Customer Reviews:
Showing reviews 1-5 of 12
 mathematical must read December 15, 2009
Richard Brice
1 out of 1 found this review helpful
this book is more than 50 years old, but it still provides valuable insight for any math-oriented high school student and especially so for those students who plan for careers in mathematics or any of the sciences.
 Entertaining and educational for the few November 12, 2009
Gaetan Lion
2 out of 2 found this review helpful
This book is for very few as it is not for the following group of readers:
a) only peripherally interested in math;
b) interested in math but wanting to learn more in a concise manner and readily bored with exhaustive math history and early 20th century verbosity;
c) mathematicians who already know that stuff;
d) interested in math but requiring well organized and structured material.
If you do not belong to any of the above four groups of readers, you probably will like this book. You may even love it. To improve the probability you will like it you should not read chapters sequentially. This will bore you. Instead jump in directly to the mathematics domains you are familiar with and you like best. For instance, chapter VII covers Probability and chapter IX covers Calculus. If you like Geometry, you are in luck as the authors dedicate two chapters to it (IV and VIII).
The chapter on calculus covers a lot of grounds including not only derivatives but also definite and indefinite integrals, calculus and the laws of motions, and trigonometry. Your head may spin after this broad and deep excursion into calculus. And, this may be one of the authors' most successful chapters.
The authors divulge a lot of fascinating information even though the latter is not always easily extractable. This includes very intuitive explanations of the discovery and calculations of Pi, e, i, and logarithms. They explain how mathematicians leveraged those discoveries. The numbers Pi and e have so many applications that they suggest our civilization in terms of mathematical understanding and its practical application would be truly primitive if not for them (Pi, e). Similarly, they show how the invention of logarithm essentially powered math and physics forward by rendering complicated calculations simple (replacing exponents by multiplication, multiplication by addition, etc...). They also make fascinating connections between algebra (equations) and geometry (visual representations of the same equations).
Their narrative on large numbers is pretty interesting. It taught me that even though Sergey Brin and Lawrence Page are very successful billionaire geniuses, they apparently do not know how to spell math terms. Indeed, Google refers to a very large number consisting of 1 followed by 100 zeros. But, it is spelled Googol! At least, Brin and Page got Googleplex right when naming the company headquarter (Googleplex equals 1 followed by a Googol of zeros). Those numbers are gigantic as The Harper Collins dictionary of Mathematics discloses there is only 10 to the 85th power number of atoms in the universe (less than a Googol that is 10 to the 100th power and obviously a lot less than a Googleplex).
In the appendix of the calculus chapter, the authors open the door on upcoming mathematical developments. Indeed, they introduce Pathological Curves which will become a foundation for Mandelbrot's Fractal Geometry as explained in The Fractal Geometry of Nature. In turn, the latter will leverage this concept to develop a new theory of finance in The (MIS)Behaviour of Markets: A Fractal View of Risk, Ruin, and Reward. And, Taleb will turn the same concept into a bestseller in The Black Swan: The Impact of the Highly Improbable. In the same appendix, the authors also introduce the Criscross Curve. Stephen Wolfram will leverage this concept and develop cellular automata as explained in A New Kind of Science. As you can see, ultimately everything is related.
However, if you want to learn math basics in a more effective and efficient manner, I recommend instead the series: Forgotten Statistics: A Refresher Course with Applications to Economics and Business, Forgotten Algebra and Forgotten Calculus. Those will give you a pretty good foundation on which to build upon. If you want to deepen your knowledge of statistics I also recommend the excellent Intuitive Biostatistics.
Philosophy of Mathematices September 13, 2009
Kirk 19707
1 out of 1 found this review helpful
The book provides a logical and entertaining explanation of the principals of mathematics and their development.
gift August 20, 2009
Frances F. Sabin (Portland, OR USA)
Book given to Grandson, a junior in high school who has a passion for Mathematics and how it can be applied. He reports he is very pleased to have it.
Math Puzzles That Challenges the Brain November 10, 2006
Kenneth N. Steward
4 out of 6 found this review helpful
I am thoroughly enjoying the challenges to my brain that I am finding in this book. it was well worth the price I paid
Showing reviews 1-5 of 12
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