Abstract Algebra

Math 3230, Fall Semester 2023
University of Connecticut

Instructor

Introduction

This is a first course on Abstract Algebra intended for math majors. Abstract Algebra starts with familiar objects and operations, like the integers and the rational numbers, isolates properties of their basic operations, and then recasts those operations in general settings. Our focus will be on group theory, which is closely connected to the idea of symmetry and which is a crucial tool in geometry and which has wide-ranging applications to Physics, Chemistry, and other sciences.

Schedule

This course meets (in-person) every Tuesday and Thursday from 8:00 a.m. to 9:15 a.m. in Monteith 226.

Textbook

We will rely on Abstract Algebra: Theory and Applications by Judson. This is an open educational resource and can be downloaded from the link.

Campus Wire

We will take advantage of the Q&A site campuswire for online questions and answers. You should register on the site before class starts.

Overleaf and TeX

I strongly advise everyone to learn the basics of TeX so that they can type up their problem solutions. The easiest way to work with TeX is via the cloud resource overleaf.com. There are many tutorials on that site that provide an introduction to TeX. In addition, this video might be helpful.

Class mechanics

This class will operate following the “flipped” model.

Refer to the course content page or the navigation links for this site. For each week of the course, I have provided:

  • a set of problems chosen from the book that we will discuss in class during that week;
  • a set of video lectures on the topic of the week.

Typically, the problems given in Week N pertain to the topic discussed in Week N-1, though this is not a hard-and-fast rule.

In addition, I will refer you to online quizzes, typically weekly, on the course huskyct site.

Each class period will be devoted to problem-solving and discussion. I will provide a list of problems from the book that we will work on in class. As we progress:

  • I will ask students to present their work (including partial progress) to their fellow class members.
  • After we have discussed the problems on Tuesday, I may ask some (or all) students to write up solutions to problems we discussed and present those solutions on Thursday.
  • Selected problems from the class discussion will be assigned to be written up and handed in for a grade.

Assessment

Grades in this course will be based on:

  • Two take-home midterm exams (20% each). Tentatively, these will be assigned on 10/2 (due 10/9) and 11/13 (due 11/20). These dates are subject to change.
  • One take-home final exam, (40%), tentatively assigned 12/1 and due 12/15. Again, these dates are subject to change.
  • Homework, both presented in-class and handed in, and online quizzes. (20%)

Disclaimer

The instructor reserves the right to modify or adapt this syllabus to account for disruption due to COVID-19 or other unexpected circumstances.

University Policies

Students must comply with all university guidelines regarding COVID. In particular:

  • all students must wear a facemask covering their mouth and nose at all times in the classroom
  • there is no eating in class. Brief unmasking is permitted to drink.

Students with disabilities should work with the Center for Students with Disabilities to request academic accommodations. The CSD is located in Wilbur Cross, Room 204 and can be reached at (860) 486-2020 or at csd@uconn.edu. Detailed information regarding the process to request accommodations is available on the CSD website at www.csd.uconn.edu.

Students are bound by the university’s policies on academic misconduct. Academic misconduct is dishonest or unethical academic behavior that includes, but is not limited to, misrepresenting mastery in an academic area (e.g., cheating), failing to properly credit information, research, or ideas to their rightful originators or representing such information, research, or ideas as your own (e.g., plagiarism).

One additional warning: the current iteration of generative AI (ChatGPT and its relatives) cannot effectively write proofs. It outputs reasonable sounding but generally nonsensical, and sometimes hilarous, material. Using it is a bad idea.

Students, faculty, and staff are bound by the university’s policy against discrimination, harassment, and related interpersonal violence.