Syllabus

Last updated: Friday, 12 January 2024.

Purpose of this Page

This page serves as the syllabus for math306-e24, Abstract Algebra II, taught by Chris Eppolito in the Easter semester. I may change any portion of this document at any time if the need arises. In the event this is necessary, I will contact enrolled students by email.

Read this document carefully. This is a contract between us concerning how our course will run.

This is a Collaborative Syllabus

In an experimental pedagogical exercise, I've decided to make this document a collaborative effort between myself and my students this semester. As of Friday, 12 January 2024 this document is unfinished, pending feedback and input from the students. I will update this portion of the page as input arrives.

Update

We discussed and (mostly) completed the syllabus. We agreed to push off discussion of the format of the final exam until later in the semester. Most other sections are now (Wednesday, 17 January 2024) complete! My thanks to everyone for contributing to this document.

Course Information

Instructor Chris Eppolito (he/him) <- christopher-dot-eppolito-a​t-sewanee-dot-edu
Section A MW 14:00-15:15 in Woods 123
Office Hours By appointment in Woods Lab 127
Webpage Abstract Algebra II Homepage

Content

This is a standard first course in abstract algebra for mathematics majors. Due to the collaborative nature of this document, the topics and content covered may vary depending on student interest (excepting a core group of content necessary to any good course in rings and fields).

Topics

We will cover the following topics.

  • Rings (terminology, theory, and applications).
  • Fields (terminology, theory, and applications, time permitting).
  • Galois theory (time and student interest permitting).
  • Practical applications of the above (time and interest permitting).
  • Other topics of interest to enrolled students.

The schedule of topics contains our day-to-day schedule, updated as the semester progresses.

Textbook

A good education should always be play-to-win, and never pay-to-win. As such, our only required material is the textbook Abstract Algebra: Theory and Applications (the same text we used for the first semester of this course). It is available in the following formats:

TODO Course Objectives

The official description of this course from the course catalogue is…

A study of these important algebraic structures: integral domains, polynomials, groups, vector spaces, rings and ideals, fields, and elementary Galois theory.

At the end of this course, you should…

  1. be able to prove (or disprove) simple structures are rings of certain kinds,
  2. be able to give examples of various different kinds of rings,
  3. be able to read a mathematics texts, assessing and understanding their proofs,
  4. be able to construct and deliver a short-ish mathematics presentation, and
  5. frolick in the fields and rings (this is wording requested by the students).

Code of Conduct

Here is what I expect from you at a minimum.

  • Submit your own work, and adhere to the Honor Code (more below).
  • Be mindful and courteous during ALL interactions with me and your peers (including emails).
  • Communicate with me if you have any concerns—I can help you, but I need to know that you want the help! As communication is a two-way street, you also need to read the emails I send and pay attention to what is said during lectures.
  • Participation in class discussions and assignments.
  • You must check the website for updates daily. I will not remind you of deadlines: you are responsible for knowing when assignments are due and planning accordingly so that they are submitted on time.

  • Your work must clearly demonstrate the logic you used, and may only use methods and notations discussed in my lectures (or OK'd by me in advance). Everything you turn in must be legible AND well-organized, with clear logic describing your solution.

    A few thoughts on how I do this when I work on mathematics:

    1. Write a first draft which addresses the assignment.
    2. REWRITE that draft, remembering that other people have to understand it without me there to explain it.
    3. Take some time to do other things (e.g., get a coffee or have a nap).
    4. Return to the work, and check that it still makes sense.
    5. Repeat 2–4 as necessary until my work makes me and my audience proud.

    Remember: if your work would be too messy or unclear for an English class, it's too messy for my class.

Academic Honesty

You agreed to follow the Honor Code when you joined the college. All forms of academic dishonesty, including plagiarism, are violations of the Honor Code and will be treated as such. If you ever have a question about an assignment or want additional help, ask for assistance rather than jeopardize your academic career.

Collaboration

I encourage collaboration between students on practice problems and problem sets; if you work with another student on a graded assignment, you MUST CITE THEM as a collaborator on each problem you did together.

Collaboration on Quizzes and Exams is FORBIDDEN.

Collaboration means that all parties contribute ideas to produce a solution. Copying or allowing another student to copy solutions is never collaboration—that is cheating and will be treated as such. If you have any doubts as to whether what you did (or plan to do) is collaboration, just ask me.

To summarise, if you do collaborate, remember:

  1. Cite your collaborators.
  2. You must write the solution in your own words.

Academic Accommodation

The University of the South is committed to fostering respect for the diversity of the University community and the individual rights of each member of that community. In this spirit, and in accordance with the provisions of Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act (ADA), the University seeks to provide students with disabilities with the reasonable accommodations needed to ensure equal access to the programs and activities of the University.

Any student with a documented disability needing academic adjustments is requested to speak with Student Accessibility Services (SAS) as early in the semester as possible. If approved for accommodations, the student has the responsibility to present their instructors with a copy of the official letter of academic accommodations. Please note: Accommodation letters should be dated for the current term; accommodations will not be provided without a current accommodation letter; and accommodations cannot be applied retroactively.

SAS is located in the Office of the Dean of Students (931.598.1229). Additional information about accommodations can be found on the Student Accessibility Services website.

Students who have questions about physical accessibility should inform their instructors so that we can ensure an accessible, safe, and effective environment.

Grades

YOU are responsible for obtaining the final grade you want in this course. If you want an A, make sure your grades are in the A range.

There is NO EXTRA CREDIT. If you ever want help, I can provide it as long as I know you want it! When all is said and done, you will get the grade you earn in this course.

TODO Assignment Types

The following is a short description of each of the assignment types (that may be) employed in this course.

Individual Math Discussion

A weekly scheduled one-on-one meeting with me in my office to discuss course content. Think "laid-back oral exam", with a (somewhat directed) emphasis on what you want to discuss, rather than just what I want to ask.

Students should bring some of their work to discuss. This can be a proof or something else that folks want to think about or ask questions about.

In addition, we decided that students can cancel (by 5pm the day before) up to two of these meetings without any penalty.

Homeworks

Homeworks are problems assigned during lecture, to be turned in by the end of the following lecture (or other assigned due date). All written homeworks must be written in LaTeX, and will not be accepted otherwise.

Oral Presentation

Solutions to problems or exposition of mathematical content presented on the blackboard during class periods to me and your peers.

The purpose of this assignment type (which you might not associate with mathematics courses to this point) is to get you comfortable with watching, writing, and assessing mathematics presentations.

Conference Presentation (TBD)

An oral presentation give at a conference or symposium. The Sewanee–Rhodes–Hendrix Symposium in Mathematics and Computer Science will be held here this semester.

Final Exam

The format is TBD. We will discuss at a later date (Wednesday, 17 January 2024).

Score Ledger

The last day to turn in written work is Wednesday, 1 May 2024.

Grades are decided on the following APPROXIMATE distribution (subject to change):

Grade F D C B A
Minimum Score \( -\infty \) 60 65 80 90

NOTE: Students in the past have been confused about the fact that the above distribution doesn't have plusses and minuses listed. Let me assure you that I DO give plusses and minuses. However, I also suggest that you worry less about that and more about understanding the class content.

Scores are determined by the following: Weekly meetings (40%), Homework (20%), Oral presentations (20%), and Final (20%).

Optional Extra Meetings

We discussed (at the students' request) having an extra lecture each week. We settled on 11:00 – 12:00 on Thursdays. We also agreed that anyone can cancel this meeting.