Math 120: Groups and Rings (Spring 2023)

Canvas page
Gradescope link
Instructor: Daniel Bump (office 383U)
Course Assistant: Konstantin Miagkov (office 381H)

This class will meet MWF from 9:30-10:20 in 380W

The text will be Dummit and Foote Abstract Algebra, Third edition. We will cover group theory (through the Sylow theorems), and beginning ring theory. Although groups are more "basic" algebraic objects, rings are also pervasive and useful even in thinking about groups. I will talk about rings from an early stage, and I recommend that you read Section 7.1 in the book early.

Office hours

Bump: MWF 12:15-1:15 in 383U or by appointment.
Miagkov: Tu-Thu 1-2:30 in 381H

There will be two gradesccope midterms in weeks 4 and 8, a writing project due in week 6, and a final. This policy may change but I'll confirm a definite timetable in a few days.

Midterm 1

Midterm 1 will be a Gradescope midterm, to be taken either Thursday March 28, Friday March 29 or Saturday March 30 before Noon when the Gradescope closes for this exam. Budget 1 hour 20 minutes. It will cover Dummit and Foote, through Section 3.2. It will be open book in that you may consult Dummit and Foote, but no other sources.

Writing Mathematics

The Writing in the Major (WIM) project was released Saturday, April 29, and will be due Tuesday, May 9. Before you start it, I would like you to read the following materials.

Writing Mathematics. This document explains a philosophy of mathematical writing. I would like you to follow the suggestions in this document to produce a clear WIM project.
Normal Subgroups and Homomorphisms. This is a companion piece to Writing Mathematics. It is supposed to be written in a good mathematical style and to illustrate points made in the Writing document.
normal.tex. This is the latex file for Normal Subgroups and Homomorphisms.

You are strongly encouraged to use latex for the WIM project.

In case you have not learned latex, here is a short document to help get you started. There is more in the appendix to Writing Mathematics.

Writing Latex.

WIM project

The WIM project is available on Gradescope, due May 9. For your convenience, here is a copy of the pdf filed describing the project.

WIM Project details

Announcements for Week 5

We are starting Chapter 4, and will move as quickly as we can to the Sylow Theorems. Please start reading Chapter 4 if you haven't done so already.

Homework

Homeworks will usually be due on Tuesdays in Gradescope.

Homework

Dummit and Foote

Solutions

HW1 (due Tuesday April 11, 2023)

Section 1.1 #6,12,15,22,25;

Section 1.2 # 1,2,3;

Section 7.1 # 3,5.

HW1 Solutions

HW2 (due Tuesday April 18, 2023)

Section 1.2 #9;

Section 1.3 #2 ($\sigma,\tau,\sigma\tau,\tau\sigma$ only), 5,13,20;

Section 1.4 #7, 1.5 #2, 1.6 #1

HW2 Solutions

HW3 (due Tuesday April 25, 2023)

Section 1.7 #11, 17, 19;

Section 2.2 #7, 10;

Section 2.3 #17, 25;

Section 3.1 #9, 32, 33;

HW3 Solutions

HW4 (due Tuesday May 2, 2023)

Section 3.1 #34, 36, 42;

Section 3.2 #8;

Section 3.3 #2 (Prove bijection and statement (1) only), 3;

Section 3.5 #1, 7;

HW4 Solutions

WIM project (due May 9)

See above

HW5 (due Tuesday May 16, 2023)

Section 4.1 #1

Section 4.2 #2,9

Section 4.3 #4,22

Section 7.3 #25,26,34

For #34, assume $R$ has an identity $1\in R$

HW5 Solutions

HW6 (due Tuesday May 23, 2023)

Section 4.3 #28,34

Section 4.4 #2,13

Section 4.5 #13,25

Section 7.4 #37

Section 7.5 #3

HW6 Solutions

HW7 (Tuesday May 30, 2023)

This will not be collected

Section 5.4 #12

Section 5.5 #7,8

Section 8.2 #1,4,8

Section 8.3 #2

HW7 Solutions