This course is about elementary mathematics—algebra, geometry, functions—viewed from an advanced perspective. We will see how concepts that arise early in the study of mathematics evolve at higher levels, and how simple math problems can lead to sophisticated insights. We will learn to make connections between different areas of mathematics by identifying underlying structures and principles.
Math 704 (McCallum) and Math 301 (McGraw), Tuesday 11–12, Wednesday 2–3, Thursday 12–1.
Email listserv@listserv.arizona.edu (change "firstname" and "lastname" to your own). Post messages to math407@listserv.arizona.edu.
You can earn up to 600 points: 300 points from assignments, 100 from the midterm exam, and 200 from the final exam. Your grade will depend on your score out of 600: 90% or higher for an A, 80% for a B, 70% for a C, 60% for a D. A score below 60% will give you an E.
There will be 6–8 assignments. You may discuss them with me in office hours and on the course listserv. However, your work must be your own. They should be legible, with pages stapled and your name at the top of each page. I will not accept late assignments. It is your responsibility to remember to hand in your work.
Extended analysis of a high school geometry problem (see sidebar). We generated lists of statements of things we know about geometry, and started considering the logical connections between them.
We divided the statements into axioms and theorems, or facts and deductions, as in this document. Assignment 3
We considered a Euclidan "proof" that all triangles are isosceles, and considered the definition of congruence, leading to a modern definition in terms of congruence transformations.
Final Exam, December 12, 2:00 p.m.–4:00 p.m.
This problem was suggested by Alejandro Uribe.
Download Cinderella.2 and follow these instructions to install the license key. (License has been updated, if you were having trouble before.)