Math 335 Fall 2000
Abstract Algebra

Instructor: M. O'Kennon
Office: Palenske 305        Office hours: (tentatively) 11:10-12:00 MWF.
E-mail mokennon@albion.edu

Text: Modern Algebra: An Introduction by John Durbin (4th Edition).

Suggested paraphernalia: A loose-leaf binder for written exercises and handouts.  

Abstract Algebra, as its name implies, allows us to generalize (abstract) many of the characteristics of the familiar integer, rational, and real number arithmetic to other number systems. For one example, most of the "number" systems you will meet this semester will have operations similar to addition or multiplication in that they are associative. Some will have more special properties, like commutativity (warning: you can't always assume this property!!!!). One reason that we classify systems by the properties of their operations is that once we have proved something about one system, we will not have to reprove it for another system with the same properties. One of the major goals of a class in abstract algebra is for each student to become comfortable with proofs, examples and counterexamples. You can't do this without doing mathematics. For this reason, we will become colleagues this semester. You will be discussing, writing, talking and maybe dreaming algebra. You will get a chance to work in groups and to present your group's work or your own on the board, in English (I have received work done at least partly in Klingon), and on paper. Do not be afraid to ask how I know something. If it is not clear, make me go back over the steps. Don't worry, I will do the same to you. It is important that you understand that the ground rule in mathematics is ARGUE but WITH RESPECT. A student in my class one time asked at midterm, "Are we good math nerds yet?".  It is my wish that you all become math nerds, in the best sense of the word.

Suggestions for succeeding in Math 335:  Read the assigned section of text carefully before you come to class. Understand the examples. Try to make up your own examples. At least know what each theorem is saying. Memorize all definitions (there aren't very many important ones). Discuss the material with your friends. Come to class EVERY DAY well-rested and well-prepared. There will be time at the beginning of each class for questions and for you to put your work on the board. Make sure that you have tried to answer any question for yourself before you ask it in class or in office hours. Come to office hours. (The posted office hours are just when I promise to be there, but others are available by appointment.  Please e-mail me mokennon@albion.edu)

Help!  This year we are pleased to announce our new Quantitative Skills Center, where you can get help with such things as math anxiety, note taking, study strategies, etc.  More info on the Center here!

If you know or suspect you might have a learning difficulty of some kind, please see Ms. Lori Duff in the Academic Affairs Office (phone: 0222), where they will take care of doing the appropriate thing to help me make the appropriate allowances.  I want to make sure that each student learns!  

Attendance.  Attendance is not optional.  Mathematics is a cumulative subject and each day's topic depends on the preceding material.  Days missed impact not only your own progress, but also that of your classmates.  Thus I am asking you not to miss class for frivolous reasons.  After you have missed class 3 times for any reason other than serious personal medical or family emergency, your final mark will begin to degrade by one gradation per day.   Attendance at every class session is your responsibility!

Homework.  You will have exercises (both to be turned in and for your own benefit) to do from almost every section.  Generally written exercises are due two class periods from the day they are assigned.  I will not accept any late homework without a good reason.  This is because I try to mark all homework sets within two class periods, and for fairness I mark all the sets at the same time. If yours is late, it will mean your classmates will be delayed in getting their homework back.  

How your grade will be determined. There will be six mini-tests and a final exam, all cumulative. Each test will count 10 points and the final 30. There will be several collected and marked homework sets, for a total of at least 25 points. My usual grading scale will be used, that is: 94-100 = 4.0; 87-93 = 3.7; 84-86 = 3.3; 80-83 = 3.0; 77-79 = 2.7; 74-76 = 2.3; 70-73 = 2.0; 67-69 = 1.7; 64-66 = 1.3; 60-63 = 1.0.  Attendance or lack thereof is also a factor that may change your final mark (see above).   Participation by putting problems on the board will be rewarded blatantly with the presentation of up to two certificates suitable for framing with a total worth of 4 percentage points to be added to your final mark. I hope that you will enjoy this semester.  I plan to!

Here is a tentative syllabus for the semester.  Please note that days we will not have class are marked in aqua (web version).  Test days are marked in watermelon (web version).  Some tests will be take-home, and in that case they are due on the watermelon days.