Math 321 - Abstract Algebra - Course Policies

Overview | Evaluation | Homework | Presentations | Exams
Quizzes | HRUMC | Attendance | Getting Help

Overview

Abstract algebra arose from the problem of trying to find the roots of an equation using radicals. For example, we all know how to find the roots of any quadratic equation by using the quadratic formula. There are generalizations of this to third degree and fourth degree polynomials. One of the more remarkable results of abstract algebra is that there is no such general solution for fifth degree polynomials! No matter how hard you try, you can never find a general formula (or formulas) involving addition, subtraction, multiplication, division and taking radicals that works for all fifth degree polynomials.

From these beginnings, abstract algebra has found many applications, including error detection schemes, the RSA encryption algorithm, solving Rubik's cube, characterizing all periodic wallpaper borders, and applications in chemistry. This semester we will study the three major constructions in abstract algebra, groups, rings, and fields, although we will focus on group theory and ring theory. We're going to cover alot of material this spring, and you are going to work hard, but it will also be alot of fun. I'm really looking forward to this semester.

As a general rule, you should expect to spend 8--10 hours per week outside of class working on Abstract Algebra. There will be some weeks where you spend more time (e.g. working on exams and preparing your presentations), but there may be some weeks where you spend less.


Evaluation

Your final grade will be determined by
    Homework 35%
    Two Inclass Presentations 20%
    Two Takehome Exams 20%
    Comprehensive Takehome Final Exam 15%
    Quizzes 10%

Homework

A major emphasis in this course is that you learn how to write rigorous and precise mathematical proofs. This can be a challenging endeavor and may require several iterations, but the process will not only aid your mathematical development but can also great improve your clarity of thought in other disciplines and areas as well.

With this emphasis, your homework should be precise, comprehensible, completely justified, and written in complete sentences. Most of the homework problems will be worth 5 points, and the possible grades will be 5, 4, or No Grade. A few of the problems may be worth 10 points, and the possible grades will be 10, 9, 8, or No Grade. After I have returned the homework, I will allow you one opportunity to rewrite any problem. However, you must turn in your rewrite, along with your original paper, within two class meetings of when I return the homework to the class. For example, if I return the homework on Monday, you cannot turn in your rewrite after Friday.

An important aspect of your mathematical development is that you learn to discuss mathematics with others and collaborate on problems. The homework assignments will alternate between Individual assignments and Group assignments. On the group homework assignments, you will work in groups of two and turn in one paper. It is extremely important that both of you understand every solution that your group produces. On each assignment, one student will be designated as the primary author who writes-up the solutions, and the role of primary author must alternate between the members of the group.

For the Individual assignments, I encourage you to work with other students, but each person must turn in a separate paper. Here are a few guidelines for the presentation of your homework. If you do not follow these, I will return your homework to you ungraded!

  • Your writing must be clear and legible. \newline
  • Do not turn in your first draft. You should revise, polish and rewrite your solutions. \newline
  • If you write in pen, there should be no scratch-outs. \newline
  • Do not turn in paper torn from a spiral notebook with ragged edges.
The homework is due in my office by 4:00, usually on Wednesday. Be aware that
Late homework is not accepted!! No exceptions!!

Presentations

You will each give two fifteen minutes presentations during the semester. The first one will be on a general mathematical topic of your choosing (I can recommend some good places to look for topics), and the second will be on a topic from, or application of, abstract algebra that we have not discussed in class. I'll give you detailed instructions on my expectations for these presentations.

Exams

You will have two open book, open note takehome exams during the semester. I will give you at least one week to work on each exam. See the syllabus for the due dates.

The final will be a takehome exam and is due Saturday, May 15.


Quizzes

You will have four quizzes during the semester that will consist of definitions and very basic proofs. I will let you know what your responsibilities are for each quiz. These are intended to be pretty low-stress activities.

Hudson River Undergraduate Mathematics Conference

The Sixth Annual Hudson River Undergraduate Mathematics Conference will be held at Siena College in Loudonville, New York on Saturday, April 17. The two years that I have gone to this conference, there have been about 400 undergraduates in attendance, many of whom gave talks. I would really like for as many of you as possible to give a talk at the HRUMC. As an incentive, if you present a talk you will receive an extra 5% added to your final grade.

Class Attendance

Although class attendance is not a specified percentage of your grade, I will keep a class roll to help me determine borderline grades at the end of the semester. If you do miss class, you are responsible for the material that was covered.

Getting Help

Please come see me during my office hours! If you have a conflict and cannot make my office hours, please call or email me and we can set up an appointment for another time.


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Maintained by Tommy Ratliff, tratliff@wheatonma.edu
Last modified: Sunday, January 31, 1999, 12:20 PM