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Mathematics Reading List For High School Students?
Troy writes "I'm a high school math teacher who is trying to assemble an extra-credit reading list. I want to give my students (ages 16-18) the opportunity/motivation to learn about stimulating mathematical ideas that fall outside of the curriculum I'm bound to teach. I already do this somewhat with special lessons given throughout the year, but I would like my students to explore a particular concept in depth. I am looking for books that are well-written, engaging, and accessible to someone who doesn't have a lot of college-level mathematical training. I already have a handful of books on my list, but I want my students to be able to choose from a variety of topics. Many thanks for all suggestions!"
How to Lie with Statistics, Darren Huff, 1954
*** Ponder
was full of the sort of stuff that's fascinating to inquiring minds. I read one of his collections many moons ago and was enthralled! Not common to find a math book that could be called a "page turner"
Link is to a CD-ROM of all his books
http://www.amazon.com/Martin-Gardners-Mathematical-Games-Gardner/dp/0883855453
The fact that no one understands you doesn't mean you're an artist.
Prime Obsession: A well-written history of the still-unproven Riemann Hypothesis. Maybe one of your students will solve it over summer break!
I really enjoyed this book when I was at that stage... http://books.google.co.uk/books?id=wUdtVHBr-OQC Really a book about operational research, but covers lots of maths in a really applied accessible way with examples from history (spread of cholera outbreaks, optimal fleet size to avoid submarines in WW2, enigma machine etc.) Lots of exercises, and each section is relatively self contained - so ideal for starting off the kind of short projects you are talking about. Highly recommended...
Let them loose on The Feynmann Lectures on Physics. Quite readable and bound to get them interested in one branch or another of physics.
The Golden Ratio -- or some other book on the same constant -- which goes into things like sunflowers and nautilus shells IIRC.
Mathenauts: a collection of sci fi short stories in which (in most cases) the hero is a mathematician.
https://app.box.com/WitthoftResume Code: https://github.com/cellocgw
If you're trying to get kids interested in the possibilities of math I would suggest Bringing Down The House, about the MIT Blackjack team.
Computers allow humans to make mistakes at the fastest speeds known, with the possible exception of tequila and handguns
You might look at some of Simon Singh's stuff if you haven't already- there are some good chapters in The Code Book regarding the basics of public-key cryptography which don't require any more than a basic education in algebra.
Not strictly mathematics, but Richard Feynman's "autobiography" might be a good one for inspiring your kids to show what they can do with their math knowledge.
Taking guns away from the 99% gives the 1% 100% of the power.
Courant and Robbins, "What is mathematics?"
My first program:
Hell Segmentation fault
I suggest Freakanomics.
Although not really a pure math book I think you can see the relevance. I found it very enlightening to read and it provided a very interesting insight into odd things like Why Sumo Wrestlers Cheat and How much Crack Dealers really make an hour.
IMAGE VERIFICATION IS EVIL!
I was thinking something similar, but wasn't sure if it would be outside of the scope of what the OP wanted.
In particular, I really like this: Linear Algebra Done Right.
It's an abstract linear algebra book that does a great job of motivating topics *without* resorting to determinants, which are weird to get your head around.
Anyway, getting through it would give students some good insights into the mathematical process, I think.
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Any of Smullyan's books, particularly "What Is The Name Of This Book?", "The Lady Or The Tiger", "Alice In Puzzleland". Lots of fun, and not what high school students would consider math. "Disguised" as mere logic puzzles, they are great for learning formal logic and ultimately introduces Godel's Incompleteness Theorems. Much easier and more fun than Godel, Escher, Bach (which is truly a wonderfully fantastic book, if you have the students who are ready for it).
Then there is Morris Kline's book on Calculus (now pub by Dover Books), which is something like the opposite of Spivak - it introduces differential and integral calculus through physical intuition and examples from kinematics. At least the first part, anyway.
I kinda wished I had Kline's book around back when I took calculus in hs, or perhaps the summer before. Just learning to solve problems w/o having the right intuition is not satisfying.
I'm a HS Math teacher myself and I once read a book called 'A History Of Zero'. It was pretty fascinating. It didn't deal with a lot of higher math, but had some really interesting stuff about the number which is zero. Check it out here: http://www.amazon.com/Nothing-that-Natural-History-Zero/dp/0195142373
A year and a half.
Back on topic though, I really liked "The Code Book" by Simon Singh, and it has a significant amount of number theory and statistics that is light enough for someone without too much background to pick up.
I concur.
Simon Singh is an excellent mathematics author. I picked up Fermat's Enigma this past summer (about Andrew Wiles's proof of Fermat's Last Theorem). I went into the history of the mathematics involved, to Fermat, to Andrew Wiles's story. There was a substantial amount of mathematics in there, but it was all explained well, and turned out to be a much lighter read than I initially expected from a math book.
You can always fill it out with Sphereland.
Good book. Everyone should get credit for reading anything Rudy Rucker has written. More high weirdness than math, though.
___
Here's a bunch of really good stuff:
Mathematics for the Million by Lancelot Hogben
http://www.amazon.com/Mathematics-Million-Lancelot-Thomas-Hogben/dp/0393063615
Review
"It makes alive the contents and elements of Mathematics" -- Albert Einstein"
http://www.amazon.com/Infinity-Beyond-Lillian-R-Lieber/dp/1589880366/
Infinity: Beyond the Beyond the Beyond (Paperback)
by Lillian R. Lieber (Author), Barry Mazur (Foreword), Hugh Gray Lieber (Illustrator)
http://www.amazon.com/Einstein-Theory-Relativity-Fourth-Dimension/dp/1589880447/
The Einstein Theory of Relativity: A Trip to the Fourth Dimension (Paperback)
by Lillian R. Lieber (Author), David Derbes (Foreword), Hugh Gray Lieber (Illustrator)
http://www.amazon.com/Quantity-Real-Imaginary-History-Algebra/dp/0452288533/
Unknown Quantity: A Real and Imaginary History of Algebra (Paperback)
by John Derbyshire
http://www.amazon.com/Fractal-Geometry-Nature-Benoit-Mandelbrot/dp/0716711869 The Fractal Geometry of Nature
by Benoit B. Mandelbrot
http://www.amazon.com/Chaos-Making-Science-James-Gleick/dp/0140092501
Chaos: Making a New Science
by James Gleick
Rather than just reading a book, installing the following software and working through the following tutorials should be worth beaucoup extra credit:
Geometric Algebra (GA) is one of the most exciting developments in Mathematical education and Mathematical Physics. It presents in a unified mathematical language vectors, complex numbers, quaternions, spinors, and more.
GA handles rotations easily (because it includes the quaternion algebra) and also provides a mathematical description for projective geometry. Because of this, GA is being used more and more by Computer Science (virtual reality modeling, simulation, computer vision) and Robotic Engineers (arm/body movements). ...
Geometric Algebra is also called Clifford Algebra.
Geometric algebra software GAViewer for all major OSes: http://geometricalgebra.org/gaviewer_download.html
http://www.science.uva.nl/ga/files/GABLE15plus.pdf
In this tutorial we give an introduction to geometric algebra, using our GAViewer software. In the geometric algebra for 3-dimensional Euclidean space, we graphically demonstrate the ideas of the geometric product, the outer product, and the inner product, and the geometric operators that may be formed from them. We give several demonstrations of computations you can do using the geometric algebra, including projection and rejection, orthogonalization, interpolation of rotations, and intersection of linear o set spaces such as lines and planes. We emphasize the importance of blades as representations of subspaces, and the use of meet and join to manipulate them. We end with Euclidean geometry of 2-dimensional space as represented in the 3-dimensional homogeneous model.
http://www.science.uva.nl/ga/tutorials/CGA/
This tutorial introduces the conformal model of 3D Euclidean geometry, to date the most
"Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?" - Patrick Henry
A couple more I forgot to add:
http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567
Godel, Escher, Bach: An Eternal Golden Braid
by Douglas R. Hofstadter
The big one - worth triple points.
http://www.amazon.com/Cracking-Math-Test-Graduate-Prep/dp/0375762671
Cracking the GRE Math Test, 2nd Edition
by Steve Leduc
This book is about the GRE subject exam, not the general math test. This test is intended only for college senior math majors.
This book is not listed here as a test prep book but as the only book I have ever seen that clearly explains a wide range of true higher mathematics. High school students should be able to progress more in understanding the essence of undergraduate math for math majors by reading this book than any other they could read.
"Is life so dear, or peace so sweet, as to be purchased at the price of chains and slavery?" - Patrick Henry