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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!"
Sorry, my list is lacking some depth.
How to Lie with Statistics, Darren Huff, 1954
I wrote this:
http://people.pwf.cam.ac.uk/jlnw3/maths/books/prime/
It was meant as an introduction to the idea of proof. Perhaps you might like it.
- Jax
You should definitely expose your students to the following Math books:
http://www.amazon.com/Math-SAT-800-Toughest-Problems/dp/1439200068/ref=sr_1_1?ie=UTF8&s=books&qid=1234132532&sr=1-1
http://www.amazon.com/Math-Workbook-New-SAT-Barrons/dp/0764123653/ref=sr_1_2?ie=UTF8&s=books&qid=1234132532&sr=1-2
http://www.amazon.com/Petersons-Math-Exercises-Academic-Preparation/dp/0768908078/ref=sr_1_7?ie=UTF8&s=books&qid=1234132532&sr=1-7
Principia Mathematica. It's all there ;^)
Great minds think alike; fools seldom differ.
It's normally taught as an upper-division college class but the only real prerequisite is 2nd-year high school algebra and a mind that can think abstractly.
Students will find it different enough from trig and calculus to be fresh and knowing they can do "college math" can be a real ego-boost.
By the way, if you know any elementary or middle school teachers, many of the concepts in abstract algebra can be taught to those age groups as well. Being able to do "adult math" can be a real point of pride and inspiration at those ages.
First grade isn't too early. Anyone who can add or subtract time already has the basics for abstract algebra addition and subtraction.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
*** Ponder
How to Think like a Mathematician:
http://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/0521895464
Online here (for how much longer?):
http://www.maths.leeds.ac.uk/~khouston/httlam.html
I bought this in the discount bin for $1 somewhere, I think it's (Playthinks) really good to develop logic and just try a little bit of every mathematical discipline:
http://www.amazon.com/Big-Book-Brain-Games-Mathematics/dp/0761134662
This isn't pure math, but lisp, but since Lisp is inspired by lambda calculus, perhaps it'll inspire more programming (shrugs):
http://www.cs.cmu.edu/~dst/LispBook/index.html
Even the dullest high school student has a memory that makes us adults seem slow. There is exactly one way to motivate teenagers: tell them they are not "ready", although telling them they are "not allowed" has a similar effect. With that in mind I recommend you give one or two of them a copy of All the Mathematics You Missed But Need to Know for Graduate School, and suggest they pass it onto someone else if they find it "too hard". It's a great book that gives a quick skim over all the different fields of mathematics that a graduate student in mathematics is expected to know. A typical college student will read this book, shake their head and decide that maybe graduate school isn't for them. A typical high school student, even one not interested in math, will read this book and decide that mathematics is awesome and maybe they should pay attention in class, because if they can't grasp differential linear equations then they're never going to understand Lebesgue integration and infinite Fourier series.
How we know is more important than what we know.
Excellent explanations. It is completely understandable if the student puts in the time to understand it. It requires almost no outside knowledge.
I would have loved it if someone showed me this book earlier.
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.
I read Prisoner's Dilemma by William Poundstone when I was that age, and found it to be a very intriguing introduction to game theory. It is fairly light on math, providing only enough to show that there are calculable solutions to situations that are otherwise difficult to reason through. It also provides some real life examples which are easy to relate to, e.g. letting one child cut a piece of food in half and the other choose the half they want in order to ensure "fair" portions.
It's a good choice for showing that there's more to math than finding the length of the hypotenuse.
http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1234132982&sr=8-1 Godel, Escher, Bach: An Eternal Golden Braid Very interesting book and should get students of that age excited about math and science IF they are predisposed to that sort of thing.
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.
I highly recommend The Shape of Space by Jeff Weeks. (He's a freelance geometer, something he can afford after winning a MacArthur Genius Grant.) I've used this book a couple of times -- once with bright high school kids and once with bright college freshman -- and even if they don't get everything, just a taste is enough.
It builds on Flatland (which someone mentioned above), but has the advantage of being more modern and not sexist. But very quickly you're learning about Klein bottles, connected sums, and all sorts of topology you typically don't see until you're well into your undergraduate (or grad!) program in math. All aimed at high school kids. Very cool stuff.
Oh, and the big punchline at the end: what is the shape of the universe? At least you'll get a good understanding of the possibilities...
Here's a taste for you from a page related to the book.
Courant and Robbins, "What is mathematics?"
My first program:
Hell Segmentation fault
I really like Fermat's Enigma by Simon Singh. Relatively easy read and I found it inspiring.
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!
A Pathway Into Number Theory, by R. P. Burn.
It's the most unique math book I've ever read. There is no prose in the book per se; rather, the book is a series of small tasks and questions (usually starting by identifying patterns in tables of numbers) that, as the title suggests, gently lead the reader into Number Theory. All the major topics of a first course (the fundamental theorem of arithmetic, quadratic residues and forms, etc.) are there; the beauty of the book is that each task is such a small step from the previous one that the reader is led painlessly to a mastery of each concept. (Just don't skip steps!) This feature makes is suitable for advanced high school students looking for "stimulating mathematical ideas."
It's a wonderful book, on a wonderful subject. I have often wished for books written in this format on other mathematics subjects.
It seems likes kids only do what you tell them not to do, so this advice may seem wise. However, this is a form of confirmation bias; adults notice when kids don't listen because mainly because they usually do.
If you tell someone a student some skill is difficult, they will believe you. You have set them up to expect failure. This expectation is easy to meet, and most students will give up early.
If you tell a student something is easy, they are likely to believe you. Believing a subject is easy, they are more likely to follow through to mastery because they have been set up to expect success.
Reverse psychology is a trick. Tricking students is a way to alienate them; it may work on the few, but the many will respond better to affirmative attitudes.
1. A Long Way From Euclid
Constance Reid
A survey of math from the ancient Greeks on.
Very accessible.
I spent months reading it in 6th grade.
2. Innumeracy: Mathematical Illiteracy and Its Consequences
John Allen Paulos
Lots of cool stuff on probability, estimation, and application of math to current events.