Math 350: Groups, Rings, and Fields (Fall 2019)

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.

Help hours

  • My office hours in SMUD 401:
    • Tuesday 11:00-12:30
    • Wednesday 2:00-3:30
    • Friday 10:00-11:30
  • Allison Tanguay’s help hours:
  • Dana Frishman’s help hours:
    • Monday 7-9pm in SMUD 014
    • Tuesday 7-9pm in SMUD 014

Handouts and other items

LaTeX resources

  • Overleaf LaTeX tutorials: some tutorial videos and other links about learning LaTeX. These focus on using Overleaf, an online platform 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.

Homework

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

Exams

  • Midterm 1: Friday 10/11

  • Midterm 2: Friday 11/22

    • Remember to make a one-page note sheet (front and back) for the exam!
    • All suggested problems from PSets 6-10, compiled into one file for convenience. This are good problems to try for additional review. At least one will be used as a midterm problem (possibly with small modifications)

    • Some sample exams are below. Solutions will be posted later this week.

      • Note: content varies term to term, so don’t treat these as absolute guides to what we’ve covered. In particular, these don’t really emphasize the following topics are emphasized more this semester: Group actions, quadratic integer rings, linear algebra examples. I’ve also noted below which problems in the samples cover material we haven’t discussed.<li>Sample Exam 1 (omit 3(b)) / Solutions</li><li>Sample Exam 2 (omit 5(c)) / Solutions</li><li>Sample Exam 3 (omit 2(b), 4(a,c,e), 5(b,c,f,g,j)) / Solutions</li>
    • Exam / Solutions

  • Final exam: Thursday 12/19 2pm-5pm in SMUD 206

    • Remember to make a one-page note sheet (front and back) for the exam!
    • All suggested problems from the problem sets, in one file.

    • Some sample exams with solutions are below. Note that handwritten notes on these are from Fall 2018, so they may not perfectly match the coverage and notation from this year. Please ask if you are unsure of any notations or coverage issues.

    • Many more old final exams are here. These don’t have solutions, but feel free to ask me at office hours about any of the problems. Also remember that notation and coverage may be slightly different every term.
    • Old math comps exams may also be useful for studying (only look at the Algebra sections).
    • Exam / Solutions