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.
|Meeting Time:||MWF 10 - 10:50
|Location: ||Jones 306|
Office: Jones 130
Office Hours: W 3 - 4:30 and Th 2:30 - 4:30, or by appointment/walk-in.
|Textbook:||Contemporary Abstract Algebra, Seventh Edition, by
Joseph A. Gallian|
| Grade |
| 2 Tests - 20% each, Homework
- 25%, Final Exam - 35%. The
grading scale will roughly be a 10 percentage point scale, so that a final
score of 90% is in the A range, a score of 80% is in the B range, 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).
|Prerequisites: || Math 214 - Foundations of Mathematics, and Math
211 - Linear Algebra. ||
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 Chatpers 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):
||Thurs, Oct. 6
||Due Nov. 21
||10:00 AM, Take-home
||Wed, Dec 7
- All relevant announcements will be listed here. Check back frequently (don't forget
to refresh your browser) for updates.
- Important Dates and Class Holidays:
- Wed, Sept 7: ADD/DROP DEADLINE
- Sat, Oct 8 - Tues, Oct 11: NO CLASS (Fall Break)
- Fri, Oct 21: WITHDRAW DEADLINE
- Thurs, Nov 24 - Sun, Nov 27: NO CLASS (Thanksgiving Break)
- Wed, Dec 7, 2:00-5:00 - FINAL EXAM
- (8/24) The first homework, listed below, is due at the beginning of class on
Mon, Aug 29. 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).
- (8/24) 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, Aug 24) 11-12 and/or 3-5, on
Thurs, Aug 25, 2:30-5, or on Fri, Aug 26 (times TBD).
- (9/7) The math server is back up! I will now use this course homepage for
all announcements, handouts, and assignments, as originally planned. Note
that the College shifted the add/drop deadline to TODAY, Sept. 7.
- (9/7) By next week, I will have a set schedule for office hours. Today
(9/7) I will have office hours 11-12 and 1:30-2:30. Tomorrow (9/8), I will
have office hours 2:30-4:30.
- (9/21) I made a typo on the assigned problems for HW#4. On p. 85, you
should do problem #64, not #65.
- (9/29) To review for the first midterm, which is now scheduled for next
Thursday, Oct 6, 6-7:30 pm or 8-9:30 pm, you should do as many problems as
you can from
Chapters 1-4, or from the Supplementary Exercises on pgs. 91-94. While any
problems you haven't yet done will help you prepare for the midterm, here is
a list of twenty to get you started:
pg. 35 #1, 2, pgs. 52-53 #10, 15, pgs. 66-67 #26, 34, pgs. 83-84 #21, 43,
pgs. 91-94 #1, 5, 6, 12, 16, 26, 27, 30, 33, 34, 44, 47.
- (10/3) I will have extra and extended office hours this week to help you
prepare for the first midterm exam. My office hours this week will be as
follows: Mon 3-4:30, Wed 2-5, Thurs 2-5.
- (11/28) I will have extra office hours today, Mon, Nov. 28, 2-3, and
tomorrow, Tues, Nov. 29, 2:30-4:30. I will have my regular office hours on
Wed and Thurs this week as well.
- (11/30) 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.
You should also work on any problems from the second take-home midterms which
you did not turn in for that.
- The following are the times I will be in my office on the Monday and
Tuesday before the final exam: Mon 12/5 and Tues 12/6, 8:30-10:30, 12-2, and
There will be homework assigned roughly every week. Your homework score is 25%
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 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 be a few "Group Assignments" during the semester, other than the
individual assignments. Group assignments will be completed by a group of approximately
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 in some way.
|1 ||pgs. 22-24 #11, 13, 18, 22, 26, 51, 54, 55
Please also read
the following regarding #11, 13, 18: pdf.
|Fri, Sep 2
|2 ||pgs. 52-54 #11, 17, 18, 24, 28, 35, 36
||Fri, Sep 9
|3 ||pg. 36 #10, 12, pg. 54 #34, pgs. 65-68 #4, 7, 18, 36, 52
||Fri, Sep 16
|4 ||pgs. 66-69 #19, 20, 42, 55, 56
pgs. 83-85 #22, 24, 64
|Fri, Sep 23
|Group 1||pg. 24 #44, 45, pg. 36 #16
pgs. 53-55 #23, 39, pg. 67 #38
|Mon, Sep 26
|5 ||pgs. 83-85 #26, 28, 33, 37, 54, 60
Extra (not required): pgs. 83-85 #36, 56
|Fri, Sep 30
|6 ||pgs. 167-169 #1, 53, pg. 177 #53
pgs. 243-245 #22, 42, 46
|Fri, Oct 14
|7 ||pgs. 255-257 #13. 20, 26, 45
pgs. 113-115 #2, 17, 30
|Fri, Oct 21
|8 ||pgs. 113-117 #3, 18, 28, 32, 36, 53, 56
Extra: pg. 116 #48
|Fri, Oct 28
|Group 2||pg. 116-117 #50, 52
pg. 243 #24, pgs. 257-258 #40, 52
|Mon, Nov 7
|9 ||pgs. 133-135 #1, 6, 19, 24, 27, 29, 38
Extra: Give a
complete proof of Theorem 8.3 on pg. 159
|Fri, Nov 4
|10 ||pgs. 133-135 #15, 17, 35
pgs. 149-150 #9, 15, 16, 20, 34
|Fri, Nov 11
|11 ||pgs. 193-196 #7, 14, 47, 53
pgs. 211-215 #5, 9, 54,
pg. 288 #16
|Wed, Nov 30
- 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.