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Meeting Time: | MWF 9 - 9:50 |
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Location: | Jones 113 |

Instructor: | Ryan Vinroot Office: Jones 100D Office Hours: Mon 2-3, Wed 3-4, Thurs 10-11 and 2-3:30 (also by appointment). |

Textbook: | Abstract Algebra (Third Edition) by David S. Dummit and Richard M. Foote |

Grade Breakdown: | Class Participation - 10%, Homework - 60%, 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 430 - Abstract Algebra II |

There will be no midterm. The final exam will be a take-home exam, and due by the end of our final exam time slot, which is Tues, Dec. 17, 9 AM-12 Noon (so the take-home final will be due at noon that day).

- 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, Sep 6: ADD/DROP DEADLINE
- Sat, Oct 12 - Sun, Oct 15: NO CLASS (Fall Break)
- Fri, Oct 25: WITHDRAW DEADLINE
- Wed, Nov 27 - Sun, Dec 1: NO CLASS (Thanksgiving Break)
- Fri, Dec 6 - LAST DAY OF CLASS
- Tues, Dec 17, 9:00 AM - 12 Noon - FINAL EXAM

- (8/28) I will determine regular office hours after the add/drop period. For this short week, my office hours will be: Wed Aug 28 2-3:30, Thurs Aug 29 10:30-12 and 2:30-4.
- (9/2) The first HW has been posted. My office hours this week will be: Mon 2-3, Wed 3-4, Thurs 10:30-11:30 and 2:30-3:30.
- (9/9) My office hours this week, which might end up being my standard weekly office hours, will be: Mon 2-3, Wed 3-4, Thurs 10-11 and 2-3:30.
- (9/13) I will give the first optional half lecture on Mon morning, Sept 16, at 8:30 am in our regular room. I will start the discussion on the equivalence of the Axiom of Choice, Zorn's Lemma, and the Well-Ordering Principle.
- (9/16) My office hours last week will become my permanent weekly office hours: Mon 2-3, Wed 3-4, Thurs 10-11 and 2-3:30.
- (10/9) I have to cancel my morning office hours tomorrow morning, Thurs Oct 10, 10-11 am. I will still have my afternoon office hours tomorrow 2-3:30 pm.
- (10/11) As promised, here is some optional homework based on the optional half-lectures, all of which could be done just using the notes that I followed (so you can still work on these even if you did not come to the optional half lectures): Optional HW. You may turn these in for credit (either for a counted score, or a counted attempted problem) any time before 5 PM on the last day of classes this semester.
- (11/4) I will be out of town later this week, and so my office hours will be different this week. They are: Mon Nov 4 2-3:30, Tues Nov 5 1:30-3, and Wed Nov 6 2:30-4.

**Also**: This Fri, Nov 8, you all will be running class yourselves. Your assignment as a class is to get through the material in Sec. 14.6 under "Polynomials of Degree 4" starting on pg. 613, through pg. 615 up to the fundamental theorem of algebra (which we've already covered). One of your HW scores this week will be given for showing up to class on Friday and participating in going through this material with your classmates. A moderator (sub) will be there to make sure you are there and are going through material, so class still starts at 9 AM on Friday. You should all go through the material before hand, and you can break up the presentation of the material (use the chalkboard!) any way you want. - (11/11) The following are the notes of Keith Conrad that I was using for generating sets of
*S*, I was using Section 2: Notes on generating sets. I also proved a statement that was not in these notes which we will need: Any transitive subgroup of_{n}*S*containing a transposition and an_{n}*(n-1)*-cycle is all of*S*, which we proved from Corollary 2.6 in the linked notes._{n} - (11/15) Today in the optional half lecture, we are finishing the proof of the fundamental theorem of finite abelian groups. As optional problems (due no later than the last day of classes) I am assigning 13.6, pg. 557 #14, 15, 16, 17. These problems give a proof that for any
*m*>1, there are infinitely many primes congruent to 1 mod*m*. These facts give enough for the complete proof in Sec. 14.5 that any finite abelian group is the Galois group of some extension of**Q**contained in a cyclotomic field. - (11/18) My office hours this week will be as follows: Mon (Nov 18) 2-3:30, Wed 12:30-2, Fri 3-4:30.
- (11/25) Here is a video from the Mathologer YouTube channel about Cardano's cubic formula. Since we are not covering this in Sec. 14.7 of the book, you should watch this video, which also has some nice history in it: The Cubic Formula.
- (11/25) Here are 4 more optional problems, which are due any time by the beginning of the last day of class: pgs. 637-638 #13, 16, 17, 18.
- (12/6) The take-home final is being given out in class today, and will be due by 12 Noon on Tues, Dec 17. I will be available in my office during exams from 10 AM-12 Noon and 2-3:30 PM on Mon Dec 9, Wed Dec 11, Thurs Dec 12, Fri Dec 13, and Mon Dec 16.

Homework problems will each be graded out of 10 points. Your homework score will be based on your individual problem scores, rather than your scores on assignments. In particular, there will be at least 60 problems assigned for homework throughout the semester. Your total Homework score for the course will be based on your best 50 problem scores, along with full credit for 10 other earnestly attempted problems which are turned in on time. That is, your homework counts for 60% of your grade, which breaks down as your best 50 scores out of 10 points each, plus full credit for 10 attempted problems.

Homework problems are due on the posted due date at the start of class, either turned in as a hard copy, or emailed to me as a pdf of a latex file (scanned homework is not accepted). Homework is considered on time if it is turned in, or in my inbox, at most 10 minutes after the start of class.

A total of 10 Homework problems throughout the semester may be turned in up to 2 weekdays late (by 5 PM in my office or inbox) without penalty. No other late homework will be accepted for scoring (unless you have specific accommodations). All homework problems and their due dates will be listed below.

Assignment |
Problems |
Due Date |

1 | pg. 545 #2, 4 pg. 551 #1 (just product), 3, 5, 6 |
Mon, Sept 9 |

2 | pgs. 551-552 #4, 11 pgs. 555-556 #5, 6, 13(a,b), pg. 259 #35 |
Mon, Sept 16 |

3 | pgs. 556-557 #13(c,d) pgs. 566-567 #1(a), 4, 5, 6 |
Mon, Sept 23 |

4 | pg. 557 #13(e) pgs. 566-567 #1(b), 7, 10 |
Mon, Sept 30 |

5 | pgs. 581-582 #1, 2, 12, 13, 14 | Mon, Oct 7 |

6 | pgs. 582-583 #8, 16, 17, 18 pg. 589 #1, 8 |
Mon, Oct 21 |

7 | pg. 582 #15, pg. 589 #6, pg. 596 #5(a) pgs. 603-604 #5, 10, 13 |
Mon, Oct 28 |

8 | pg. 603 #7, 8, pgs. 617-621 #4, 17, 21, 37 | Mon, Nov 4 |

9 | pgs. 617-622 #12, 13, 14, 38 Go through material on Friday in class for a HW problem credit. |
Mon, Nov 11 |

10 | pgs. 617-623 #3, 18, 22, 39, 46, 47 | Mon, Nov 18 |

11 | pg. 106 #5, pg. 623 #44 pgs. 636-637 #4, 7, 12 |
Mon, Nov 25 |