General Information
| Meeting Time |
Mon., Wed., Fri., 11:00 - 11:50 |
| Location | Modern Languages 210
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| Instructor | Ryan Vinroot (vinroot@math.arizona.edu)
Office: Mathematics 510
Office Phone: 621-4835
Office Hours: Mon. 2-3, Tues. 10-11, Thurs. 11-12, or by appointment/walk-in.
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| Undergraduate TA |
Sam Xu
Meeting Location: Lobby of the Mathematics building
Office Hours: Mon. 3-4, Tues. 3-4, Thurs. 3-5, Fri. 3-5.
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| Graduate TA |
Casey Warmbrand
Office: Mathematics 217
Office Hours: By appointment (by the e-mail above)
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Textbook |
Contemporary Abstract Algebra, Sixth Edition, by Joseph A. Gallian |
Grade
Breakdown | 2 Tests -- 100 points each, Homework -- 100 points, Final Exam -- 200 points, for a total of 500 points. The grading scale will roughly be a 10 percentage point scale, so that a final score of 450 (90%) is an A, a score of 400 (80%) is a B, etc. |
| Prerequisites | Math 323 - Formal Mathematical Reasoning and Writing. |
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Syllabus
The first week of the course will be dedicated to modular arithmetic (from Chapter 0) and symmetry (from Chapter 1), along with a short review of equivalence classes. Modular arithmetic and symmetry will serve as arithmetic and geometric introductions to groups, and a vast amount of our examples throughout the semester will come from these, along with the key tool of equivalence relations. You will be expected to know most of Chapter 0, which you should read carefully, the majority of which was covered in Math 323. We will plan to cover through Chapter 14 by the end of the semester. The first two-thirds (or so) of the semester will be about group theory, while the last part will be the beginning of ring theory, which will be continued in Math 415B in the spring.
Announcements & Dates
- Important Dates and Class Holidays
- Monday, September 4th: NO CLASS (Labor Day)
- Friday, September 15th: Drop deadline
- Monday, October 2nd: Midterm #1, In class
- Friday, October 13th: Withdraw deadline
- Monday, November 13th: NO CLASS (Veterans Day observed)
- Friday, November 17th: Midterm #2, In class
- Thursday, November 23th - Sunday, November 26th: NO CLASS (Thanksgiving Recess)
- Monday, December 11th - FINAL EXAM, 11:00 - 1:00
- (8/21) Since the TA office hours are not yet set, on Thurs., Aug. 24, I will be in my office available for questions from 2:00 until 4:30 (in addition to my normal office hours listed above).
- (8/30) Since Monday, Sept. 4th, is a holiday, I will move my Monday office hours next week to Tuesday, 11-12. So on Tuesday, Sept. 5th, I will have office hours 10-12.
- (9/12) The date of the first midterm has been set as Mon., Oct 2, during class.
- (10/2) The following is a three page handout on the conjugacy classes of the symmetric group: Handout. The material will be covered in class, but it is not in the book, and so the handout is here for you as a reading reference.
- (10/10) The date of the second midterm has been set as Fri., Nov. 17, during class.
- (10/18) I will be out of town from Thurs., Oct. 19, until the afternoon of Tues., Oct. 24. Casey Warmbrand, the graduate TA, will be teaching the class on Fri., Oct. 20, and Mon., Oct. 23. I will not have office hours while I am out of town (of course), so instead I will have office hours today, Oct. 18, from 3-4, and next Wednesday, Oct. 24, from 3-5.
- (11/12) Since Monday, Nov. 13 is a holiday, I will not have the regularly scheduled office hours. Instead, I will have additional office hours on Tuesday, Nov. 14, 3:15-4:15, and on Thursday, Nov. 16, 3:30-4:30.
- (11/27) I will not have office hours on Thursday, Nov. 30, as I will be out of town. I will have extra office hours on Tuesday, Nov. 28, from 3-4.
- (12/7) Today (Thursday, Dec. 7), in addition to my normal office hours 11:00-noon, I will also have office hours 2:30-4:00. On Friday, Dec. 8, I will be available in my office for questions from 10:00-noon and 1:30-4:00.
Homework
Homework will be assigned regularly, with papers due at the beginning of class on the due date. There will be individual assignments as well as group assignments. Homework groups will be made on the first day of class, but will not necessarily be set for the whole semester. The final homework score will consist of 70% for the individual assignment scores, 30% for the group assignment scores, and will be normalized to 100 points for the final overall score.
| Assign. # |
Due Date |
Problems
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#1 |
Mon., Aug 28 |
Individual: pgs. 23-27 #4, 10, 13, 14, 16 Group: pgs. 23-27 #11, 26, 30, 33, 48 |
#2 |
Wed., Sept. 6 |
Individual: pgs. 37-39 #5, 6, 7, 8, pgs. 53-56 #2, 6 Group: pgs. 37-39 #10, 12, 16, pgs. 53-56 #8, 16, 23 |
#3 |
Mon., Sept. 11 |
Indiv: pgs. 54-56 #4, 5, 15, 18, 19, pgs. 67-71 #1, 4, 28, 30 Group: pgs. 54-56 #9, 13, 29, 32, pgs. 67-71 #6, 29 |
#4 |
Mon., Sept. 18 |
Indiv: pgs. 67-71 #14, 19, 27, 34, 44 Group: pgs. 67-71 #45, 52, pgs. 82-85 #18, 22, 30 |
#5 |
Mon., Sept. 25 |
Indiv: pgs. 82-85 #7, 10, 28, 36, 42, 60 Group: pgs. 82-85 #6, 13, 15, 20, 33, 64 |
#6 |
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Indiv: pgs. 112-114 #1, 2, 4, 17, 27, 37 |
#7 |
Mon., Oct. 9 |
Indiv: pgs. 112-114 #3, 18, 36, 38, 41 Group: pgs. 90-91 #1, 2, 4, 5, pgs. 112-115 #24, 28, 44 |
#8 |
Mon., Oct. 16 |
Indiv: pgs. 112-114 #8, 13, 19, 23, 32, 42 Group: pg. 114 #45, 46, pgs. 132-3 #4, 20, 26, pg. 211 #14 |
#9 |
Mon., Oct. 23 |
Indiv: pgs. 132-134 #22, 25, 32, pgs. 210-212 #7, 8, 37 Group: pgs. 132-134 #18, 24, 36, 37, pgs. 210-212 #6, 31 |
#10 |
Mon., Oct. 30 |
Indiv: pgs. 132-134 #2, 6, 33, pg. 211 #19, pg. 148 #2, 8, 14 Group: pgs. 132-134 #12, 16, 40, 42, pg. 211 #22 |
#11 |
Mon., Nov. 6 |
Indiv: pgs. 148-149 #16, 17, 26, 33, pg. 165 #2, 10 Group: pgs. 149-151 #22, 28, 47, pg. 165-166 #12, 15 |
#12 |
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Indiv: pgs. 166-167 #30, 38, pgs. 211-212 #16, 36, pgs. 191-194 #7, 39, 50, 52 |
#13 |
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Indiv: pgs. 191-194 #8, 22, 24, 37, 45, 58, pg. 213 #44 |
#14 |
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Indiv: pgs. 225-227 #6, 10, 15, 16, 22 |
#15 |
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Indiv: pgs. 240-243 #8, 17, 18, 22, 26, 44 |
Review |
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pgs. 90-93 #8, 9, 18, 20, 23, 30, 33, 34, 41, 44 pgs. 174-176 #1, 4, 6, 8, 12, 17, 18, 19, 34, 39, 50, 51 pgs. 230-232 #4, 7, 11, 18, 26, 28, 35 |
Resources
- As listed in the General Information above, there is both an Undergraduate Teaching Assistant (Sam Xu) and a Graduate Teaching Assistant (Casey Warmbrand) for this course. Both TAs will have office hours where you may ask questions about assignments or lectures. Other than the TA office hours and my own office hours (listed above), you can also go to the office hours of Professor Vélez, who is teaching Section 1 of Math 415A. Professor Vélez's office hours are as follows: Mon. 12-12:50 in Math 219, Wed. 10-10:50 in Math 220, and Fri. 9-9:50 in Math 219.
- There are some very useful links related to abstract algebra on the homepage of the author of the text, which is here. Also, if you find any errors in the text, come talk to me and we can send an e-mail to the author explaining the error.
- There are several opportunities for undergraduates interested in mathematics, funded by the Mathematics department, including being an Undergraduate TA or an Undergraduate Research Assistant. If you are interested, feel free to ask me or someone else in the Mathematics department about these opportunities. Information is available here.
- There is a mathematics problem solving seminar which meets once a week, and is devoted to mathematical techniques that you might not see in the normal undergraduate curriculum. The seminar meets every Monday from 4:15 until 5:30 in Math Room 501, and there is PIZZA at the end of every seminar. One of the purposes is to prepare students for the annual Putnam competition in December, but the seminar will also continue in the Spring semester. Please contact me or one of the other seminar organizers if you would like more information.
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