I use my own lecture notes for this course. They can be purchased from Xanedu Publishing by going to
then click on "Copley Custom Textbooks" in the top bar and choose "Catalog of Custom Textbooks." Then click on "View Titles E through J" and scroll down to "Foundations of Mathematics, 3rd Edition." This is a desktop publisher that I use to keep the text inexpensive for my students. I do not receive any royalties. Below is the table of contents for the notes. You can also open a pdf version of Chapter 3 to see my style of writing and approach for my students. I am interested in constructive feedback about these notes. F
Preface:
Chapter 1: Introductory
Concepts
Chapter 2: Choose Method
Chapter 3: Direct Proofs
Chapter 4: Equivalent forms of statements
Chapter 5: Induction
Chapter 6: Relations
Chapter 7: Calculus Revisited
Chapter 8: Infinity
Chapter 9: Additional Problems
Appendix A: Notation and Definitions
To help inform this teaching of this course, over the past 4 years, I have been videotaping students doing their homework. Attached is a paper describing how I did the videotaping and what I have gained from watching these videotapes. (This paper was published in the proceedings of the Kaist International Math Education Conference, 2005.) Along with this paper is video with clips referred to in the paper. You can also watch a video in which two students are working one problem, pretty much from start to finish (with down-time edited out). Some questions are embedded in the video which might be thought about or discussed before continuing. My students have also be giving Power Point presentations. When you open this Power Point presentation, you should then press Alt d, v to "view" the show. Pressing "right arrows" will move you forwards through the show. Pressing "left arrow" will move you backwards if you want to view the animation again.