I’ll assign readings that include examples as well as concepts and ask the students to supply proofs, for instance to find proofs by induction of the formula for the sum of the first n squares, or for Fibonacci numbers in terms of the n-th power of a matrix. I’ll have them study concrete number theory concepts (such as quadratic extensions of Q, primality testing, and factorization) that illustrate general concepts in algebra.

• References: I can scan and email the students the relevant pages of the textbooks by Rosen or Ireland-Rosen that I’ll want them to read.
• Prerequisites: The mathematical maturity that comes with at least 2 years of university courses. Some prior exposure to proof-based mathematics would be helpful. Most important is a willingness to invest time and effort into a reading course that is not a formal course that counts toward their GPA.
• Meetings: once per week between Sept 12, 2022 and Dec 9, 2022
• Type: Reading
• Size: 1-3 students

Instructor: Neal Koblitz, Mathematics, University of Washington