Math 430 - Abstract Algebra II - Spring 2017

General Information:

Meeting Time:MWF 9 - 9:50
Location: Jones 306
Instructor:Ryan Vinroot
Office: Jones 100D
Office Hours: M 2:30-4, W 4-5, Th 11-12 and 3:30-5 (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. 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.
Course Summary: We will begin on the first day with a quick overview of group theory that you saw in Abstract Algebra I, by proving the (First) Isomorphism Theorem of Groups. The second day will continue this discussion, and we will prove the so-called Second and Third Isomorphism Theorems of Groups. We will then move on to the main topics of the course, which will be Rings and Fields. We will plan to cover material from Part II - Ring Theory (Chapters 7, 8, and 9) and Part IV - Field Theory and Galois Theory (Chapters 13 and 14) from the textbook. Hopefully, by the end of the course we will cover Section 14.7 from the book, which covers the insolvability of the quintic equation (a historically big accomplishment of Abstract Algebra).

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 10, from 9 AM until 12 Noon.

Exam Calendar (Tentative):
Exam Date Time/Due Location
Midterm Given Mon, Mar 20 Due Fri, Mar 31 at 9 AM Take home
Final Exam Wed, May 10 9 AM - 12 Noon Jones 302
  • 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 27: ADD/DROP DEADLINE
    • Sat, Mar 4 - Sun, Mar 12: NO CLASS (Spring Break)
    • Fri, Mar 17: WITHDRAW DEADLINE
    • Wed, May 10, 9:00 AM - 12 Noon - FINAL EXAM
  • (1/18) My office hours during this first short week of classes are: Wed 4-5, Thurs 11-12 and 3-5. Regular weekly office hours will be announced soon.
  • (1/23) My office hours this week are: Mon 3-5, Wed 4-5, Th 11-12 and 3:30-5.
  • (1/30) My weekly office hours for the semester are set as follows: Mon 2:30-4, Wed 4-5, Th 11-12 and 3:30-5. You can always email me to make an appointment if you would like to talk to me outside of these.
  • (2/6) My office hours today have to be cut to 3-4 pm. My other office hours this week are my normal ones.
  • (2/20) I will have extra available time in my office tomorrow (Tues, Feb 21). I will be available 10-11:30 and 1-3. Feel free to drop in with any questions.
  • (3/1) I corrected the due date for HW #5, it is due on Friday March 17 (and not during Spring Break as previously posted). Also, I will be in class about 25 min early this Wed (today) and Friday (Mar 3) to discuss any homework problems, past or present.
  • (3/3) Here is an article that is well-written and about things going on in number theory now related to unique (or non-unique) factorization, it would make good Spring Break reading: Class Numbers and the Symmetries of Groups
  • (3/20) The take-home midterm is being handed out today in class, and is due next Friday, Mar 31, at the beginning of class. No late midterms will be accepted (that is, late penalties do not apply since it is not homework).
  • (3/27) I have weird office hours today (Mon, Mar 27): Instead of 2:30-4, my office hours will be 3-3:45 and 4:30-5. I apologize for any inconvenience.
  • (3/27) There will be optional half-lectures this Wed, Mar 29 and this Fri, Mar 31, at 8:35 am in the regular room. I will be going through the proof that e is transcendental. If you missed today's (Monday) optional half-lecture, you will not be behind on Wednesday, so please come if you are interested and I promise you will not be lost!
  • (4/19) Here are the notes which prove the multiplicative group of a finite field is cyclic, without using the Fundamental Theorem of Finite Abelian Groups: Notes.
  • (4/19) I am giving everyone a penalty-free extenstion for Homework 8. You may turn it in at class time on Monday, Apr 24.
  • (4/26) There is a last optional problem set posted. If you turn it (or email me a pdf) by 9 AM on Wed, May 3, it will count as extra credit towards your homework score for the class (that is, there is no penalty at all to your grade for turning in problems from this HW). This material will be covered on the final exam, so the problems are important to look at before the final, but turning them in is completely optional.
  • (4/26) The final exam is on Wed, May 10, in Jones 302 from 9 AM until 12 Noon. This will be a timed cummulative final, which will be closed book and closed notes. There will be more emphasis on the second half of the semester's material than on the first half. I will post my exam period office hours soon.
  • (4/28) My office hours during exams will be as follows. I will give priority to Calculus students during my office hours during the first week:
    Mon, May 1: 12 Noon-2 pm
    Tues, May 2: 12 Noon-2 pm, 4-5 pm
    Wed, May 3: 9-10 am, 12 Noon-2 pm, 3-5 pm
    Mon, May 8: 12 Noon-2 pm, 4-5 pm
    Tues, May 9: 9-10 am, 12 Noon-2 pm, 3-5 pm


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 OK. You should not, under any circumstances, attempt to look up solutions or hints to problems online. I will consider this plagiarism, and treat this as an honor offense. 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 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 be allowed exactly 1 unpenalized late-by-one-day homework (so once during the semester, a HW can be turned in one weekday late by 5 pm with no penalty). After that, late penalties are:
10% off if it is turned in after the beginning of class, but it is in my hands, 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 #4, 7, pg. 231 #7, 9, 10
Don't turn in: pg. 101 #3, 8, pg. 231 #8, 11, 17
Mon, Jan 30
2 Turn in: pg. 238 (7.2) #3(a,b), pg. 247-249 (7.3) #2, 11, 17, pg. 256 (7.4) #7
Don't turn in: pg. 238 #4, pg. 247-249 #1, 9, 16, pg. 256 #9
Mon, Feb 6
3 Turn in: pg. 256-257 (7.4) #8, 13, pg. 264 (7.5) #3, pg. 267 (7.6) #1, 3
Don't turn in: pg. 257-258 #10, 19, pg. 264 #1, pg. 267 #2, 4
Mon, Feb 13
4 Turn in: Show that the following elements in the following rings are
universal side divisors (see pg. 277): 2 in Z, 1+i in Z[i], x in F[x] where F is a field.
pg. 278 (8.1) #9, 10, pg. 282 (8.2) #1, 3
Don't turn in: pg. 278 #8
Mon, Feb 27
5 Turn in: Write a full proof of the first claim in Corollary 19 on p. 291
(the proof is outlined above Corollary 19).
pg. 293 (8.3) #4, 6, pg. 306 (9.3) #1
Don't turn in: pg. 293 #8
Fri, Mar 17
6 Turn in: pg. 519 (13.1) #2, 4, pg. 530 (13.2) #8, 14, pg. 545 (13.4) #3
Don't turn in: pg. 519 #6, 7, pgs. 530-531 #2, 3, 4, pg. 545 #1, 2
Fri, Apr 7
7 Turn in:pg. 545 (13.4) #4, 5, pgs. 551-552 (13.5) #3, 8, and this problem (pdf)
Don't turn in: pg. 531 #19, pg. 545 #6, pg. 551 #1, 2
Fri, Apr 14
8 Turn in: pg. 551 (13.5) #6, pg. 567 (14.1) #4, 5, 7 pg. 581 (14.2) #1
Don't turn in: pgs. 566-567 #1, 2, 3, pg. 581 #2
Fri, Apr 21
penalty-free extension to
Mon, Apr 24
9 Optional: pg. 582 (14.2) #12, 13, 14, 15, 16 Wed, May 3, 9 AM

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). 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 that is set at the beginning of the semester in order to get credit.