Instructor: Lubos Thoma

Office: Tyler Hall 214

Tel: 874.4451

Email: thoma@math.uri.edu

Class Schedule: MWF 11am--11.50am, Crawford 223

Office hours: MW 3.00 - 4.00 pm, F 1.00 - 2.00 pm and by appointment

**Important dates:**

Exam 1:
Friday February 25, in class.

Exam 2:
Friday April 15, in class.

Final Exam:
Wed May 18, 11:30 am - 2:30 pm
Spring 2005 final exam schedule

Project due:
Wednesday May 4. The project description will be distributed in class.

**Description:**
The section to be covered are listed on the class schedule.
We will cover roughly one section per
lecture. However, some sections will require two or more lectures.
It is helpful to read the text before class.

Topics to be covered include elementary number theory,
permutations, groups, subgroups, homomorphisms and factor groups,
rings, ideals and factor rings, fields, and extension fields.

Modern abstract algebra has a wide variety of applications:
mathematics itself, physics, automata and theoretical computer science,
cryptography and information theory, biology, and others.
We will see some applications in the class.

There are several goals of this class: to introduce you to
modern abstract algebra (groups and rings), to expose you
to the axiomatic approach in modern mathematics, and last but
not least to make you more familiar with proofs.

**Textbook:** John R. Durbin,
Modern Algebra, An Introduction,
5th edition, ISBN: 0-471-43335-7, John Wiley & Sons, Inc.

**Exams:**
Exams will draw from material covered in class, that is,
any theorems, proofs, example, or homework problem that we cover
in class is a possible material for the tests. So, the best way
to prepare for the exams will be to start with your class notes.
There will be two in-class exams and a comprehensive final.
Dates see above.

**Homework:**
You learn more by doing, than by watching others give demonstrations.
Therefore, homework is very important. When you sit down to do your homework
is when you realize whether or not you understood the material from class.
You also learn by practice, so do as many of the examples assigned as possible.
I will assign homework on a regular basis. Your solutions should be written
up with your best effort at explanation and should be neat.
These problems will challenge your problem solving abilities.
You may work in groups provided you follow the following
guidelines: each person must write up each problem in their own
words, no copying. Whenever you would like to discuss the class material,
have any questions or are stuck on the homework, please visit me in my office
either during my office hours or by appointment. l. thoma

**Project:**
The purpose of the project is that you learn to work with literature
and other sources of information. The project will be distributed in class.

The project is due Wednesday May 4, 2005. However, feel free to
show me a draft version earlier for comments.

**Grading:**
Your grade will be based on your exam scores, final exam score,
project, and homework grades.

homework 25%

in-class exams 20% each

project 10%

final 25%

**Suggestions:**

1. Read the book carefully.
I chose this book because I believe it gives
nice explanations. It is helpful to read sections before we talk
about them in class.

2.
Do all of the homework assigned. If you don't gain
experience in doing the problems yourself, it will be hard to remember
how to do them on a test. It is helpful to start study groups
and work together on homework. I do believe that how well you do in
this course will depend on how well you study.

3.
Attend class to keep current, ask questions, and learn knew topics.
Also, attending class allows you to see what is emphasized. Remember the
material for the tests will come from what was emphasized.

4.
Be sure to keep current of all topics. You will need to study
a little almost everyday. If you don't understand something, don't let
it wait too long because the concepts in this class build, one upon
the next. You don't want the ``snowball effect'' to take over.

5.
You may not understand an idea at first. Give it time to sink in.
Sometimes you must go over it several times before it begins to make sense.
It is not unusual for someone to be stuck on a particular kind of problem
and not understand it in class. You may need to have it explained again,
later. Please feel free to ask me to do so outside of class.