Monday, April 13, 2009

Review of ‘Taming The Infinite’ by Ian Stewart

This is a fantastic book on the history and applications of mathematics. It starts with Hindu Arabic numerals and ends with Chaos Theory. Of course every major mathematical theorem or topic during this period could not be stated in a book of this size and as the author states he had to be selective. My only complaint about the selection is the lack of ‘linear algebra’ because it is perhaps the second most (first being calculus) powerful mathematical tool ever invented.
To fully appreciate this book you must have a reasonable mathematical ability such as a good pass at Further Mathematics A level or equivalent.
Stewart does write in a way that will appeal to most readers and also you can dip into any chapter without digesting the previous chapters. The author has hit the right tone and progression.
A lot of research and time must have been invested into writing this book because of the coverage of applications, the history behind important mathematical developments, profiles of the leading mathematicians etc. I really do like the broad range of mathematical applications throughout the book. The author explains where differential equations are used in the field of physics and modern technology such as radio, tv and commercial jet aircraft and how important Navier Stokes Equation is in fluid mechanics. It goes on to explain where coordinate geometry and trigonometry are used in real life such as graphics, stock market fluctuations, navigation, surveying etc. This is an excellent resource for any A level mathematics teacher who wants to inspire his/her pupils.
The history of mathematics starts with the Hindu Arabic numerals and how they were brought to Europe by Fibonacci. It highlights major historical figures in the mathematics by placing a brief biography in a light shaded grey with an image of the mathematician. However I did not find this sort of feature for Leibniz which is a serious omission since he and Newton founded calculus.
I found the following minor typos:
1. Page 73 the result ‘sin(theta/2)=sqrt(1-cos(theta))/2’ should be ‘sin(theta/2)=sqrt(1-cos(theta)/2)’.
2. On page 156 the statement of Riemann Hypothesis should read ‘complex zeros lie on the line z=1/2 plus or minus it’ not ‘z=1/2 plus it’.
3. Page 260 the statement is written ‘x(t+3)’ should be ‘x(t+ epsilon)’.
This is an excellent book and would recommend that anybody interested in mathematics should purchase this book. The book is a fantastic resource for any college or university library.
Kulδεερ Siηgh
Sunday, 12 April 2009
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Gabriel said...

I do agree with you, this is an excellent book in History of Mathematics, making Maths coming alive as well.
However I was surprised by a comment related to Archimedes, attributing to him the fact that he could have used huge mirrors to burn Roman ships. It has been proved that in spite of what legends says about that, it would have been impossible to build mirrors at that time capable of focus the sun rays with such precision.

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