Math 331 Algebraic Systems - Fall 2021

Timings

• Lecture: 3-4pm MWF, Ridgeley 122

• Office hours: 4-5:30pm M + 11:15am-12:45pm F over Zoom.

Textbook

Learning Modern Algebra, A. Cuoco and J. J. Rotman; First Edition (Chegg, Amazon) - required for the course. You might be able to find a free pdf online, but make sure it's the 2013 edition.

These notes from David Mond may also be of use to you as they cover some similar content.

We'll also draw on this article by G. G. Joseph and this book by Berlinghoff & Gouvêa (both can be found for free online).

Class structure

We won't follow a typical 'three hours of lecturing' format, since this class is most fruitful when we're communally engaging with the practice of doing math together.

Mondays- I will survey the content for the week at a high level to set you up to complete the reading and accompanying exercises.

Wednesdays- From week 3 onwards a student will present a topic / section from the text (more detail below). We'll then spend some time talking about the pedagogical aspects of the material (the connections subsections in the textbook).

Fridays- We'll discuss how the week's material connects to the wider story of math (historical and conceptual), and go through exercises together.

Assessment

• Homework (15%)

• Self-reflections (5%)

• Participation (20%)

• Midterm 1 (20%)

• Midterm 2 (20%)

• Final (20%)

• Piazza bonus points (up to one homework)

Homework - Biweekly homework sets due via Gradescope. The first homework is due 9/12.

Self-reflections - A significant part of doing mathematics or honestly any academic discipline is thinking critically about your personal learning process and learning practices (i.e. how you learn and what you're doing about it) and making improvements to the latter in order to support the former. I would like each of you to reflect on your engagement with this class; what's working for you, what's not working, what's difficult right now, different ideas for how to structure your notes,... Every two weeks I'll provide a few prompts that I'd like you to respond to however suits you best. Feel free to be creative in your responses, like using mindmaps, memes, illustrations, cartoons, stories, music, or anything else that helps you reflect on your growth.

Participation - A key theme that we'll work around is the value and skill-set of effective mathematical communication. There will be two ways we put this into practice: presentations and exercises. On each Friday from weeks 3-13 (approximately) the first topic of the class (~10-15 minutes) will be led by a student. Each student is expected to lead on one Friday (possibly multiple students on the same day if there are any timing issues). This is graded mostly for completion; the main benefit is intended to be the experience of leading the class. I am available to meet with you on the week of your presentation to talk it through with you beforehand. We'll also go through exercises together on Fridays and this discussion / opportunity for group conversation also counts towards this component. This part of the grade also includes attendance, see below.

Attendance - Attendance to lectures is required. Attendance here is more than just physical presence; if I notice that you are on your phone for the entire lecture you won't get the attendance grade for that day!

Midterms - The midterms will both be take-home assignments that you have 24 hours to complete.

Final - The final exam will be a two hour written exam consisting of both shorter mathematical questions and open-ended essay questions.

Piazza bonus points - Each time you post a (mathematical!) question or answer on Piazza, you will receive 1 bonus point. These count as 1 point towards a homework up to a maximum of 10 points. For example, if you dropped 15 points on homework throughout the semester and asked 5 questions on Piazza, your score for homework would be as if you only dropped 10 points.

Resurrection final - I will use a 'resurrection final' where at the end of semester I will calculate three grades: G1 = grade calculated as above, G2 = grade calculated with Midterm 1 counting 0% and Final counting 45%, and G3 = grade with Midterm 2 counting 0% and Final counting 45%. Your final grade will be max(G1, G2,G3). In other words, the final can count in place of your lower midterm grade.

Dropped scores - I will drop the the lowest homework score, and allow for four missed lectures without penalty.

Integrity

• Attempting to cheat in this course is unacceptable and will be strongly penalised. A first offense will be penalised with a zero grade on the relevant piece of assessment. A second offense will be penalised with an immediate fail grade. I will review every flagged case and will send anything that is remotely questionable to the Academic Integrity Office.

• Collaboration is permitted (actually encouraged!) on homework assignments, however each student must write up solutions in their own words. Please write the names of any other students you have collaborated with at the top of each assignment. Significant similarities between submissions from different students that fail to mention any collaboration counts as an act of cheating and will be penalised as such.

Syllabus