Abstract Algebra: Math 3550
Spring 2009
Instructor: Bryan Shader
Office: Ross Hall 203 or 321
Phone: 766-6826
Office Hours: Monday 2--3, Thursday 10--11 or by appointment
e-mail: bshader@uwyo.edu
webpage: http://www.uwyo.edu/bshader/3550-09.html
Text: A First Course in Abstract Algebra by J. Fraleigh, 7th edition
Course Objectives
- To explore a fascinating, beautiful new world (of mathematics).
- To learn the fundamental properties of the basic algebraic
structures (groups, rings, fields) from an axiomatic point of view.
- To develop the ability to think abstractly, and to clearly explain difficult ideas and thoughts.
- To enhance proof development and writing skills.
Course Expectations
- Work hard and regularly. This will be a difficult
class. Re-write your notes. Read and
re-read the pertinent sections of the book.
- Memorize definitions and main results. Strive to truly understand
the proofs. Repeatedly work through the proofs until you
completely understand them. The arguments given in the proofs
presented in class are the prototypes for the type of arguments that
you'll need for the homework.
- Create, and be familiar with a large inventory of examples. The
best way to combat abstractness is to have some concrete examples to
play with.
- Be willing to seek help. There will be times in this course
that you will be frustrated. This is natural. This is not
an easy
course. Anytime you are learning a difficult new task, you encounter
frustration.
Don't let the frustration get you down. Come in and talk
with
me!
- Start your homework assignments early. In order to have acceptable proofs you will have to go through many revisions.
- Enjoy! You will be exploring an exciting new world, and will be challenging yourmind. What a wonderful opportunity!
Grading
Quizzes
8%
Field guide 8%
Homework 20%
Two midterm exams 20% each
Final exam 24%
Quizzes
There will be a weekly, 5-minute pop
quiz, in which you will be asked to state definitions or
theorems. Definitions and theorems that you are suspected
to know will be indicated in class as they are presented. You
will need to spend time daily learning these. Don't hesitate to
make "flash-cards"to aid in your study. Missed quizzes can
be made-up only if they are
related to an university excused absence.
Homework
Approximately every week you will be
assigned a set of homework problems.
You will be given a week to complete these. Most of the problems
will
be asking you to prove a result. Your proofs should be (a)
logically
and mathematically correct, (b) clear and to the point, and (c) in
complete mathematical sentences. You should plan on writing,
re-writing, re-writing,
and re-writing your proofs before they are in acceptable form.
This will
require that you start work on the homework as soon as it is
assigned. I don't mind
you mildly discussing the problems with other students. However,
the proofs that you write
down should consist of your ideas expressed in your own words.
Late assignments will not be accepted.
Field guide
Much of this class deals with new and abstract objects. To help better understand
these objects, you will put together a field guide of abstract algebra. The
field guide will contain material that helps you understand the new objects
that we will encounter. Correct definitions, Examples, Illustrations,
and Explanations should be included. The field guide will be collected
twice during the course, and graded on correctness, completeness, and
richness.
Exams
There will be 3 exams (2 midterms and the final). The final will not
(technically) be a cummulative exam, and will only cover the material
presented in the last third of the course.
All information in this syllabus is tentative. If the instructor
finds that changes are necessary, they will be announced