Algebra I - MAS 5311-001 - Fall 2009
| Instructor |
Brian Curtin |
| Office |
PHY 318 |
| Phone |
(813) 974-4929 |
| e-mail |
bcurtin(at)cas(dot)usf(dot)edu |
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subject line must
contain MAS5311 |
| Office Hours |
M 2:00--2:50, W 10:45--11:35, 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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will be PDF of syllabus handed out in class |
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| Meeting time: |
MWF 11:00-11:50. We meet in
PHY 108.
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| Prerequisites: |
Undergraduate linear algebra (MAS 3105) and abstract algebra (MAS 4301).
Although we will develop each topic from the basics, the pace and
depth will make the course challenging. Our text includes very few examples,
which you are expected to know from previous study. 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.
This book is now being publised by the AMS.
(
publisher)
(
Amazon)
(
Barnes and Noble)
The previous version was published by by Brooks Cole/Cengage Learning
as ISBN: 978-0-534-19002-6. I've also seen the book with a chinese cover.
You may use any of these editions, but I must warn you
that some of the earlier printings of the brooks/cole version
had some typos.
I will ask the library to keep its copy on reserve.
We will cover much of Part I in this course, and we will cover
Part II in the second semester Algebra II. 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. Most of them will be graded, the others 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. Students should plan on turning in at least half of the
assigned problems completed for a satisfactory homework grade.
Homework should be turned in within 1 1/2 weeks of the day it is assigned.
Here is a list of sections to be covered and homework to be assigned. In addition to
this list I may also assign some ``qualifier style'' problems.
| Chapter | Sections covered | Problems |
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| 1 | all | 1, 5, 6, 8, 9 |
| 2 | all | 1, 4, 5, 9 |
| | 7, 12, 13 |
| 3 | all | 3, 4, 5, 6, 8, 9, 12 |
| 4 | all | 1, 2, 3, 5, 7 |
| 5 | A--C | 1, 2, 5, 6, 8, 9, 18 |
| 6 | A--C | (Midterm out while covering this) |
| 7 | A, B | 1, 2, 4, 5 |
| 8 | A--D | 1, 3 , 10 |
| 10 | A, B (modified) | 1, 3 |
| 11 | all | 1, 4, 5, 7, 8 |
| 12 | all | 4, 5, 8, 9 , 10 |
| 13 | A, B |
| 14 | A, B (time permitting) | (final out while covering this) |
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| Exams: |
There will be a take-home mid-term exam on Chapters 1 - 5 given
out at the end of class on Monday, October 2 and due
at the beginning of class on Monday October 12.
There will be a take-home final exam covering Chapters 6-14 given
out Wednesday, December 2 (the last week of class) and due
Wednesday December 9 by 11:00am (the
allocated time for the final exam).
Each will be made available on the class website within 12 hours
of the time it is given out. 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 30%, Final 30%, Homework 40%. |
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| Notes and Tapes: |
You are expected to take notes.
All unauthorized recordings of class are prohibited.
Recordings that accommodate individual student needs must be
approved in advance and may be used for personal use during the
semester only; redistribution is prohibited. |
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| Course Objectives: |
(a) Learn some interesting algebra.
(b)
Prepare for
Algebra Qualifying exam (along with Advanced Linear Algebra--MAS 5107
and Algebra II--MAS 5312). Among the topics of the qualfying exam
to be covered in this course are "Group theory up to Sylow's theorems;
elementary theory of rings and modules, including the structure of
finitely generated modules". |
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| Important dates: |
| August 24 (M) |
First day of Class |
| September 7 |
Labor Day (no class) |
| October 5 |
Take-home midterm given out |
| October 12 |
Take-home midterm due |
| October 31, 5:00pm |
Last day to withdraw |
| November 11 |
Veteren's day (no class) |
| November 26,27 |
Thanksgiving (no class) |
| December 2 |
Take-home final given out |
| December 4 |
Last day of class |
| December 9 (W) |
Take-Home Final due 1100am |
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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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| Religious: |
Students who anticipate the necessity of being absent from
class due to the observation of a major religious observance must
provide notice of the date(s) to the instructor, in writing, by the
second class meeting. |
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| Emergency: |
In the even of an emergency, it may be necessary for USF to suspend
normal operations. During this time, USF may opt to continue delivery of
instruction through methods that include but are not limited to: Blackboard,
Elluminate, Skype, and email messaging and/or alternate schedule. It is the
responsibility of the student to monitor the main USF website, emails and
MoBull messages for important information about the closure. For information
about the continuation of instruction students are directed to their individual
blackboard course sites. |
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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 post final grades, although there may be means
to make it acceptable within FERPA. I am told that I am ought not
send grades via e-mail. However, I will do so for those who
make arrangements in advance, agreeing to this form of grade
delivery and accepting its inherent risks of privacy violation.
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| USF policy: |
Students are
referred to the graduate catalog
for university policy on academic dishonesty. |
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| 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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| Blackboard mailing list: |
Blackboard provides nice tools for communicating with
your classmates. However, I am told that the university
considers such mailings as an extension of the classroom
environment. Please show respect to your classmates and to
me. If the mailing list is abused, I will, after
one warning, disable it (at least temporarily).
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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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