Mathematics Reading List For High School Students? 630
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!"
My math is cool (Score:5, Insightful)
A History of PI (Score:2, Insightful)
I second a previous poster's suggestion of Simon Singh's The Code Book.
Telling students the material is hard is foolish (Score:5, Insightful)
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.
Re:Any abstract algebra text (Score:1, Insightful)
I agree completely. High school students are definitely capable of handling abstract algebra, though they should be encouraged to ask you for help with it, since they'll run into a lot of concepts they haven't seen in raw form before (equivalence relation, isomorphism, etc) and will probably get stuck on one of them somewhere. I'm personally a big fan of I.N. Herstein's topics in algebra, but that's somewhat expensive. A good, free, alternative is Robert Ash's Abstract Algebra, which you can download at http://www.math.uiuc.edu/~r-ash/Algebra.html. You can also purchase a paper copy for ~$30. Note that while it says "the basic graduate year," the first five chapters comprise the basic undergraduate year.
Here are several (Score:3, Insightful)
First, let me add my recommendation for GEB. It's an amazing book.
Here are some others that I think are good:
Re:Telling students the material is hard is foolis (Score:3, Insightful)
Umm.. the material likely *is* too hard for them. You're not tricking them at all.. you're just giving them the opportunity to accept the challenge.
Re:How to Lie with Statistics (Score:3, Insightful)
I would go for things in other fields that are math-heavy - economics, science, business, stuff like that.
Shows the usefulness of math!
Re:Any abstract algebra text (Score:3, Insightful)
Abstract algebra is beyond the capabilities of most adults.
True. We're talking about children though. All you need is a good teacher to fire up their imagination, and they can learn anything.
That's all it takes. But you better make sure it's a good teacher.
Re:Real analysis (Score:3, Insightful)
High school kids need to be exposed to the fun parts of math, not the parts that make people that love math groan. Even complex analysis is far more enjoyable (not to mention useful) than real analysis. Nobody likes to sit around proving the obvious for no other reason than to prove that you can do it, and high school students will never realize that the reason for all of the rigor is to expose the edge cases where things break down.
Re:Any abstract algebra text (Score:3, Insightful)
I think perhaps a better subject to teach would be topology. I realize this is probably a more rigorous class than abstract algebra, but I think you can skip some of the details and present it to them in an easily understandable way. Also, the pre-requisites are fairly minimal if you don't advance to algebraic topology, you really only need a decent background in set theory. I think for an average high school student it'd be hard to grasp the idea of what a homomorphism is, or an automorphism. These are largely shown through proofs. However, you can show what a homeomorphism is visually by using say, a rubber band, or a piece of clay. I think at the high school level you really only need to impart the idea behind the math and perhaps get them interested.
Also, if you skip metric spaces you can bypass the analysis prerequisite. I think you could easily teach them what a topological space is, the fundamental idea behind homeomorphisms, closure, compactness, connectedness, path-connectedness*, and the separation axioms.
This [amazon.com] is the book I used in my topology class, although I think it'd serve better as a reference to the teacher than the students.
They might not understand the prototypical example of a topological space which is connected but not path-connected though.
Re:How to Lie with Statistics (Score:3, Insightful)
Being about "how not to use math" and about math as such are pretty different things. It's like you were teaching a class on car repair and assigning a book on consumer fraud.
No. It's like you were teaching a class on car repair and telling your students how to not screw up. e.g. "Do not ever adjust the stabilizer based on popular arguments such as ___ and ___ because it will only screw with the engine and may even cause permanent damage." It's actually very relevant, especially in the early stages of learning.
A few of my favorites (Score:2, Insightful)
Re:High school is preparation for life (Score:5, Insightful)