General Information:
| Meeting Time: | MWF 9 - 9:50 |
| Location: | Morton 203
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| Instructor: | Ryan Vinroot
Office: Jones 130
Office Hours: M 3-4, W 3-4, Th 3-4:30 (and Th 10-11:30 AM), or by appointment/walk-in.
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| Textbook: | Contemporary Abstract Algebra, Seventh Edition, by
Joseph A. Gallian |
Grade
Breakdown: | 2 Tests - 20% each, Homework/Quizzes
- 30%, 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-, etc. |
| Attendance & Lecture 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. Please do not email or text
during lecture, and keep all cell phones/hand held devices/laptops put away
during lecture (especially during exams).
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| Prerequisites: | Math 214 - Foundations of Mathematics, and Math
211 - Linear Algebra. |
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Syllabus:
In the first short week of class, we will go over some of the main topics 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. The first homework, due on the first Monday of class, will cover this
material. It will be graded as if it is a take-home exam from Math 214, and
should be treated as such when you work on it. Like Math 214, this course will
concentrate on the writing of proofs, and so you should have a firm grasp on
these basic skills in order to get through this class.
After the quick review in the first week, we will 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
through this material linearly. We will first cover Chapters 1-4 (and a touch
of 8), which give
an introduction to groups. The other main topic of the course is that of
rings, and the next topic we will cover is the introduction to rings in
Chapters 12-13. We will then go back to groups, and cover topics on
permutation groups, cosets, and group isomorphisms in Chapters 5-7. Finally,
we will learn about group and ring homomorphisms, along with factor groups and
factor rings, in parallel in Chapter 9-10 and 14-15. By the end of the
semester, we will have covered topics in Chapters 1-15 (although not every
topic in every chapter).
Dates & Course Announcements:
Exam Calendar (Tentative):
| Test 1 |
Tues, Feb 28/Wed, Feb 29 |
7:30-9 pm |
Morton 203
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| Test 2 |
Due Mon, Apr 9 |
Take-home |
Take-home
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| Final Exam |
Fri, May 4 |
9-12 |
TBA
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- All relevant announcements will be listed here. Check back frequently (don't forget
to refresh your browser) for updates.
- Important Dates and Class Holidays:
- Fri, Jan 27: ADD/DROP DEADLINE
- Sat, Mar 3 - Sun, Mar 11: NO CLASS (Spring Break)
- Fri, Mar 16: WITHDRAW DEADLINE
- Fri, May 4, 9:00 - 12:00 - FINAL EXAM
- (1/18) The first homework, listed below, is due at the beginning of class on
Mon, Jan 23. The purpose of the first homework is to review crucial
concepts from Math 214. I will grade this homework very carefully, and it
should be completed as if it is a Math 214 take-home exam (although using any
class material is fine).
- (1/18) I will determine my regular weekly office hours as we all settle in
to our semester schedule, but during this first short week, I will be
available in my office for questions as often as possible. Please feel free
to drop by today (Wed, Jan 18) 2:30-5, on
Thurs, Jan 19, 9-11:30, or on Fri, Jan 20, 2-3:30.
- (1/27) Here is the handout on properties of powers in groups which I gave
to you in class: pdf.
- (2/3) Here are some notes on the group U(n), including a full
solution to Problem 13 from Chapter 0, as well as a proof of closure of the
operation in U(n), which I left as an exercise for you in
class: pdf.
- (2/3) I originally made a small typo in HW 4 below, which I have now
fixed. You should do Problem 36 in Chapter 3, not Problem 37.
- (2/6) Quiz 1 will be on Mon, Feb 13, at the end of class. It will cover
any material in the book or from lecture from Chapters 1, 2, and through page
60 of Chapter 3.
- (2/8) On Thurs, Feb 9, my office hours will be shifted to 3:30-5 (instead
of 3-4:30, as I have to sub for a class 2-3:20).
- (2/20) Here are some problems from the Supplementary Exercises in the book
which you can work on to prepare for the exam. Many of these are closer to
more challenging homework problems, but nonetheless will help you become more
comfortable with the material. The first list of problems require a good
working knowledge of the material covered, while the second list of problems
are more challenging (but still good problems to work on). Make sure you
can do all of the problems in the first list before working on the problems
in the second list:
pgs. 91-94 #1, 2, 5, 11, 12, 16, 18, 27, 30, 31, 33, 44, 47
pgs. 91-94 #6, 9, 13, 17, 20, 23, 34
- (2/24) I will have the following extra/extended office hours next Monday
and Tuesday, before the midterm: Mon, Feb 27, 2:30-4:30, and Tues, Feb 28, 2:30-4:30.
- (2/29) I will have extended office hours today, Wed, Feb 29, 2:30-4:30.
- (3/26) My regular office hours 3-4 pm today are canceled.
- (3/28) My morning office hours on Thurs, Mar 29, will be 9:30-11 AM rather
than 10-11:30 AM.
- (4/18) Here is an optional homework assignment, related to the rationalizer
of a group element, and when it is a subgroup. There is no penalty for not
doing this assignment, but you may turn it in any time before the final exam,
for extra points towards your HW/quiz score for the
course: Extra HW.
- (4/23) I will have additional office hours on Tues, Apr 24, 2:30-4 pm, to
answer questions about the last homework, due on Wed, Apr 25.
- (4/25) The following are a collection of problems which would be good to
do in preparation for the final. Some of these problems are more involved
than those you might be expected to do on the Final Exam, but are good
problems for review anyway:
pgs. 91-94 #2, 11, 28, 35, 40
pgs. 176-177 #24, 33, 35, 44, 45, 51
pgs. 230-233 #1, 3, 7, 10, 12, 15, 28, 39
pgs. 276-278 #7, 14, 15, 19, 29.
- (4/26) I will have office hours during the first week of Final Exams on the
following days and times:
Mon, Apr 30, 12-2,
Tues, May 1, 12-2, 4-5,
Wed, May 2, 12-2, 3-4:30,
Thurs, May 3, 12-2, 3-4:30.
Homework and Quizzes:
There will be homework assigned roughly every week. 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. I will be grading four
problems on each homework in detail, which will be worth 10 points each, and 10
points of your homework will be for completeness of the assignment, for a total
of 50 points for each homework. 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 clearly and neatly. Be sure to completely 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 next weekday after that 2 days late, and so on. Everything
is easier, of course, if you turn in the homework on time!
There will also be 2 quizzes (15 min during class) during the semester, the
first of which will be before the first midterm. Your homewok and quizzes will
count for a total of 30% of your final grade.
| Assignment |
Problems |
Due Date |
| 1 | pgs. 22-24 #11, 13, 18, 22, 26, 51, 54, 55
Please also read
the following regarding #11, 13, 18: pdf.
|
Mon, Jan 23 |
| 2 | pg. 52 #1, 4, 8, 11, 12
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Fri, Jan 27 |
| 3 | pgs. 53-54 #19, 28, 29, 34, 35, 36
pg. 36 #10, 11
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Fri, Feb 3 |
| 4 | pgs. 65-69 #8, 18, 20, 36, 51, 52, 56, 59
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Fri, Feb 10 |
| 5 | pg. 68 #42, pgs. 83-85 #4, 21, 22, 28, 37, 54, 64
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Fri, Feb 17 |
| 6 | pgs. 167-169 #4, 10, 36
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Fri, Mar 2 |
| 7 | pgs. 243-244 #9, 12, 22, 42, pgs. 255-257 #8, 20, 26, 45
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Fri, Mar 16 |
| 8 | pgs. 114-117 #17, 28, 33, 36, 40, 15, 18, 53
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Fri, Mar 23 |
| 9 | pgs. 133-135 #1, 4, 6, 15, 22, 29, 32, 35
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Fri, Mar 30 |
| 10 | pgs. 149-151 #8, 16, 20, 34, 43
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Fri, Apr 13 |
| 11 | pg. 212 #8, 9, pgs. 193-196 #7, 8, 14, 40, 47, 53
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Fri, Apr 20 |
| 12 | pgs. 212-215 #11, 13, 21, 56, pgs. 269-270 #4, 10
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Wed, Apr 25 |
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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