Algebra: Preparation and Abstraction

Instructor: Dheeran E. Wiggins
Email: dheeran2@illinois.edu
Here is the syllabus.
This honors project was developed for James Scholar Honors students enrolled in Math 405: Teacher's Course, as taught by Dr. April Hoffmeister.

Welcome to Algebra: Preparation and Abstraction. In this Teacher's Course honors project, we will look at

linear systems and \(\mathbb{C}\)-linear spaces.
polynomial rings \(R[x_1,\dots,x_n]\) and extensions \(\mathbb{k}(\theta)/\mathbb{k}\).
group actions \(G \curvearrowright \Sigma\) on spaces.

We will approach these topics from the perspective of teachers. Namely, we will look to assess how worthwhile pre-abstract and abstract perspectives are on this material. Given your backgrounds in mathematics, I believe the content of this project is certainly within reach for all of you. Not all the covered material will be results or techniques you have previously seen, so some assignments may seem daunting. That being said, I will do my best to guide you through the material at a comfortable pace.

Assignments and Deliverables

This honors project will be based on a few problem sets. I strongly encourage you to work together on these, but working independently is fine. In either case, please submit your own work. We will meet semi-regularly to discuss your solutions and any questions.

You will also prepare slides and give a final talk on a topic from these assignments, plus you will submit a writeup analyzing the potential effectiveness of adding abstraction to high school and early-college algebra curricula.

Assignments and Deliverables

Materials