Math 430 - Abstract Algebra II - Spring 2019

General Information:

Meeting Time:MWF 11 - 11:50
Location: Morton 37
Instructor:Ryan Vinroot
Office: Jones 100D
Office Hours: Mon 3:30-5, Wed 3-4, Thurs 10-11 and 4-5 (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. 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 1, from 9 AM until 12 Noon.

Exam Calendar (Tentative):
Exam Date Time/Due Location
Midterm Due Mon, Mar 25 In class Take-home
Final Exam Wed, May 1 9 AM - 12 Noon Morton 37
  • All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
  • Important Dates and Class Holidays:
    • Mon, Jan 21: NO CLASS (Martin Luther King Holiday)
    • Mon, Jan 28: ADD/DROP DEADLINE
    • Sat, Mar 2 - Sun, Mar 10: NO CLASS (Spring Break)
    • Fri, Mar 15: WITHDRAW DEADLINE
    • Wed, May 1, 9:00 AM - 12 Noon - FINAL EXAM
  • (1/16) I will determine regular office hours after the add/drop period. For this short week, my office hours will be: Wed, Jan 16 (today) 3-4 pm, and Thurs, Jan 17, 10-11 am and 2-3 pm.
  • (1/23) My office hours this week will be as follows: Wed, Jan 23 2:30-4 and Thurs, Jan 24 9:30-11 and 2-3.
  • (1/28) HW #1 is due today at the beginning of class, either as a hard copy handed in to me, or a pdf of a LaTex document emailed to me. HW #2 has been posted and is due next Monday. My office hours this week will be: Mon Jan 28 4-5, Wed Jan 30 2:30-4, Thurs Jan 31 9:30-11 and 2-3.
  • (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.
  • (2/4) My regular weekly office hours for the semester will be as follows: Mon 3:30-5, Wed 3-4, Thurs 10-11 and 4-5.
  • (2/8) I fixed a typo on the assigned HW #3 due on Monday. I meant for #32 to be assigned, not #31. That has been fixed below.
  • (2/14) Before Spring Break (which is already in two weeks and 1 day), the group HW proving the properties of the Lattice Isomorphism Theorem will be due. Just one HW needs to be turned in per group, with everyone's name on that HW. This is due by class on Friday, March 1.
  • (3/11) There will be one more HW due before you have the take-home midterm. HW 6 will be due on Mon, Mar 18, and on that day in class I will hand out the take-home midterm.
  • (3/11) I am handing back the group homeworks with comments on them. I have made copies so that each person in each group has a copy. A second draft of the group HW will be due on Friday, Apr 12. Each group needs to turn in a second draft in order to receive a score on the homework.
  • (3/29) I very slightly shortened the HW due on Mon, Apr 1. For Problem 5 on pg. 293, you only need to do parts (a) and (b). I realized part (c) uses a result that we haven't proved (and won't need otherwise) that any non-maximal ideal of a commutative ring is contained in some maximal ideal (which can be proved using Zorn's Lemma).
  • (4/22) My afternoon office hours have to shift to 30 minutes earlier today, so they will be 3-4:30 today.
  • (4/24) The Final Exam will be in our regular lecture room, Morton 37, on next Wed, May 1, 9 AM-12 Noon.
  • (4/26) My office hours on the two days before the Final Exam are as follows:
    Mon, Apr 29 - 9:30-11, 12-2, and 3-4:30
    Tues, Apr 30 - 9:30-11, 12-2, and 3:30-5.


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. 101 #2, 9, 10
Mon, Jan 28
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
Mon, Feb 4
3 Turn in: pgs. 146-147 #1, 13, 23, 30, 32
Don't turn in: pgs. 146-147 #4, 14, 15, 21, 27
Mon, Feb 11
4 Turn in: pg. 147 #17, 34, pg. 231 #7, 9
Don't turn in: pg. 147 #31, pg. 231 #8, 10, 11
Mon, Feb 18
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
Mon, Feb 25
Group Turn in: Prove all properties of the bijection in the
Lattice Isomorphism Theorem (Theorem 20, pg. 99)
Fri, Mar 1
6 Turn in: pgs. 256-257 #8, 11, pgs. 264 #3, pg. 267 #3, 4 Mon, Mar 18
Midterm Take-home Midterm due Mon, Mar 25
7 Turn in: Prove that Z[√-2] is a Euclidean domain
pgs. 278-279 #10, pg. 282 #3, pgs. 293 #5(a,b), 6(a,b)
Don't Turn in: pg. 278 #9, pg. 283 #7(a,b), pg. 293 #3, 4, 6(c)
Mon, Apr 1
8 Turn in: pg. 306 #3, pg. 311-312 #2, 3, 17, pg. 315 #3
Don't Turn in: pg. 306 #4, pgs. 311-312 #1, 4, 18, pg. 315 #7
Mon, Apr 8
Group Second Draft of Group HW due Fri, Apr 12
9 Turn in: pg. 311 #6, 7, pg. 519 #4, 6, 7
Don't Turn in: pg. 311 #5, 8, pg. 519 #3, 5, 8
Mon, Apr 15
10 Turn in: pg. 519 #1, pg. 530 #7, 12, 13, 14
Don't Turn in: pg. 519 #2, pg. 530 #4, 5, 10, 17
Mon, Apr 22
Not due Don't Turn in: pgs. 529-530 #2, 3, 6, 16, pg. 545 #1-4 Last material for Final Exam

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.