Algebra II - MAS 5312-001 - Spring 2008
| Instructor |
Brian Curtin |
| Office |
PHY 318 |
| Phone |
(813) 974-4929 |
| e-mail |
bcurtin@math.usf.edu |
| Office Hours |
F 11-11:50 and by appointment |
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Disclaimer:
Any announcment made in class supercedes the contents of this web page.
Extended Syllabus
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PDF of syllabus handed out in class |
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| Meeting time: |
MWF 10:00-10:50. We meet in
PHY 109.
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| Prerequisites: |
Undergraduate linear algebra (MAS 3105), abstract algebra (MAS
4301), and Algebra I (MAS 5311).
Although we will develop each topic from the basics, the pace and
depth will make the course challenging. The prerequisites will give you
a foundation upon which to build your understanding. In this course you
will be required to generate and write proofs. The prerequisites will have
given you some facility in this. (Of course it is not expected
that you have completely mastered these skills when you begin the course).
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| Text: |
''Algebra, a graduate course'' by I. Martin Isaacs.
(
publisher)
(
Amazon)
(
Barnes and Noble)
I will ask the library to keep its copy on reserve.
We will cover much of Part II in this course. Although slightly
reorganized, together this meets most of the content for Algebra
I and II described in the
course
description. |
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| Homework: |
There will be 4 to 8 problems assigned from each section
covered. A few of them will be graded, some will earn credit for
being turned in. The homework is intended to give you problems to
practice the material which we are covering
in class. You are likely to find that most of your understanding comes
from doing problems. I do not expect that students will do every
problem, but they should attempt most of the problems and turn in at least
half of them completed over the course of the semester for a satisfactory
grade on homework. Homework should be turned in within 2 weeks of the
day it is assigned.
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| Exams: |
There will be a take-home mid-term exam on Chapters 16 - 19 handed
out in class on Friday,
February 29 and due at the beginning of class on
Friday, March 7.
There will be a take-home final exam covering Chapters 20--27 given
out
Monday, April 25 and due Monday, May 2 by noon (the
allocated time for the final exam).
There will be no make-up exams or
extra time granted to take the exams. If you are unable to turn
either exam in strictly on time, you must make arrangements with
the teacher before it is due.
During the exam periods you may ask me about the exams, you may
consult your notes, and you may consult the textbook. No other source
of information may be sought or used, including but not restricted to
your classmates, your classmates' notes, your friends, other professors,
books other than the Isaacs' Algebra, online information sources such
as webnotes and math newsgroups. You are not to discuss the exams
with your classmates during this time (even comments that some
problem is easy can provide improper assistance).
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| Attendance: |
Attendance will not count toward your grade.
However, students are responsible for material presented in lecture
even if it is not in the text and vice versa. |
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| Grades: |
Midterm 40%, Final 40%, Homework 20%. |
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| Notes and Tapes: |
You are expected to take notes and/or tapes.
They may not be sold or offered for sale. |
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| Course Objectives: |
(a) Learn some interesting algebra.
(b)
Prepare for
Algebra Qualifying exam (along with Advanced Linear Algebra--MAS 5107).
Among the topics of the qualfying exam
to be covered in this course are field theory up to the fundamental theorem
of Galois theory; finite fields. |
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| Accommodations: |
Any student with a disability is encouraged to meet with me
privately during the first week of class to discuss accommodations.
Each student must bring a current Memorandum of Accomodations
from the Office of Student Disability Services which is prerequisite for
receiving accommodations. Accommodated examinations through the Office of
Student Disability Services require two weeks notice. All course
documents are available in alternate format if requested in the students
Memorandum of Accommodations.
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| FERPA: |
The Family Education Rights and Privacy act ("FERPA" or "The Buckley
Amendment") prohibits USF's release of student information, including
grades except under circumstances designed to insure student privacy.
I will not be posting grades, although there are means to make it
acceptable within FERPA. Instead, for those too impatient to wait for
their final grade to appear, I will provide grade information in response
to an e-mail containing the course name/number, your name and student id,
along with a request for grade information.
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| USF policy: |
Students are
referred to the graduate catalog
for university policy on academic dishonesty. |
| Cell phones: |
There are legitimate reasons to keep a cell
phone on during class, such as an on-call job or a sick child. If you do
not have such a reason, turn off your cell phone. If you
must have a cell phone on during class, give me advanced notice (just
before class, or early during the semester if this will be on-going).
You may step out into the hall to take your call, and then
return to class. If you have not given me notice, you are not welcome to
create any further distraction by returning to the class room after your
call--you can collect your things after class.
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Some Advice
Proofs:
The prerequisites of Algebra I include several courses which have
taught mathematical proofs. Nonetheless, writing a mathematical proof may
remain difficult for students. There are two aspects to writing a proof at
the level of this course which may cause difficulty.
The first part of writing a proof is having an idea of how to proceed.
This is the aspect which is less practiced in earlier courses.
There is no one way to ensure sucess here, but practice and persistence
help. Here are some things to think about in your efforts.
- What are the definitions of the hypotheses? Of the desired
conclusions? You are unlikely to get anywhere unless you know
where you are starting and where you are going, so learn the
definitions of the concepts involved.
- Is this similar to a result you already know? Many of the same
ideas get used over and over under slightly different circumstances.
Review the proofs given in the text and in class.
- What can we say about an object satisfying the hypotheses? Know
the tools/facts which have already been developed.
- Can you verify the fact for a small, specific example? Can you
then extend techniques to the general case?
Sometimes you may find yourself stuck. This is part of the learning
process and there is no shortcut. After you have thought about a
problem for awhile it is fine to talk to other students or to me.
(You are always welcome to come to my office hours). However, you are
cheating yourself if you seek out assistance before you have really
thought about a problem, and you will find yourself having great
difficulty on the exams.
The second part of writing a proof is turning an idea into a rigorous
proof. It is often the case in mathematics that we think about problems
in one way, but then must write about them in a slightly different way.
The work you did to produce an idea must now be cleaned up and turned into
a coherent text. I have found that students who really understand their
arguments are able write them down much more clearly than those who do not.
In writing proofs, I would recommend the following approach to homework.
write the proof and set it aside for a day or two. If, when you return
to it, you do not understand what you wrote, then the chances are that
it is either incorrect or poorly written (or both). In this case, try again.
I know that time may not always permit this, but you might want to try this
with one or two problems from homework each week.
Getting stuck, getting help:
There is no shortcut to learning math--you must work out problems
to develop and reinforce your understanding of concepts and computations.
It is only natural that some of the homework problems resist initial attempts
at solution. In fact, getting stuck is an important part of the
learning process because it helps isolate deficits in our understanding
and forces us to master the material. Thus, it is important that we
first seriously attempt to solve a problem ourselves before seeking
outside assistance. Outside assistance is not bad, but
to seek it out too soon or too often is to cheat ourselves of an
opportunity to learn. Indeed hard earned knowledge will stick the
longest and the best.
Around the Web
The following websites treat topics relevant to graduate algebra,
and may be useful as supplemental sources of information.
I can't take any credit or blame for anything on these sites--I
did a search and then took a quick look to see that they seemed
appropriate. For your consideration are the following:
Online textbook "ABSTRACT ALGEBRA, Second Edition"
by John A. Beachy and William D. Blair
Some notes by Bruce Ikenaga
Some notes by J. Brudan
Some problems and notes by Robin Chapman
Online textbook "Elements of Abstract and Linear Algebra" by Edwin H. Connell
Some Materials for the Graduate Algebra Course by E. L. Lady
Some course notes by J. Milne
Online textbook "Abstract Algebra:The Basic Graduate Year" by Robert Ash
Some lecture notes in abstract algebra by D. Wilkins
Course notes by F. Anderson
Course notes by F. Anderson
Course notes by F. Anderson
Here are some other sites that the curious may find of interest.
A search will turn of many other sites on the general topics. I've
only included those which I have found to have material relevant to
the course and which are fairly comprehenseive (I may have missed some,
but you can do a search as well as I).
Definitions (including those of algebraic objects):
Eric Weisstein's World of Mathematics
Biographies of mathematicians (some of whom developed the material we will
learn in this class):
MacTutor (St. Andrews)
Eric Weisstein's World of Biography
Allmath biographies
History of math (including modern algebra):
MacTutor (St. Andrews)
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