General Information:
| Meeting Time: | MWF, 10:00 - 10:50 |
| Location: | Jones 306
|
| Instructor: | Ryan Vinroot
Office: Jones 130
Office Hours: Mon, Wed 3:30-4:30, Th 9-10:30, or by appointment/walk-in.
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|---|
| Textbook: | Contemporary Abstract Algebra, Seventh 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 in the A range, a score of 400 (80%) is in the B range, etc. |
| Attendance Policy: | You are expected to attend all lectures. Attendance
is crucial in order to succeed in the course. Any legitimate absence for a test
must be discussed with me prior to the test date. |
| Prerequisites: | Math 214 - Foundations of Mathematics, and Math
211 - Linear Algebra. |
|
Syllabus:
The first couple of days, we will go over the highlights of "Chapter 0" of the
text, which is mainly a review of what you saw in Math 214. You should read
this entire chapter very carefully, as the concepts will be used throughout the
course. Like Math 214, this course will concentrate on the writing of proofs.
After this quick review, we will then jump right into the first main topic of the course:
groups. Chapters 1-11 of the book cover topics on groups, but we will not go
straight through this material. We will also be covering rings, and
concentrate on the topics in Chapters 12-15. Many of the concepts which are
important for groups have analogies for rings, and so we will be learning this
material in parallel. By the end of the semester, we will have covered much of
the material in Chapters 1-15.
Dates & Course Announcements:
Exam Calendar:
| Test 1 |
Mon, Oct 5 |
In class |
Jones 306
|
| Test 2 |
Fri, Nov 13 |
Take home |
Take home
|
| Final Exam |
Wed, Dec 16 |
2-5 |
Jones 306
|
- Important Dates and Class Holidays:
- Sat, Oct 10 - Tues, Oct 13:
NO CLASS (Fall Break)
- Wed, Nov 25 - Sun, Nov 29: NO CLASS (Thanksgiving Break)
- Wed, Dec 16: FINAL EXAM
- The first homework, listed below, is due at the beginning of class on
Monday, Aug 31.
- I wrote up some notes (pdf) regarding the
group U(n). These notes have a solution to Problem 13 on page 22 of
the text (a homework problem), which guarantees the existence of inverses
in U(n). Also, I explain in the notes why the product modulo n
of two elements in U(n) remains in U(n), which was left as an
exercise for you to think about.
- The following are a selection of review problems from the book to prepare
for the Final Exam:
pgs. 91-94 #1, 21, 39, 44
pgs. 176-177 #24, 33, 35, 44, 45, 47
pgs. 230-233 #1, 3, 7, 15, 28, 39
pgs. 276-278 #7, 14, 19, 29.
Homework:
There will be homework assigned roughly every week. Your homework score is 20%
of your final grade. Completion of all homework problems is required, and your
grade on a homework assignment will be based on completeness, as well as on the
details of the solutions of the problems graded. Individual homework
assignment should be completed by the student alone, although I am always open
for questions, either in office hours or by email.
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. Late homework will be marked off 20%
for every day late. Homework turned in after class on the due date is
considered one day late, and the day after 2 days late, and so on. Everything
is easier, of course, if you turn in the homework on time!
There will be several "Group Assignments" during the semester, other than the
individual assignments. Group assignments will be completed by a group of 3 or
4 students in a collaborative effort, but only one write-up of the problems
will be required. All students in the group receive the same score for the
homework. The responsibility of writing up solutions should be shared. I
suggest rotating this responsibility among the group members.
| Assignment |
Problems |
Due Date |
| 1 | pgs. 22-24 #11, 13, 26, 30, 32, 54
|
Mon, Aug. 31 |
| 2 | pgs. 52-54 #11, 24, 28, 36
pg. 36 #11, 12
|
Wed, Sept. 9 |
| 3 | pgs. 53-54 #14, 35
pgs. 65-69 #18, 26, 31, 56
|
Wed, Sept. 16 |
| Group 1 | pgs. 23-24 #27, 44, pg. 36 #16
pgs. 53-55 #23, 39,
pg. 67 #38
|
Mon, Sept. 21 |
| 4 | pg. 66 #20, pgs. 83-85 #21, 22, 24, 64
|
Fri, Sept. 25 |
| 5 | pgs. 83-85 #28, 33, 37, 56, 62
Optional: pg. 83 #36
|
Wed, Sept. 30 |
| 6 | pgs. 243-245 #22, 40, 46
pgs. 256-257 #26, 42, 45
|
Mon, Oct. 19 |
| 7 | pgs. 115-117 #18, 28, 36, 40, 53, 56
Optional: pg. 116 #48
|
Mon, Oct. 26 |
| 8 | pgs. 134-135 #15, 24, 26, 29, 32, 35
|
Mon, Nov. 2 |
| 9 | pgs. 150-151 #16, 24, 34
|
Fri, Nov. 6 |
| 10 | pgs. 193-196 #7, 8, 14, 53, 54
|
Mon, Nov. 23 |
| 11 | pgs. 194-196 #22, 52, pgs. 212-215 #13, 50, pg. 269 #7
|
Wed, Dec. 2 |
Resources:
- There are some very useful links related to abstract algebra on the
homepage of Professor Joseph Gallian, the author of the 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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