MTH316 Algebra

Spring 2004

Instructor: Lubos Thoma
Office: Tyler Hall 214
Tel: 874.4451

Class Schedule: MWF 11am--11.50am, Ballentine 101
Office hours: MWF 12.00 - 1.00 pm and by appointment

Homework:   Homework 9 is due Monday May 3.

Final Exam:     Monday May 10, 11.30am--2.30pm     Spring 2004 final exam schedule
        This is a comprehensive final exam.

Printable syllabus:   postscript     pdf

Important dates:
        Exam 1:     Friday February 20, in class.
        Exam 2:     Monday April 5, in class.
        Project due:     Monday April 26
        Final Exam:     Monday May 10, 11.30am--2.30pm     Spring 2004 final exam schedule

        Project due:     Monday April 26, 2004. The project has been distributed in class.
                        If you do not have a copy, please let me know. Feel free to show me a draft version earlier for comments.

Description:   We shall cover most of our textbook. 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:         J. and L. Gilbert, Elements of modern algebra, fifth edition

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 has been distributed in class. If you do not have a copy, please let me know.
The project is due Monday April 26. 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%

  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.