Abstract Algebra has its origins in the number theory of antiquity, and arose as a subject in the late 18th Century as a tool to help to understand the zeroes of polynomials. From these origins, it has grown mightily and now it pervades much of modern pure mathematics. Curiously, this formerly purest of pure disciplines has become rather practical. Simply put, abstract algebra underlies the security and integrity of all modern digital communication.

    Our course is not about the uses of abstract algebra in digital communication. Its goal is to introduce you to the mathematical methods of inquiry (definition, conjecture, and proof), and train you in the rigour of thought that is unique to mathematics. The vehicle for this will be our study of the elementary properties of groups, a mathematical structure that encapsulates the idea of symmetry.

    A key role in this course will be played by your homework, which will serve as a dialog between us. Homework is assigned daily and collected at the beginning of the next class period. Late homework is not accepted. Homework will be graded promptly (by the grader or by Frank) and returned the following class period. Your homework write ups are expected to represent your own work and should be carefully and neatly written. An important part of your education is learning from your peers. I encourage you to discuss problems with others in the class, but the problem write ups must be your own (n identical solutions will each receive 1/n of the credit).

    The key component of careful thought is recognizing and communicating correct arguments, while avoiding false statements. Accordingly, full credit will be given for well-written, correct solutions that are unblemished by false assertions.

    Abstract Algebra, like other advanced mathematics courses requires students to be engaged in classroom discourse. To encourage class participation, good questions will be rewarded with specially prepared coupons (on post-it notes), which may be redeemed for extra credit. The individual value of the coupons will be determined later. Expect between 1/3 and 1/2 of a homework assignment. Active participation can raise your grade.

    I have four office hours scheduled each week. The times can be changed (except that Wednesday is off limits). Appointments may be made, as well. The most reliable way to contact me is via email - I read and respond to it whenever I am in my office.

    Right now, I do not have any professional commitments planned that will require me to miss class, except for the Tuesday before Thanksgiving.