General Information:
| Meeting Time: | MWF, 11:00 - 11:50 |
| Location: | Psychology 305
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| Instructor: | Ryan Vinroot
Office: Mathematics 510
Office Hours: Mon 2-3, Tues 10-11, Thurs 11-12, or by appointment/walk-in.
Tutoring Room: Thurs 3-4 (in Math 220)
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| Undergraduate TA: |
Brendan Fry
Office Hours: Mon 3:30-5:30, Tues 4-5, Thurs 4-5:30.
Meeting Location: Mathematics Lobby
Tutoring Room: Thurs 3-4 (in Math 220)
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| Graduate TA: |
Casey Warmbrand
Office: Mathematics 217
Office Hours: Wed 1-2.
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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 415A - Introduction to Abstract Algebra. If you did not pass Math 415A, you will be dropped from this course. |
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Syllabus:
In the first week of class, we will prove the fundamental theorem of finite abelian groups, or the classification of isomorphism classes of finite abelian groups. This will serve as a quick review of major concepts from group theory from last semester. Also in the first week, you are expected to read in detail Chapter 12 to review the introductory concepts from ring theory which were covered at the end of 415A. The first homework will cover these topics. The first half of the the semester will be mainly dedicated to ring theory, with particular focus on polynomial rings. Polynomial rings are essential in understanding algebraic extensions of the rational numbers, which will be the main topic of the second half of the semester, along with general field theory. There will be various topics in group theory throughout the semester as well. The goal will be to give an introduction to Galois theory at the end of the semester, which is a theory linking fields, rings, and groups, through the structure of the relationship between the field of rational numbers and its algebraic extensions.
Dates & Course Announcements:
- Important Dates and Class Holidays
- Mon, Jan 15: NO CLASS (Martin Luther King Jr Holiday)
- Tues, Feb 6: Drop Deadline
- Tues, Mar 6: Withdraw Deadline
- Sat, Mar 10 - Sun, Mar 18: NO CLASS (Spring recess)
- Fri, May 4: FINAL EXAM
- (1/10) Since Mon, Jan 15, is a holiday, I will not have office hours. Instead, I will have extra office hours on Tues, Jan 16, 3:00-4:00.
- (1/22) Brendan Fry's office hours will be different this week (Mon Jan 22-Thurs Jan 25) than those listed above. This week his hours are Mon 4-5:30 and Tues 2-5, all in the Mathematics Lobby.
- (1/26) Please note that the due date for Homework #3 has been shifted to Wed, Jan 31 (at the beginning of class, as usual).
- (2/4) On Problem 42 in Chapter 15 (on p. 288), "(a)" should actually be "< a >", or the principal ideal generated by a. It should be noted that "(a)" is also common notation for the principal ideal generated by a, but this is not the notation that this book has chosen. Thanks to the students who pointed out this typo.
- (2/6) On Wed, Feb 7, and Fri, Feb 9, we will discuss Group Actions in lecture. Some of the material we will cover is not in the text, and the parts that are in the text are rather spread out, so for your convenience, a handout of the material we'll cover is here. This material will not be covered on the first test on Feb 14, but will be covered on the second test. A problem set for the material is on page 7 of the handout, and these problems are due on Mon, Feb 19.
- (2/28) Brendan Fry will not have office hours on Thurs, March 1. Please let me know if you would like to ask me questions on Thursday afternoon, as I will be available.
- (4/16) I will *not* have my regular office hours on Thurs, Apr 19, from 11-12. Instead, I will have office hours on Wed, Apr 20, from 3-4. I will be in the upper division tutoring room on Thursday afternoon as usual.
- (5/2) On Thursday, May 3, I will have office hours from 11-12 as usual, and in addition from 2-3 (the tutoring room is closed that day).
Exam Calendar:
| Test 1 |
Wed, Feb 14 |
In class |
Psych 305
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| Test 2 |
Wed, Apr 4 |
In class |
Psych 305
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| Final Exam |
Fri, May 4 |
11-1 |
Psych 305
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Homework:
Homework is due at the beginning of class on the due date of the assignment, and credit will not be given to late homework. Problems will be assigned roughly on a weekly basis. You may work with other students on problems, but each student must turn in their own write-up of their assignment. If any problems are completed in a collaborative effort, please indicate so on the paper turned in. The overall homework grade will be 20% of the final grade.
515B Students: You will have an extra assignment/project which will be due at the end of the semester. Please see me about this.
| Assignment |
Problems |
Due Date |
| 1 | pgs. 226-227 #11, 29, 30
pgs. 242-243 #28, 29, 40, 42, 47, 49
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Wed, Jan 17 |
| 2 | pgs. 255-257 #13, 22, 26, 39, 42, 43, 49, 54
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Wed, Jan 24 |
| 3 | pgs. 269-271 #14, 15, 20, 28, 38, 49, 56
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Wed, Jan 31 |
| 4 | pgs. 286-289 #13, 26, 38, 42, 46, 51, 60
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Wed, Feb 7 |
| Review Problems | pgs. 275-277 #4, 6, 9, 10, 14, 16, 18, 22, 25, 29, 31, 34, 38, 40, 47
pgs. 286-290 #12, 20, 43, 52, 62
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Not Due |
| 5 | The problems on pg. 7 of this handout
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Mon, Feb 19 |
| 6 | pgs. 299-300 #12, 16, 22, 29, 30
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Fri, Feb 23 |
| 7 | pgs. 300-301 #38, 42, pgs. 316-317 #8, 10, 12, 16, 26, 31
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Fri, Mar 2 |
| 8 | pg. 317 #33, pgs. 333-335 #1, 9, 10, 22, 33, 38
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Fri, Mar 9 |
| 9 | pgs. 348-349 #18, 19, 22, 26, 31, 32
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Fri, Mar 23 |
| 10 | pgs. 365-366 #2, 7, 8, 10, 14, 16, 20, 21
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Fri, Mar 30 |
| Review Problems | pgs. 339-340 #5, 12, 13, 19, 20, 22, 24, 30, 31, 32
pgs. 347-348 #6, 7, 11, 16, 24, pgs. 365-366 #3, 4, 5, 6, 13, 17, 18, 29
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Not Due |
| 11 | pgs. 366-367 #28, 30, 31, 32, 33
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Fri, Apr 13 |
| 12 | pgs. 378-379 #8, 10, 14, 18, 33
pgs. 388-389 #15, 17, 26
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Fri, Apr 20 |
| 13 | pgs. 378-379 #20, 21, 32
pgs. 388-389 #8, 22, 25, 30
pgs. 395-396 #4, 16
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Fri, Apr 27 |
| Review Problems | pgs. 275-277 #5, 11, 20, 28, 30, 32
pgs. 339-340 #3, 4, 10, 21, 26, 28, 33
pgs. 397-398 #4, 6, 7, 8, 10, 13, 14, 18, 22, 23
Any previous review problems you have not worked on
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Not Due |
Resources:
- There is a tutoring room in Math 220 for all upper-level mathematics courses (Math 300-499, except 302A and 302B). The online tutoring schedule may be found here.
- 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 main purpose is to learn about some interesting new mathematical problems while having fun, and the seminar is very casual and laid back. The seminar meets every Wednesday from 4:15 until 5:30 in PAS 418, and there is PIZZA at the end of every seminar. Please contact me or one of the other seminar organizers if you would like more information.
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