Math 350: Groups, Rings, and Fields (Fall 2018)

This course is an introduction to abstract algebra, a central pillar of modern mathematics that concerns generalizations of the familiar addition and multiplication operations from ordinary arithmetic. The course focuses on three types of algebraic structures: groups, rings, and fields. For each structure, we study certain transformations between such structures, a library 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 (a subject that I will most likely teach a semester-long course about in the spring).

Help hours

  • My office hours in SMUD 401:

    • Tuesday 2:45-4:15
    • Wednesday 1:15-2:45
    • Friday 1:30-2:30
  • Kat Mendoza’s help hours in SMUD 208 (will be in 007 after renovation is finished):

    • Monday 7-9
    • Tuesday 7-9
  • James Corbett’s help hours in SMUD 208 (will be in 007 after renovation is finished):

    • Tuesday 6-8pm
    • Wednesday 6-8pm
  • Fernando Liu Lopez’s help hours in New Science Center D107 (ground floor, right behind the Science Library space):

    • MWF 2-4pm
    • TuThu 2-5pm
    • Or by individual appointment at this link

Handouts and other items

LaTeX resources

  • Overleaf LaTeX tutorial: this tutorial is a nice introduction for beginners. It focuses on using Overleaf, which allows you to write LaTeX documents online without installing any software.
  • Overleaf Primer by Kristin Heysse (Macalester). Another tutorial on writing in LaTeX on Overleaf.
  • Detexify: this is an absurdly useful tool that allows you to sketch a symbol and quickly learn the LaTeX command for it.


Problem sets will be posted here. All problem sets are due at 10pm, via Gradescope.


  • Midterm 1: Friday 10/5

    • Sample exams from previous semesters:

      • Note: These exams should give some impression of the length and format of the exam, but the topic coverage is slightly different from previous semesters. In particular: both exams use topics from Chapter 6 (direct products), and use the notation Z(G) (for the center of a group G) that we have not used in class.
      • Spring 2016
      • Fall 2017
    • Exam / Solutions

  • Midterm 2: Friday 11/30
  • Final Exam: Wednesday 12/19, 9am-noon in SCCE A131
    • Remember to make a one-page note sheet (front and back) for the exam!
    • Reading/finals week hours:
      • Thursday 12/13: 1:30-3:00 with Charley
      • Friday 12/14: 10:15-11:45
      • Monday 12/17: 9:30-11:00
      • Tuesday 12/18: 9:30-11:00 with Charley
    • Review sessions (with Math Fellows): Thursday and Saturday 5-7pm (check email for room assignment)
    • Fernando’s reading/finals office hours: 10am to 4pm every weekday.
    • Sample Exam 1 / Solutions
    • Sample Exam 2 / Solutions
    • Review guide of topics that may appear on the exam.
    • Many recent exams (these don’t have solutions; let me know if you want to check your work for any of them)
    • Another good source of problems: look at the Algebra sections of Old Comprehensive Exams (this is an especially good place for review if you’re planning to take the math comps).
    • Exam / Solutions