Numbers: A Very Short Introduction

Screen Shot 2013-07-04 at 8.26.25 AMIn most people’s minds, math is about numbers and numbers are math. The connection is so prevalent that sometimes it’s very hard to explain to people that you are actually doing math when all you do is write unrecognizable symbols on a blackboard or a piece of paper. Nonetheless, the study of numbers can open up vistas to all sorts of interesting mathematical objects, as well as a lot of interesting and non-trivial research on numbers themselves. For instance, integers are probably the most accessible of all numbers, and yet certain properties of integers are so hard to understand that even those professional mathematicians who have worked on them all their lives feel like they have only been scratching the surface of all the problems that one can possibly dream of.

This short introduction introduces the reader to the full richness of numbers, the way in which various sets of numbers arose, and various intriguing and fascinating properties that various collections of numbers have. The book is particularly detailed and comprehensive when it comes to discussing various sets of integers and their properties. I am a theoretical physicist with a lifelong armature interest in math, but even I have never heard of several collections of integers that had been discussed in this short introduction.

The book is very detailed, and it doesn’t condescend to the reader. Many examples are given somewhat detailed proofs, and at no point does the reader get the impression that this is a watered-down popular math book. Many arguments can be challenging and need to be read carefully and if you are not willing to untangle them you will not benefit too much from the text. I certainly appreciated all the effort that has been put into making this book this educational and informative.

Unfortunately, the book’s biggest strength is also its biggest weakness. This book will probably be on the advanced side for the most general readers. It is certainly amongst the most intellectually demanding of all VSI books. If you are up for a challenge, however, it will be the best introduction to numbers short of actually opening a textbook on the subject.
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Bojan Tunguz

Bojan Tunguz was born in Bosnia and Herzegovina, which he and his family fled during the civil war for the neighboring Croatia. Over the past two decades he has studied, lived and worked in the United States. He is a theoretical physicist with degrees from Stanford and University of Illinois. Tunguz has taught physics at several prominent liberal arts colleges and has been writing about physics, science and technology for more than a decade. He also has a wide spectrum of interests, and reads and writes about current events, society, culture, religion and politics. Over the years he has reviewed many of the books that he has read, and posted his reviews on various online outlets. In 2011 he had become a top 10 reviewer on Amazon.com, where he continues to be very active. Aside from reading and writing, Tunguz enjoys traveling, digital photography, hiking, and fitness. He resides with his wife in Indiana. You can follow my review updates on the following pages as well: Facebook: http://www.facebook.com/tunguzreview Twitter: http://www.twitter.com/tunguzreviews Google+: https://plus.google.com/u/0/104312842297641697463/posts

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