Course Information
Modern Algebra, Math 407/507
Fall, 2001

Office Hours: T 9:00-10:30am, W 9:00-10:00am and 2:00-3:00pm, F 11:30am-12:30pm, and by appointment or e-mail.

Objectives: The main goal of the course is for you to learn to express and construct abstract mathematical ideas and arguments precisely.  Achieving this is a long-term process, likely requiring much time and effort. This term you will develop this ability while studying groups (which can arise in physics and chemistry) and rings (like integers and polynomials).  The goal for the year-long sequence is to understand the proof that there is no formula, involving only basic arithmetic and radicals, for the zeros of a fifth degree polynomial in terms of its coefficients.  Groups and fields (which we will study next term and which are special cases of rings) are used in the proof of the "insolvability of the quintic".

Prerequisites: The official prerequisites for this course are Math 287, Discrete Structures, and Math 330, Linear Algebra.  Most important from these is familiarity with methods of proof and practice constructing proofs.  Many examples will depend on ideas from 330.

Materials: The text is Algebra, by Artin, Chapters 2, 10.  We may also use the software Maple or Finite Group Behavior, (http://unr.edu/homepage/keppelma/fgb.html) to form conjectures and solve problems.

Format and Evaluation: Time in class will be spent exploring the material through discussions, group and individual work, and lectures. As an aid in achieving correct, clear, complete proofs, each homework assignment may be resubmitted once with changes made on a facing page (a thin binder may be useful).  Quizzes will cover definitions and/or proofs from the book.  Exams will be take-home.
The two exam dates below are somewhat tentative, the final date is firm, so please mark it down now.
 

Overall percentages of 90%, 80%, 70%, 60% will guarantee the letter grades A, B, C, D.  Cutoffs for +/- will be determined at the end of the semester, but will be within 3 percentage points of these values.

Philosophy: I believe that all of you can succeed and that hard work counts for a great deal.  I expect you to attend each class session and to be responsible for material covered in any sessions you are forced to miss.  Studying together and discussing problems are encouraged, after you have worked hard yourself to understand the material or solve a problem, since this can be a very effective and rewarding way to learn mathematics.  However, you must write up homework on your own in order to guarantee your own understanding of the material.  Sharing or obtaining complete solutions is not allowed.

Accommodations: If you have a diagnosed disability or believe you have a disability that may require reasonable accommodation on the part of ISU, please call 282-3599 to make an appointment with Dian Jenkins, Director, ADA and Disabilities Resource Center.

Expectations: For most of you the following points are likely obvious or second nature, but I believe it is useful to state them explicitly.

In this class you will be expected to become largely responsible for your own learning.

You should strive to learn actively, both within and outside of class, by

• attending every class session;
• reading the material for the first time before the class in which it will be covered;
• participating in group work and lectures during class;
• taking thorough notes;
• formulating questions;
• recording and asking questions on material and problems you do not understand;
• working at least 2-3 hours (on average) outside of class for every hour in class;
• learning from mistakes of your own and others (including me);
• being organized, clear, and accurate;
• developing efficient and effective study, work, and problem-solving skills;
• learning to read the textbook effectively, which may involve rereading, maybe many times;
• seeking out additional resources for help on material or additional skills;
• taking responsibility for learning material not explicitly covered in class, or which you did not understand or missed.

I plan to be prepared, patient, available, approachable, and fair.

I look forward to a successful and rewarding semester of learning together.