Math 621
Algebra I
Spring 2015
Professor R. Goldin
Exploratory Hall 4214
rgoldin (at) gmu (dot) edu
Office Hours: Tues and Thurs, 12:45-1:15pm and 2:45-3:15pm, and by appointment
Course Description. This is a
graduate level course to group theory. Students who are not
familiar with basic group theory will be expected to do additional work
in the first few weeks to catch up to those who are. The prerequisite
for this course is MATH 315 or equivalent and MATH 322 or equivalent.
This is a proof-based course, so students should be comfortable with
writing extensive proofs. The text for the course is Abstract Algebra
(Third Edition), by Dummit and Foote. We will cover roughly Chapters
1-6.1, 7-9, parts of Chapter 10-12 and 13 with some ommissions. Time
permitting, we may add additional sections in Ch 10-12 and Chapter 14.
After finishing this course, you should be prepared to (study for and)
take the Ph.D. preliminary algebra exam.
Problem Sets. There
will be approximately ten problem sets throughout the semester (though
there may be as few as eight or as many as 12). You may work with other
classmates on problem sets, but you are not allowed to collaborate with
anyone not enrolled in the course who has advanced knowledge of the
material. We will
be presenting these problems in class, and you are expected to
participate. The problem sets are due when stated, but you will not
turn them in on the due date. Select problems will be part of three
Problem Sets Mashes, collected three times over the
semester (announcements will be made about 1 week in advance). You are
expected to TYPE the Problem Set Mashes! Do not wait until the
announcement is made to turn in the problems,
or you will be unable to complete them in time. No late Problem
Set Mashes will be
accepted. If you have a reason you can't make it to class, you can
email it to me on time, and bring me a hard copy the next time you come
to class.
Attendance and Participation.
Attendance will count for this course. There will be a sign-in sheet
each day; please only sign yourself in. You may miss two classes with
no penalty at all. you do not need to email me. You are expected to
present some problems from the homework during class. I will make sure
that everyone is called on at some point, so pease be prepared!
Presentations. Some students
will have the opportuntity to present important topics in the course.
If you present, you will have one free pass on turning in the homework
over the semester; your presentation grade will replace the homework grade. Presentations will be graded on how well you know
the material you are presenting.
Midterm Exam. There is one
midterm exam, currently scheduled for Tuesday March 24. (Note this is different than the original date of Tuesday March 17). There is no
makeup for this exam except for extreme circumstances. If those
circumstances warrant a makeup, you must let me know beforehand, unless
the circumstances prohibit that. A makeup exam may be oral instead of
written, or it may consist of an extra problem set, at my discretion.
Final Exam. The final exam is a take home exam. Details to come.
Grading. The grade in this
course will be based on class participation, problem
sets/presentations, and exams. Class attendence is require. There will
be one midterm exam, one final exam, and approximately four turned-in
composite of problem sets over the semester. The grade will be
determined by:
15% Midterm exam
15% x 3 Each Problem Set Mash or new-topic presentation
25% Final exam
15% Class participation and attendance