Start a Math Library for 50$ (and a penny)
Sunday, December 28th, 2008There are several great lists on well-written mathematics books on Amazon and other sites, but they all cost hundreds to thousands of dollars. There is nothing for the poor, aspiring mathematician on a budget. So here, for first time, is a collection of books that are inexpensive and meet the following criteria:
- Extremely well-written with clear presentations
- Easily read in discrete chunks
- Beautiful and plentiful illustrations
- Breadth and depth of subject matters
- Accessible to anyone who has mastered Calculus
The different books in the library are diverse and filled with everything from brilliant expositions of modern mathematical topics, original papers by the greatest mathematicians in history, and popular mathematical puzzles and games.
Mathematics: its content, methods, and meaning. The first book on the list was the Princeton Companion to Mathematics of it’s day. With contributions from some of the greatest mathematicians of the last century, Mathematics: its content, methods, and meaning, covers everything from real analysis to group theory. At over 1000 pages and filled with illustrations, it is an extremely accessible introduction to several mathematical subjects.
At the time it was published, Professor Morris Kline called it an ” … amazing panorama of mathematics proper … the best answer in print to what mathematics contains both on the elementary and advanced levels.” On Amazon, the Dover edition will set you back $25.71 (I purchased it for approximately $10 during a sale) and the 1963 MIT 3 Volume set will set you back $13.88.
God Created the Integers. Edited by Stephen Hawking, this 1300 page volume contains the original works of mathematicians from Euclid to Kurt Godel.
Reading the original works of great mathematicians is important for several reasons. One of the most important is that it reveals the very human and creative nature to mathematical discovery. Mathematics is more enjoyable when one interacts with the original documents with all their quirks and experiences firsthand how much art and creativity is involved in the process. I recently purchased a new copy for $3.99 at Borders. Used copies sell for the same amount on Amazon ($4.39 currently).
The Road to Reality. For applied mathematics, I originally was going to complement the above with Hawking’s “On the Shoulder of Giants” which has many of the original works of Physics. This would have kept the price under $50. Physics does not age as well as Mathematics, though, so I have substituted “The Road to Reality”. Penrose’s book provides a modern and accessible introduction to modern physics and applied mathematics.
Reading this book, one feels like a graduate student in Oxford listening to Penrose give a lecture on an English afternoon. It is beautifully illustrated and the mathematics used in modern physics is carefully and intuitively laid out. It can be purchased for $14.72 used on Amazon.
The Colossal Book of Mathematics.The most playful book on the list is by one of the greatest popular mathematics writer of this and the last century — Martin Gardner. I grew up reading his columns in old Scientific Americans in my high school. Gardner knew better than anyone how to make mathematics fun, how to recapture that moment when you first realized how beautiful and unexpected its results could be.
This book contains his best columns over several decades, from Surreal Numbers to the Game of Life to Penrose Tiles and the Plainiverse. It’s a wonderful book and can be purchased used for only $15.60 on Amazon. And, of course, it is filled with the same beautiful illustrations as the others.
How to Lie With Statistics.The final book on the list is not a formal introduction to statistics (see Kolmogorov in Mathematics: its content, methods, and meaning for that), but it critically teaches skepticism towards the application of mathematics. It is also very fun and can be the book in your library that you can lend to friends.
Statistics – like many mathematical disciplines – is widely misused. Anyone who reads this book and anyone can will be able to discern when politicians are lying, even when they are talking about subjects the listener knows nothing about. In medicine, readers will be able to discern which procedures have no medicinal value even when backed up by studies. Whether the subject is crime, sports, immigration, or the environment, this book will provides a magic decoder ring to detect when numbers are being used to mislead rather than inform. It can be purchased used on Amazon for $1.42.
Altogether, the total comes to $50.01 for over 4,000 pages of mathematics if you buy used. And it’s only slightly more if you buy new. If you are on a budget, you will not regret buying any of these books, even with the free resources of Wikipedia and Arxiv.
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