Math 350: Groups, Rings, and Fields (Fall 2026)

Abstract algebra, a central pillar of modern mathematics, studies generalizations of the familiar operations of addition and multiplication from ordinary arithmetic. The course focuses on three types of algebraic structures: groups, rings, and fields. For each type, we study structure-preserving transformations, a collection of important examples, and ways to construct one object from another. Time permitting, we will discuss several applications of abstract algebra, including a preview of public-key cryptography.

Help hours

• My tentative office hours in SMUD 401:
  • Tuesday 2:30-4:00
  • Wednesday 9:30-11:00
  • Friday 1:00-2:00
  • Please notify me if these don’t work well for you. I may revise them.
• Allison Tanguay, the Math Specialist and Associate Director of the Q Center, is available to support you in several ways.
  • Drop-in help hours: MWF 9am-noon, and TTh 12:30-2:30, in SMUD 208.
  • You can schedule individual meetings.
• Our Math Fellows (TAs) are Sam Johar and Erika Salvador. Their help hours are
  • Monday 6-7:30pm in SMUD 208a (Sam)
  • Tuesday 9-10:30pm in SMUD 208 (Sam)
  • Wednesday 6-7:30pm in SMUD 208a (Erika)
  • Thursday 7:30-9pm in SMUD 208a (Erika)

Handouts and demos

• Syllabus
• Platonic solids and permuations

Links

• Boardwork from my tablet.
• Zoom link for online office hours, classes, etc.

Homework

• Gradescope instruction. Our Gradescope course code is JN3RGY.
• Problem Set 1 — due Wednesday 9/9 at 10pm. Solutions
  • Symmetric group drill on two-line and cycle notation.
• Problem Set 2 - due Wednesday 9/16 at 10pm. Solutions
• Problem Set 3 - due Wednesday 9/23 at 10pm. Solutions
• Problem Set 4 - due Wednesday 9/30 at 10pm. Solutions
• Problem Set 5 - due Wednesday 10/7 at 10pm. Solutions
• See this Google drive folder for any solutions that have been shared.

Exams

• Midterm 1 will be held on Thursday, October 8, from 6:00pm to 7:15pm, in SMUD 014.
  • Some sample exams from past semesters. Note that coverage and notation varies semester to semester, so none of these exactly match our course’s coverage, but they will give an idea of style, content, and difficulty.
  • Coverage: any material covered on or before Thursday, October 1, or on problem sets 1 through 5. Concretely, this means Saracino chapters 0 through 6 and 8, but not including the proof of Theorems 8.4 or 8.5.
  • You are allowed to bring one page of notes, front and back, and the official course textbook.
• Midterm 2 will be held on Thursday, November 19, from 6:00pm to 7:15pm, in SMUD 014.