Math 350: Groups, Rings, and Fields

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

• 9/4: Syllabus
• 11/8: Project topic options

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.

Homework

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

• Course Survey / Gradescope instructions (please submit by 9/10)
• Problem Set 1 (due 9/12) Selected solutions (Problems 6, 7, and 9)
• Problem Set 2 (due 9/19) Selected solutions Part 1 (Problems 1, 2, 5, and 6) Part 2 (Problems 9 and 10)
• Problem Set 3 (due 9/26) Solutions
• Problem Set 4 (due 10/3) Solutions
• Problem Set 5 (due 10/17) Solutions
• Problem Set 6 (due 10/24) Solutions
• Problem Set 7 (due 10/31) Solutions
• Problem Set 8 (due 11/7) Solutions
• Problem Set 9 (due 11/14) Solutions
• Problem Set 10 (due 11/28) Solutions
• Problem Set 11 (due 12/10) Solutions

Exams

• 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
  • Review guide
  • Practice Exam / Solutions
  • Old Exam (Fall 2017) Solutions
    • NOTE: the emphasis and coverage was slightly different, so don't treat this as a model for what exactly to expect. But it may be useful for review anyway.
  • Exam / Solutions
• 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