, can then be read backwards to find the factorisation and hence the roots of a given equation.
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Format: Hardcover
I came across this book because a friend of mine uses it in a college class for math ed. It's really well written and makes the material accessible for people whose math background isn't necessarily very strong. I bet it could even be used for high school students. The exercises and projects are really good, too.
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Format: Hardcover
If you like math and want to read a short history of it, you'll like this book. It is written at a "popular mathematics" level, so it is accessible to nearly anyone who would take an interest in it. The writing is vibrant and to the point. The content is exemplary for a first look at the subject. The structure of the book is practical, intelligent, and effective. It begins with a 59 page summary of the history of mathematics, and this summary hits the high points. Then there are 25 chapter sketches over the next 179 pages, the chapter lengths being either 6 or 8 pages (meaning numbered pages, where a book leaf has 2 pages). These sketches discuss a single topic from the history, going into detail not given in the summary. The sketches and the summary each conclude with 2 pages of questions and projects that are as interesting and stimulating to read as the rest of the book.

Throughout the book the authors refer the reader to books and articles listed in their bibliography, which has 141 entries. After the 25 sketches there is a 7 page section called "what to read next" which directs the reader to specific math books and also to web sites they believe will be especially helpful. They include in this discussion 15 historical books they think you ought to read. This section could be thought of as a partial annotation of the bibliography.

Here are the topics covered in the sketches:

1. writing whole numbers
2. where the symbols of arithmetic came from
3. the story of zero
4. writing fractions
5. negative numbers
6. metric measurement
7. the story of pi
8. writing algebra with symbols
9. solving first degree equations
10. quadratic equations
11. solving cubic equations
12. the pythagorean theorem
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