Math is Pretty

There 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.

Wislawa Szymborska has long been one of my favorite poets.

The Ball

As long as nothing can be known for sure
(no signals have been picked up yet),
as long as Earth is still unlike
the nearer and more distant planets,

as long as there’s neither hide nor hair
of other grasses graced by other winds,
of other treetops bearing other crowns,
other animals as well-grounded as our own,

as long as only the local echo
has been known to speak in syllables,

as long as we still haven’t heard word
of better or worse mozarts,
platos, edisons somewhere,

as long as our inhuman crimes
are still committed only between humans,

as long as our kindness
is still incomparable,
peerless even in its imperfection,

as long as our heads packed with illusions
still pass for the only heads so packed,

as long as the roofs of our mouths alone
still raise voices to high heavens–

let’s act like very special guests of honor
at the district-firemen’s ball
dance to the beat of the local oompah band,
and pretend that it’s the ball
to end all balls.

I can’t speak for others–
for me this is
misery and happiness enough:

just this sleepy backwater
where even the stars have time to burn
while winking at us
unintentionally.

~ Wislawa Szymborska ~

The latest release of LINA has several new features, but the most important one is that it enables Open Source software to be shared in a new way – virally. Now, ordinary people can share Open Source programs with each other as easily as they share photographs and music.

There is no need to worry which operating system Sandy is running because the attachment is a universal installer containing the universal Linux binaries that make up the OrangeHRM application. It will install on any operating system LINA is installed on — Windows, Mac OS X, or UNIX.

So, Frog and I have spent a year together and I’m pretty convinced that I have the world’s best dog. Of course, I was convinced that my last dog was the world’s best dog so I’m pretty biased.

Two of my three impressions of Frog were right – he’s amazingly sweet, still has webbed feet, but is not as fond of water as I originally thought. He does like Frisbees, though — I have no idea how he managed this:

He also likes to bury bones which I had only seen in old Loony Toon cartoons before having him. I try to discourage so he plays innocent, not aware that he’s wearing the evidence.

Frog fell in love with the upstairs dog, Sadie, the first few months at the new house.

He knew she liked toys, so he would bring a toy to the top of the stairs and stay there pining for her. When that didn’t work, he would bring toy after toy to the top of the stairs in the hopes that if he produced enough she would appear. And there he would wait.

And sometimes, his magical thinking would pay off:

Lately, Frog’s been mentoring a puppy that my parents adopted, Clover. Clover is an amazing ball of energy and most resembles a mosquito the way she gets in Frog’s face. Clover worships Frog and Frog is amazingly patient with her. He’s been trying to teach her basic games like chase and tug of war. It’s fascinating to watch him dangle a rope in front of her and gently tug it away. Again and again, until she starts tugging and he gently tugs back.

Unmentioned in all this is how sweet Frog is with me and the rest of the LINA crew. I think all of us have experienced him placing his head on our foot and trying to fall asleep. The deaf dog way of saying I like you and I want to know when you’re going to leave.