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Math through the Ages: A Gentle History for Teachers and Others (Maa Textbooks), by William P. Berlinghoff, Fernando Q. Gouvêa
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What's new in this edition? We have added new content and also tried to make improvements to the existing material.
There are five new historical sketches, on:
The tangent function and how it made its way into trigonometry. Logarithms, both decimal and natural. Conic sections: ellipses, parabolas, and hyperbolas. Irrational numbers. The derivative. As always, each of these comes with Questions and Projects that try to address both the mathematics and the history, challenging students to go deeper into the topic.
We also worked through the whole book to improve, correct, and update. Research on the history of mathematics continues, and we have learned new things over the last ten years. Historians make mistakes, especially when they are quoting other historians, and we have tried to correct all the ones that we knew about. Many new books have been published over the last dozen years, so the bibliography has been completely updated and the notes on "what to read next" reflect the latest resources. The questions and projects have been examined and, when it seemed appropriate, revised. The Instructor's Guide was thoroughly revised as well.
- Sales Rank: #852288 in Books
- Published on: 2015-11-06
- Original language: English
- Dimensions: 10.75" h x 7.75" w x 1.25" l, 1.40 pounds
- Binding: Hardcover
- 331 pages
Review
'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
About the Author
William Berlinghoff was educated at the College of the Holy Cross, Boston College, and Wesleyan University, where he received his PhD in Mathematics. He began his teaching career at the College of St Rose in Albany, New York, was Professor of Mathematics at Southern Connecticut State University, and was Visiting Professor of Mathematics at Colby College in Waterville, Maine. He regularly taught a mathematics course for liberal arts students that drew heavily on the historical development of the subject. He is the author or a co-author of several college texts for liberal arts mathematics, including A Mathematics Sampler (5th edition, 2001). He was also a Senior Writer for MATH Connections, a Standards-based secondary school core curriculum. Fernando Q. Gouvea was educated at the University of Sao Paulo and at Harvard University, where he received his PhD in Mathematics. He is Carter Professor of Mathematics at Colby College, where he teaches, among other things, a course on the history of mathematics. He was a participant in the Institute for the History of Mathematics and its Use in Teaching, organized by the Mathematical Association of America. Fernando was the editor of MAA Focus from 1999 to 2010, and he is now editor of MAA Reviews and of the Carus Mathematical Monographs series. In addition to this book, he has written p-adic Numbers: An Introduction (2nd edition, 1997), A Guide to Groups, Rings, and Fields (2012) and several other books, research papers, and expository articles.
Most helpful customer reviews
10 of 12 people found the following review helpful.
I've Read Better... AND Clearer!!!
By Juliann Davison
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.
7 of 9 people found the following review helpful.
Skin-deep quasi-history
By Viktor Blasjo
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.
So the authors' account would be more accurate turned on its head: Harriot's "principle" was simple enough, but the systematic factorisation theory he works out from scratch. In other words, Harriot's contribution lay not in some pixie-dust "revolutionary step" but in honest hard work. Let us not fool our students to think otherwise.
5 of 6 people found the following review helpful.
Brilliant textbook for future math teachers
By Graham Saint
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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