MTHSC 8520 Syllabus
Spring Semester 2018

Time: 11:15 - 12:05; M,W,F.
Location: E004 Martin Hall.
Instructor: Kevin James
Office: O-21 Martin Hall
Phone:
Email: kevja@clemson.edu
Web: http://www.ces.clemson.edu/~kevja/

Office Hours

Office hours are by appointment. Please email me to make an appointment or simply drop by my office.

Required Text

``Abstract Algebra'' by David S. Dummit and Richard M. Foote, 3rd edition.

Goals and Objectives.

This course will cover advanced concepts of abstract algebra, including Modules, Tensor Products, Field Theory and Galois Theory. We will cover additional topics of interest to the students and professor as time permits.

Course Contents.

Selected sections form chapters 9-14 of Dummit and Foote and additional sections as time permits. This is only a general guideline and may change.

Learning Outcomes.

Student who complete this course will be able to:
  1. Compute the invariant factors and elementary divisors of a finitely generated module over a PID.
  2. Compute the tensor product of two modules.
  3. Write down bases for extension fields.
  4. Compute the Galois group of a finite extension of fields.
  5. Deduce information related to a field extension such as the number and relative degrees of its subextensions from its Galois group.
  6. Compute the splitting fields of polynomials of small degree and will build an understanding of the general case.
  7. Discern if a polynomial's roots are exressible in terms of radicals by considering the Galois group of the splitting field of the polynomial.
  8. Prove that there is no formula for the roots of an arbitrary quintic polynomial in terms of radical expressions involving the coefficients of the polynomial.

Time Requirements.

Please be sure to devote at least six hours per week outside of class to this course.

Grading Policies

The grading in this class will be as follows:

The standard grading scale will be used

Make-up Policy

Absolutely NO late homework will be accepted and there will be No make-ups for missed quizes or exams. In the event, that a student misses an exam due to a documented excused absence, that student's final exam score will be substituted for the missing exam score. Any student who misses an exam and cannot provide documentation indicating that the absence was excused will recieve a 0 for the exam.

Attendance Policy.

I will not check attendance in this class. You may leave after 15 minutes if the instructor is absent.

Academic Integrity

As members of the Clemson University community, we have inherited Thomas Green Clemson's vision of this institution as a high seminary of learning. Fundamental to this vision is a mutual commitment to truthfulness, honor, and responsibility, without which we cannot earn the trust and respect of others. Furthermore, we recognize that academic dishonesty detracts from the value of a Clemson degree. Therefore, we shall not tolerate lying, cheating, or stealing in any form.