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 publickey cryptography (a subject that I will most likely teach a semesterlong course about in the spring).
Help hours

My office hours in SMUD 401:
 Tuesday 2:454:15
 Wednesday 1:152:45
 Friday 1:302:30

Kat Mendoza’s help hours in SMUD 208 (will be in 007 after renovation is finished):
 Monday 79
 Tuesday 79

James Corbett’s help hours in SMUD 208 (will be in 007 after renovation is finished):
 Tuesday 68pm
 Wednesday 68pm

Fernando Liu Lopez’s help hours in New Science Center D107 (ground floor, right behind the Science Library space):
 MWF 24pm
 TuThu 25pm
 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

 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, 9amnoon in SCCE A131
 Remember to make a onepage note sheet (front and back) for the exam!
 Reading/finals week hours:
 Thursday 12/13: 1:303:00 with Charley
 Friday 12/14: 10:1511:45
 Monday 12/17: 9:3011:00
 Tuesday 12/18: 9:3011:00 with Charley
 Review sessions (with Math Fellows): Thursday and Saturday 57pm (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