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Math Through the Ages: A Gentle History for Teachers and Others, Expanded Edition (Mathematical Association of America Textbooks) 2nd Edition
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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.Read more ›
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
13.Read more ›
Most Recent Customer Reviews
Got the book fairly quickly which was great! However, I knew the book was used, but when I received it some of the pages were barely hanging on and was forced to tape them back so... Read morePublished 2 months ago by Joe
I like the structure of the book and choice of topics.
It is a very good idea to give exercises in the book on history of mathematics. Read more
Bought this book for class. But if you want to know about the history of mathematocans with all the excitement and personal lives, I would recommend!!Published 9 months ago by Amazon Customer
Another required book for a course. Some useful information, but the book is not formatted very well. Read morePublished 17 months ago by Vallon
This book will bring one up to speed on ancient problem solving techniques. It feels a little light on information, though. More detail would've been appreciated.Published 19 months ago by Tristan - New York
I WAS HAPPY TO FIND MY SCHOOL BOOKS ON A BUDGET AND ITS IN EXCELLENT CONDITION IT MAKE RETURNING TO SCHOOL WORTH ITPublished on August 14, 2013 by michele