### Some Interesting Books

When preparing the capstone for secondary teachers class, I found it extremely difficult to find any fully relevant texts (which is why we don't have an assigned textbook). Here is a list of some of the books I used as references this year.
*Glimpses of Algebra and Geometry* by Gabor Toth. I like the first six chapters, which are about the rational, irrational and complex numbers. Written at a high undergraduate level, it makes no attempt to be accessible to secondary students. But it's written well and has good ideas.
*Foundations of Analysis* by Edmund Landau. Starts from the Peano Axioms and the number 1, through the construction of N, Q, R and C. I find this a weird combination of fascinating and boring. Constructing these numbers rigorously was the first experience of my life when I felt I understood solidly what math was about. I had planned to spend the first couple of weeks on this stuff. Then I realized it was kind of boring and if I had to cut some things out of the curriculum, I should cut out the boring things.
*Math Made Visual* by Alsina and Nelsen. Visual proofs are often the most beautiful proofs. I particularly like the trigonometry diagrams.
*Interactive Mathematics Program, Years 1-4* by Alper, Fendel, Fraser and Resek. There are a lot of rich problems in these high school textbooks, some of which I used in our class. The Teachers Guides gives some discussion of the problems... the Student Books have very little in the way of reference material (that's supposed to be developed in the classroom).
*Mathematics for High School Teachers* by Usiskin, Perissini, Marchisotto and Stanley. This is the closest thing there is right now to a standard text for capstone courses for secondary teachers. There is a lot of good stuff in it, but it is, in my humble opinion, embedded in a lot of tedious stuff.
*Calculus Connections, Geometry Connections, Algebra Connections: Math for Middle School Teachers*, three books published by Prentice Hall. Seems like a good idea, but I couldn't find anything in it that I wanted to use for the course.
*Mathematical Connections* by Al Cuoco. Good stuff about nth differences.

*Eric Hsu*

April 20th, 2008