Math 430 - Abstract Algebra II - Spring 2020

General Information:

Meeting Time:TTh 2 - 3:20
Location: Morton 203
Instructor:Ryan Vinroot
Office: Jones 100D
Office Hours: Mon 2-3pm, Tues 11-12, Wed 1:30-3:30 (also by appointment).
Textbook:Abstract Algebra (Third Edition) by David S. Dummit and Richard M. Foote
Class Participation - 5%, Midterm - 30%, Homework - 35%, Final Exam - 30%. The grading scale will be the standard 10 percentage point scale, so that a final score of 93 or higher is an A, 90-92 is an A-, 87-89 is a B+, 83-86 is a B, 80-82 is a B-, 77-79 is a C+, 73-76 is a C, 70-72 is a C-, etc.
Attendance & Lecture Policy:It is expected that you attend all lectures, with exceptions minimized. It is greatly appreciated when you are on time. Please do your best to stay awake and attentive during lecture, please do not email or text during lecture, and keep all cell phones/hand held devices/tablets/laptops put away during lecture (unless you are specifically writing notes on a tablet). While it is understandable that you may miss a lecture here and there, or be sleepy in class once in awhile, repeated absences, late arrivals, naps, or general non-attentiveness will negatively affect your class participation score.
Prerequisite: Math 307 - Abstract Algebra I. In particular, it is expected that you are able to write clear proofs with techniques you have learned in Math 307 and Math 214.
Course Summary: We will begin the course by continuing the group theory you saw in Abstract Algebra I. In particular, we will first cover the Isomorphism theorems for groups (where the first isomorphism theorem serves as a review of much of the group theory you saw in Math 307). We will then cover a few more topics on group theory from Chapters 3 and 4 of the text, including composition series and the Sylow theorems. We will then move on to ring theory, and plan to cover material from Chapters 7, 8, and 9 from the text (where some topics from 307 will be quickly reviewed). Finally, we will finish the course with a study of field extensions in Chapter 13 of the book.

Dates & Course Announcements:

Midterm and Final Exams:

There will be one midterm (details will be determined later). The final exam will be timed. The midterm and the final will each count as 30% of your final grade. The final exam will be on Wed, May 13, from 2 PM until 5 PM.

Exam Calendar (Tentative):
Exam Date Time/Due Location
Final Exam Wed, May 13 2 PM - 5 PM TBA
  • All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
  • Important Dates and Class Holidays:
    • Fri, Jan 31: ADD/DROP DEADLINE
    • Sat, Mar 7 - Sun, Mar 15: NO CLASS (Spring Break)
    • Fri, Mar 23: WITHDRAW DEADLINE
    • Wed, May 13, 2:00 PM - 5:00 PM - FINAL EXAM
  • (1/22) I will determine regular office hours after the add/drop period. For these first two weeks, my office hours will be: Fri Jan 24, 1 pm-2 pm; Mon Jan 27, 11 am-12 noon; Tues Jan 28, 3:30 pm-4:30 pm; Wed Jan 29, 2 pm-3 pm; Thurs Jan 30, 1-2 pm.
  • (1/30) Here are some notes on the material on group actions we covered in class. A more expanded version would be in Sections 4.1-4.3 of the textbook, although this also contains several results you saw in Math 307 (such as Cayley's Theorem and Lagrange's Theorem) which use the notion of group actions.
  • (1/30) My office hours next week will be as follows: Mon Feb 3, 2 pm-3pm; Tues Feb 4, 11 am-12 noon; Wed Feb 5, 2:30 pm-4:30 pm.
  • (2/6) I have set my regular weekly office hours for the semester (unless otherwise notified) as follows: Mon 2-3, Tues 11-12, and Wed 1:30-3:30. As always, I am happy to try to find another appointment if these times don't work for you.
  • (3/2) Today, Mon Mar 2, I have to shift my office hours to 1-2 instead of 2-3. I apologize for any inconvenience this causes.


Homework problems will be a very important part of the course, and there will be homework assigned almost every week. Proofs and computations should be written carefully and neatly, with attention paid to the completeness of your argument and clarity of your steps. Individual homework assignments should be written up by yourself, although some collaboration while working on the homework is fine, and encouraged as long as the work you turn in is your own formulation of a solution. You should not, under any circumstances, attempt to copy solutions to problems online (although I know this is very tempting), as this will have to be treated as plagiarism. Instead, email me for a hint, or discuss problems in a group of classmates. There will be homework problems which will be turned in and graded, and other homework problems which will be suggested, but not to turn in.

Homework is due at the beginning of class on the due date of the assignment, and if you like you may email me a pdf of your homework (only) if you LaTex it (which is not required but welcomed). Homework that is turned in or in my email inbox 10 minutes after the beginning of the class is considered late. Everyone will get one free pass for a one-day late HW without penalty (by 5 pm the day after it is due). Late penalties are:
10% off if it is turned in after the beginning of class, but it is in my hands (on my door), or in my email inbox as a pdf by 5 pm on the day it is due.
20% off if it is turned in by 5 pm the next weekday after the due date.
20% more off for each (week)day late, turned in by 5 pm, thereafter.
Everything is easier, of course, if you turn in the homework on time!

Homework scores will each be out of 50 points. Your lowest homework score of the semester will be dropped.
Assignment Problems Due Date
1 Turn in: pg. 101 #3, 4, 7, 8
Don't turn in: pg. 96 #11, 18, 19
Thurs, Jan 30
2 Turn in: pg. 106 #7, pg. 116 #1, 2, pg. 122 #8
Don't turn in: pg. 106 #2, pg. 117 #10, pg. 122 #14
Thurs, Feb 6
3 Turn in: pgs. 146-147 #1, 13, 23, 30, 32
Don't turn in: pgs. 146-147 #4, 14, 15, 21, 27
Thurs, Feb 13
4 Turn in: pg. 147 #17, 34, pg. 231 #7, 9
Don't turn in: pg. 147 #31, pg. 231 #8, 10, 11
Thurs, Feb 20
5 Turn in: pg. 238 #3(a), pgs. 247-249 #2, 11, 16, 17
Don't turn in: pg. 238 #2, pgs. 248-249 #7, 9, 25
Thurs, Feb 27
Group Turn in: Prove all properties of the bijection in the
Lattice Isomorphism Theorem (Theorem 20, pg. 99)
Tues, Mar 3
6 Turn in: pgs. 256-257 #8, 11, pgs. 264 #3, pg. 267 #3, 4 Thurs, Mar 20

Math Major Writing Requirement (Math 300):

If you are a math major, and you would like to complete your major writing requirement through a writing assignment in this class, please let me know in the first week of class. This writing assignment will not count towards your grade in this class, but will rather just serve as your Major Writing Requirement (Math 300). You should only do this if all of the following hold: (1) you are not doing an honors thesis in Mathematics, (2) you are not doing your COLL 400 requirement in Mathematics, and (3) you are a senior. If you decide to do this, you must write your paper on a topic in Abstract Algebra (or a closely related subject) approved by me, and you must keep to a schedule of turning in drafts we agree on at the beginning of the semester in order to get credit.

Student Accessibility Services:

William & Mary accommodates students with disabilities in accordance with federal laws and university policy. Any student who feels they may need an accommodation based on the impact of a learning, psychiatric, physical, or chronic health diagnosis should contact Student Accessibility Services staff at 757-221-2512 or at to determine if accommodations are warranted and to obtain an official letter of accommodation. For more information, please visit the SAS webpage.