Abstract Algebra I

Math 456 Fall 2023

Things to be Working On:

  • Have a wonderful Winter Holiday!!!

 

Course Documents: 


 Professor McNicholas
  • Email: <emcnicho>
  • Office Hours:  
  • Class Meetings: 
    • Eaton 308, Mon/Wed 9:10-10:40 am;  Final Exam Time: Dec 11th (Mon) 7-10pm

Week Topic  Assignments

1

8/28-9/1

Dummit & Foote 1.1, Gallian Ch.s 1 & 2, Pinter Chs. 1-3

  • Perusall Assignment:  Syllabus & Mystery Group Project Description (due Tuesday 8/29)
  • Complete the Pre-Semester Survey: https://forms.gle/tAW6SpF8tvej3n7D8
  • Read over Chapter 0 - Preliminaries: Posted Soon on Perusall
  • Perusall Assignment:  Humanizing Mathematics (due Friday 9/1)
  • Homework 1: posted soon (due Tuesday 9/5)

2

9/4-9/8

M 9/4 Labor Day - No Class

D&F 1.1, 2.1;  Gallian 2 & 3; Pinter 4 & 5

  • Perusall: Euler's Formula & Group Theory due Sunday 9/3
  • Homework 1Turn in conversation recording and one of Problem 1, Problem 4, OR Problem 5 through WISE by 11:30pm Tuesday 9/5.  Remember, you need to meet with your homework group for these assignments and only one member of the group needs to upload their solutions to WISE.  Groups ar listed on the linked overleaf site.
  • Work on your mystery group journal (see Class Notes for ideas of lines of investigation).  
    • Set 1: Zach, Tyler, Ben, Harry, Yize, Zeke, and Brooke - I will be collecting your journals next Friday 9/8

3

9/11-9/15

D&F 1.2-1.5, Gallian 1, 5, & 10 Pinter 7&8

  • Perusall: Group Theory Overview due Sunday 9/10
  • Homework 2: Turn in conversation recording and one of Problem 1, Problem 4, or Problem 5 through WISE by 11:30pm Tuesday 9/12
  • Mystery group journal (see Class Notes for ideas of lines of investigation). 
    • Set 2: Anders, Allen, Taden, Leeloo, Whitley, Evan, and Dayton - I will be collecting your journals Friday 9/15

4

9/18-9/22

D&F 1.5-1.6, Gallian 3-4

  • Perusall: Group Theory & The Rubik's Cube due Sunday 9/17
  • Homework 3: Turn in conversation recording and one of Problem 3, Problem 4, or Problem 5 through WISE by 11:30pm Tuesday 9/19
  • Week 4 Google Survey: Please fill in this Survey ASAP if you want me to consider your preferences in assigning groups for Homework #4
  • Mystery group journal (see Class Notes for ideas of lines of investigation).  
    • Set 3: Colin, Ash, Indi, Jimmy, Beck, Mitchell, and Chris - I will be collecting your journals Friday 9/22

5

9/25-9/29

D&F 1.7-2.2

  • Perusall: Change Ringing and Other Applications of Permutation Groups (2 parts) due Sunday 9/24
  • Homework 4: Turn in conversation recording and one of Problem 2, 3, or 4  through WISE by 11:30pm Tuesday 9/26
  • Mystery Journal: Second Chance for first turn-in.  If you haven't turned in your group journal yet, you can turn it is by Friday 9/29 for up to 75% of the points for the first check-in.

6

10/2-10/6

D&F 2.2-2.3

  • Perusall: No Perusall this week, but another assignment will be posted soon due Sunday 10/8
  • Homework 5: Turn in conversation recording, Problem 5, and one of Problem 1, 3, or 4  through WISE by 11:30pm Tuesday 10/3

7

10/9-10/13

10/13 Mid-Semester Day, No Class

D&F 2.4-3.1

  • Perusall:  Classification of Finite Simple Groups and the Monster (2 parts) due Sunday 10/8
  • Homework 6: Turn in conversation recording, and one of Problem 3, 4, or 5  through WISE by 11:30pm Tuesday 10/10
  • Mystery group journal (ssee Class Notes for ideas of lines of investigation).  
    • Set 1: Zach, Tyler, Ben, Harry, Yize, Zeke, and Brooke -  I will be collecting your journals for the second time Thursday 10/12

8

10/16-10/20

D&F 3.1-3.2

Midterm 10/18

  • Perusall:  Quintessential Quaternions & Extra Credit 3b1b More on the Quaternions due Sunday 10/15
  • Celebration - Outside of Class Portion: Turn in before class on Wednesday 10/18
  • Mystery group journal (see Class Notes for ideas of lines of investigation). 
    • Set 2: Allen, Taden, Leeloo, Whitley, Evan, and Dayton - I will be collecting your journals for the second time Friday 10/20
9

10/23-10/27

D&F 3.2

  • Perusall:  Genius Box & Conway Reflects due Sunday 10/22
  • Homework 7: Turn in conversation recording, and one of Problem 5, 6, or 7  through WISE by 11:30pm Tuesday 10/24
  • Mystery Journal: (see Class Notes for ideas of lines of investigation).   
    • Set 3: Colin, Ash, Indi, Jimmy, Beck, Mitchell, and Chris - I will be collecting your journals for the second time Friday 10/27

10

10/30-11/3

D&F 3.3

  • Homework 8: Turn in conversation recording, and one LaTeXed problem through WISE by 11:30pm Tuesday 10/31

11

11/6-11/10

D&F 3.3-3.4
  • Perusall:  Map of Mathematics due-ish Sunday 11/5
  • Week 10 Survey: Please fill out before class Monday 11/6
  • Homework 9: Turn in conversation recording, and one of Problem 3 or 4  through WISE by 11:30pm Tuesday 11/7

12

11/13-11/17

D&F 3.5 & Ch. 4

  • Perusall:  A not so useless perspective due Sunday 11/12
  • Homework 10:Turn in conversation recording, and one of Problem 1 or 4  through WISE by 11:30pm Tuesday 11/14
  • Mystery group journal (see Class Notes for ideas of lines of investigation). 

13

11/20-11/24

Fall Break 11/22-11/24 No classes

  • Perusall: Group Actions Take 2 due Sunday 11/19

14

11/27-12/1

D&F Ch. 4

  • Perusall:  Kreweras Orbit Structure & A5 is Simple due Sunday 11/26
  • Homework 11Turn in conversation recording, and one of Problem 1 or 4  through WISE by 11:30pm Wednesday 11/29  (I will accept the homework through Friday 12/1 but if you want feedback before the Quiz Monday you need to turn it by Wednesday night)
  • Mystery group journal (see Class Notes for ideas of lines of investigation).  
    • I will be collecting everyone's group journals for the third and final time Friday 12/1

15

12/4-12/8

D&F Ch. 4 
  • Perusall: No more new Perusalls, but I invite you to go back and complete any assignments you missed for partial credit.
  • Homework 12Turn in conversation recording  by 11:30pm Wednesday 12/6  (I will accept the homework through Friday 12/8 but if you want feedback before the Final Monday you need to turn it by Wednesday night)
  • End of Semester Survey: https://forms.gle/r3J7cPcWtKN4TGE48

16

12/11-12/15

  Final Exam:  Dec 11 (Mon) 7-10 pm  5-6:30pm


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.htmlhttp://htmlspirograph.com/#0,50,0,1,1,-1.44,30,-700,1174,2.5,120,860,-3.6,100,1050,75,0,0,1,1064https://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: 8/28 (M) First day of classes

Week 2: 9/4 (M) Labor Day - No Classes

Week 4: 9/11 (M) Add/Drop Deadline

Week 7: 10/13 (F) Mid-semester break - No Classes

Week 10: 11/2 (Th) Withdraw Deadline

Week 11: 11/8-11/14  Registration for Spring

Week 13: 11/22-11/24 (W-F) Fall Break -  No Classes

Week 15: 12/6 (W) Last Day of Classes

Week 16: 12/11 (M) Final Exam 7-10pm