General Information:
| Meeting Time: | MWF, 12:00 - 12:50 |
| Location: | Jones 306
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| Instructor: | Ryan Vinroot
Office: Jones 130
Office Hours (Tentative): Mon 3:30-4:30, Wed 3:30-4:30, Thurs 9-10:30, or by appointment/walk-in.
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| Textbook: | A First Course in Abstract Algebra, Seventh Edition, by
John B. Fraleigh |
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 in the A range, a score of 400 (80%) is in the B range, etc. |
| Prerequisites: | Math 307 - Algebra I. |
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Syllabus:
We will be covering topics in Groups, Rings, Fields, and Galois Theory, which
extend the concepts covered in Math 307. We will start with Sections 16 and 17
of the text, which cover Group Actions, and then we will cover the Sylow Theorems in Sections 36 and 37. We will then move to Rings, and quickly
review some of the topics in Sections 22, 23, 26, and 27 which were covered in
Math 307. Ring theory continues in Chapter IX (Sections 45-47), which
concentrates on the various classes of rings based on factorization
properties. This will be followed by Chapter VI (Sections 29-33), which covers
the topic of Extension Fields. Finally, we will finish the semester by
covering as much as Chapter X as time allows, which covers the topic of Galois
Theory. Galois Theory will link all of the topics covered previously in the
following way: Field extensions are contructed by polynomial rings modulo a maximal
ideal, and Galois theory connects the subgroup structure of the automorphism
group of a field extension (which is an instance of a group action) to the
subfield structure of that field extension.
Dates & Course Announcements:
- Important Dates and Class Holidays:
- Sat, March 7 - Sun, March 15:
NO CLASS (Spring Break)
- Fri, May 8: FINAL EXAM
- Here is a pdf of some notes on Group
Actions. There is some material in these notes which is not in Section 16
of Fraleigh, and likewise, some material in Section 16 of Fraleigh which is
not in these notes.
- Here are some notes on the conjugacy classes
of symmetric groups. Use them as a guide if you get stuck on Problem 8 on
page 333 of the homework.
- I will be in (or near) my office the following times before the Final:
Mon (May 4) 9-12, 2-5; Tues (May 5) 9-1, 3-5; Wed (May 6) 8:30-11:30; Thurs
(May 7) 9-1, 2:30-5.
Exam Calendar:
| Test 1 |
Wed, Feb 25 |
In class |
Jones 306
|
| Test 2 |
Fri, Apr 3 |
Take home |
Jones 306
|
| Final Exam |
Fri, May 8 |
9-12 |
Jones 306
|
Homework:
For each homework problem assigned, a complete solution with each step
explained should be written up. Be sure to explain your steps and reasoning
for calculations as well as for proofs. 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.
| Assignment |
Problems |
Due Date |
| 1 | pgs. 159-160 #9, 11, 12, 14
pgs. 164-165 #6, 8
|
Mon, Feb 2 |
| 2 | pg. 327 #11, 14
pg. 333 #8, 9
|
Mon, Feb 9 |
| 3 | pg. 327 #17, 18, 22
pg. 333 #5, 6, 7
|
Fri, Feb 20 |
| 4 | pg. 208 #24, 25
pgs. 244-245 #17, 30
pg. 253 #24
|
Wed, Mar 4 |
| 5 | pg. 400 #26, 31
pgs. 406-407 #12, 17, 18
pg. 413 #9, 15
|
Fri, Apr 3 |
Resources:
- There are some very useful links related to abstract algebra on the
homepage of Professor Joseph Gallian (the author of another Abstract Algebra text), which is here.
- There are several opportunities for undergraduates through the William &
Mary mathematics department, including research in mathematics. If you are interested, feel free to ask me or someone else in the Mathematics department about these opportunities. Information is available here.
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