MCS  313:  Abstract Algebra
Fall 2006

 MCS-313 homepage Reading and class schedule Peer review guidelines Prof. Barbara Kaiser Proof checklist Feedback Homework guidelines

Course Information

Overview:  Abstract algebra has its roots in the centuries-old efforts of mathematicians to find solutions to polynomial equations.  Over the last few hundred years,  as the subject has evolved, it has become the source of some of the most widely used tools in mathematics. Groups, rings, fields, and related algebraic structures are used in almost all areas of mathematics--analysis, topology, number theory, discrete mathematics--as well as in physics,  chemistry, computer science and other disciplines. This course will be an intensive study of the basics of "abstract algebra" including the theory of groups, rings and fields.

Course Objectives:

• To develop the ability to think abstractly, make conjectures, and understand and construct rigorous mathematical proofs.
• To understand the basic philosophy, purpose and history behind the development of abstract algebraic structures.
• To develop the ability to work with the most common algebraic structures -- groups, rings and fields -- and to become familiar with the most important examples of these structures.
• To understand how mappings can preserve algebraic structure, and through such mappings, learn how to determine when two seemingly different algebraic structures are in fact "isomorphic," i.e., "the same."
Prerequisites:  The formal prerequisites are MCS-221 and either MCS-220 or MCS-236.  More to the point, you should be comfortable with creating and writing proofs, basic logic, and elementary set theory.

Course web site:  The best source of information about this course is available at  www.gac.edu/~kaiser/mcs313/. There you will find a complete syllabus, course description, current homework assignments, and so on.

Text:   Contemporary Abstract Algebra, sixth edition, by Joseph Gallian.

This book is intended to be read.  For each class session, you are encouraged to read the pertinent portion of the text at least once  beforehand and at least twice afterwards.  Study the book with a pencil in hand.  Make notes in it.  Mark where you have questions.   Do NOT try the exercises without reading the text;  simply skimming the examples is not sufficient.   You will find that it will be  necessary to read the text several times before attempting any exercises.  To survive this course, you must learn how to read a math book!

Classes:    Classes will be used for lectures, problem solving, discussions, and other fun activities.   You should prepare for classes by doing the reading beforehand (reading assignments are posted on the Web),  thinking about the problems in the text, and formulating questions of your own.  You should also participate as much as possible in class.  Class meetings are not intended to be a complete encapsulation of the course material.  You will be responsible for learning some of the material on your own.

Attendance, both physical and mental, is required.

Should you need to miss a class for any reason, you are still responsible for the material covered in that class. This means that you will need to make sure that you understand the reading for that day, that you should ask a friend for the notes from that day, and make sure that you understand what was covered. If there is an assignment due that day, you should be sure to have a friend hand it in or put it in my departmental mailbox (in Olin 324). You do not need to tell me why you missed a class unless there is a compelling reason for me to know.

Homework:  I will assign homework at the beginning of each chapter by posting them on the web. The problems will be designated as ``practice problems'', ``mastery problems'' or ``exam problems''.

Practice problems are meant to give you practice solving, writing and reading mathematics.  For these problems, you will be assigned a partner.  You may work on the problems with anyone you like  except your partner. You should write up your solutions and give them to your partner for peer review.  These problems will not be handed in; however, you will be graded on how many you do and on the quality of your review.   Reading and evaluating others' work will greatly help your  performance on the other homework and on the tests.

Mastery problems are homework problems which are graded on an ``acceptable'' or ``incomplete'' basis.  You may resubmit incomplete problems until they are acceptable.  You may discuss the problems with each other, if you like, but I recommend that you work more independently, since  you will learn more that way.  Your  grade on mastery problems will be based on what percentage of the problems you finish.

Exam problems are problems that each of you must do individually.  You can think of these as miniature take-home tests; you are on your honor not to cheat by consulting other people or books.  These problems will be graded using a 5 point scheme for each problem, and, except in extreme circumstances, you only have one chance to do each one.

Tests:  We will have two midterm exams, tentatively scheduled for Oct.11 and Nov. 18. The final is on Sat., Dec. 18, at 8:00am.

Academic Integrity  You are expected to to adhere to the highest standards of academic honesty, to uphold the Gustavus Honor Code and to abide by the Academic Honesty Policy. Copies of the honor code and academic honesty policy can be found in Academic Bulletin and in the Gustie Guide.

On practice problems and mastery problems, I encourage you to discuss problems and their solutions with each other; however, each of you should make a real effort to solve each problem by yourself, and you should give credit to any people or texts that helped you find solutions.  Should I detect students copying each others work, I will first talk with the people having similar work. In case of a second infraction, I will give you a 0 on that assignment and notify the Dean of Faculty. Further violations will result in increasing penalties, up to failing the course.

On tests and exam problems, you are expected to work completely by yourself, and to sign the honor pledge on each of these assignments. The first violation of this policy will result in a 0 on that assignment and notification of the Dean of Faculty. Further violations will result in failing the course.