Course Description:

This is the first semester of a two-semester sequence designed to cover the fundamental structures of abstract algebra (groups, rings, fields, associative algebras, vector spaces, modules) with many important concrete examples (e.g., polynomial rings, matrix rings, symmetry groups, and fields of complex numbers).

The fall semester introduces group theory, based heavily on examples from linear algebra (matrix groups), but also investigating the concept of symmetry more generally. This approach requires a thorough review of topics from linear algebra, and the syllabus devotes considerable time to that. Although the topics may look similar, there will be much to learn in this "second pass" through linear algebra, emphasizing its algebraic features.

The spring semester (Math 334) introduces rings, fields, and modules. It covers topics in number theory and Galois Theory, as well as advanced topics in linear algebra (canonical forms). If times permits, the semester will conclude with an introduction to representation theory.

In Math 333-334 we will pay close attention to the language and formal structure of mathematics. This means that precise definitions, theorems, and proofs will be the primary mode of discourse. You should have been exposed to this approach already in Linear Algebra and perhaps other courses.  Beginning in Math 333a, it will be elevated to paramount importance.  

Early homework assignments will contain  problems designed to sharpen your skills in dealing with definitions and formulating proofs. Since students occasionally find this difficult, I will  schedule several informal discussion periods where we can focus on purely mechanical aspects of proof-writing. I guarantee that you will all become adept at this important mode of mathematical communication.

Algebra, by Michael Artin, Prentice-Hall (1991).

The fall semester (Math 333) will cover the first five chapters of this book.

Three lectures per week (MWF 2:00-3:00).

Weekly homework, two midterm tests, and a final. These will be weighted as follows in determining the final course grade:

The two midterm tests will have both in-class and take-home components. The final will be take-home.The weekly homework will contain a mixture of basic and challenging problems, the latter indicated  by a star (*).  All of these should be handed in for grading.  Basic problems are designed to help you learn the essential concepts and practice new techniques. Mastery of the basic problems will be sufficient to guarantee at least a 3.0 in the course. 

Math Question Center (MQC):

I encourage collaboration on the homework, and many students find it useful to work together in the Math Question Center (Sunday through Thursday 7-9PM, Hilles 011/012). I will be in the Math Question Center on Monday evenings -- it's a good time to come and ask me questions about the course.

Office Hours:

You can find me in my office at the following times: Monday and Wednesday 3:00-3:30 (after class), and Friday 3:00-4:00. I am also in the Math Question Center (see above) on Monday nights, and am happy to arrange other consultation times by appointment.

Electronic Resources:

(1) Blackboard will be the primary source for course materials. You are responsible for getting the weekly homework assignments from Blackboard. I will also post solutions to homework and tests, handouts, links to course-related websites, and other materials that might be quite important (e.g. corrections to and hints to homework assignments, reminders of test dates, etc.). Please check Blackboard regularly.

(2) Mathematica will be used occasionally in this course, but perhaps not as extensively or centrally as in other courses. You are probably already familiar with Mathematica. If not, this would be a good time to make your acquaintance. Please ask me if you have questions about using or obtaining access to Mathematica.

Over the course of Math 333-334 you might find some of the following commands useful: Factor, Mod, PolynomialMod, GCD, ExtendedGCD, PowerMod, EulerPhi, PrimitiveRoot, as well as all of the basic commands for manipulating polynomials and matrices. A new command FiniteGroupData has just appeared in Mathematica V.7, and it will be interesting to connect it to the group theory that we will study this fall in Math 333.

Collaboration:

I encourage collaboration on the homework, both standard and special problems. Indeed, I expect you will learn a great deal about this course from each other. It will be to your advantage to form study groups, and many students facilitate this by working together in the Math Question Center.

Collaboration on homework naturally raises the question, "how much is OK?" I expect that you will share ideas, and perhaps work together at a blackboard, but eventually each student must write up his/her work independently, without reference to another students work or to written work that has been produced jointly. Verbatim copying from another person's paper or blackboard work is definitely "not OK". The safest approach is to write up your final solutions in a different place, and on a fresh sheet of paper.

It's important not to misunderstand these guidelines, so please ask me if you have any questions. You might also want to refer to the department's published guidelines on homework collaboration, which are available on the department website.

It goes without saying that collaboration on tests is never permitted. All inquiries about problems on the tests should be directed to me.

Honor code principle:

You must never present others' work as your own. If you have used other students' work in the preparation of homework you must acknowledge it. If you obtain solutions to assigned problems (on homework or take-home tests) from sources other than the textbook or class notes, you must acknowledge such sources. This especially applies to material obtained electronically, e.g., on the web. 

If there are questions about honor code issues, you should seek clarification and guidance from me.