Abstract Algebra II

Math 457 Spring 2024

Things to be Working On:

• Study for Final Celebration of Knowledge.  Study Guide here
• Have a wonderful summer!

Course Documents: 

• Class Notes
• Homework
• Feedback Notes
• Syllabus

• Email: <emcnicho>
• Office Hours:  
  • Office Hours: https://sites.google.com/willamette.edu/emcnicholas/home (In addition to the office hours posted on the website, I’m also available by appointment for in-person or Zoom meetings)
• Class Meetings: 
  • Tu/Th 9:40-11:10am, Location Ford 204 ;  Final Exam Time: 7-10pm

1

1/15-1/19

(Tuesdays class cancelled - snow day)

Fundamental Theorem of Finite Abelian Groups, Inner and Outer Direct Products

(DF Ch. 5 & 6)

• Pre-semester survey (please fill out by January 5)
• Perusall: Syllabus (due 11:30pm Monday 1/22)
• Homework Set #1 due Friday 1/26

2

1/22-1/26

Fundamental Theorem of Finite Abelian Groups, Inner and Outer Direct Products

Introduction to Rings

(DF Ch. 5, 6, 7.1)

• Perusall: Dummit & Foote 7.1 (due 11:30pm Monday 1/29)
• Homework #2 (due Wednesday 1/31)

3

1/29-2/2

Polynomial Rings, Factor Rings, Ring homomorphism

(DF 7.2-7.3)

• Perusall: Unit Conjecture (due 11:30pm Monday 2/5)
• Homework #3 (due Wednesday 2/7)

4

2/5-2/9

Ideals, Factor Rings, Ring homomorphism

(DF 7.3-7.4)

• Perusall: Students Unravel Widely Believed Conjecture (due 11:30pm Monday 2/12)
• Homework #4 (due Wednesday 2/14)

5

2/12-2/16

6

2/19-2/23

7

2/26-3/1

8

3/4-3/8

ED => PID => UFD

(DF 8.2-8.3)

• Week 8 Survey (https://forms.gle/CnYptUNLZXPJ1kq49) please complete by Monday night 3/4
• Perusall: Polynomial Building Blocks (due 11:30pm Monday 3/4)
• Homework #7 (due Wednesday 3/6)

3/11-3/15

Individual Celebration of Knowledge, Polynomial Rings

(Pinter 24 & 25)

• Individual Celebration of Knowledge Tuesday 3/12: Study Guide
• Perusall: Pinter Ch. 24 (due 11:30pm Monday 3/11)

10

3/18-3/22

Polynomial Rings, and Irreducibility

(Pinter 25 & 26)

• Homework #8 (due Wednesday 3/20)

11

3/25-3/29

12

4/1-4/5

Extension Fields

(Pinter 27 & 29)

• Perusall: Pinter Ch. 27 Field Extensions (first 2 pages) and Pinter Ch. 28 Vector Space Review (due 11:30pm Monday 4/1)
• Homework #9 (due Wednesday 4/3)

13

4/8-4/12

Degrees of Extension Fields

(Pinter 29 & 31)

• Homework #10 (due Wednesday 4/10)

14

4/15-4/19

Galois Theory

(Pinter 31 & 32)

• Perusall: Pinter Ch. 30 Constructible Numbers & 31 (Preamble to Galois Theory (first 2 pages) (due 11:30pm Monday 4/15)
• Homework #11 (due Wednesday 4/17)

15

4/22-4/26

Galois Theory 

(Pinter 32 & 33)

• Perusall: Quanta Article on Galois Theory (due 11:30pm Monday 4/22)

16

4/29-5/3

• Homework #12 (due Monday 4/29)
• Perusall: Finite Fields & the Parker Square (due 11:30pm Tuesday 4/29)
• Study for Final Celebration of Knowledge.  Study Guide here

17

5/6-5/10

Related Websites:

3blue1brown Essence of Linear Algebra - Excellent video series explaining many of the key concepts of Linear Algebra 

Explore group tables and diagrams: https://hobbes.la.asu.edu/groups/

Create your own frieze patterns (like the one shown below) with specified symmetry group: https://eschersket.ch/

Picture cyclic groups forming before your eyes using these spirograph simulators: https://seedcode.com/SpirographN/sgn.html, http://htmlspirograph.com/#0,50,0,1,1,-1.44,30,-700,1174,2.5,120,860,-3.6,100,1050,75,0,0,1,1064, https://nathanfriend.io/inspiral-web/

Header image used with the permission of the artist, Professor Emeritus Junpei Sekino.  Learn more about Professor Sekino, and see more of his amazing artwork here: https://www.sekinoworld.com/home/

Important Dates

Week 1: 1/16 (Tu) First day of classes

Week 4: 1/29 (M) Add/Drop Deadline

Week 10: 3/19 (Tu) Withdraw Deadline

Week 11: 3/25-3/29 Spring Break

Week 13: 4/8-4/11  Registration for Fall

Week 14: 4/17 (W) SSRD No Classes

Week 16: 4/30 (T) Last Day of Classes

Week 17: Final Exam