#
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:**

- (864) 656-6766 (office)
- (864) 656-3434 (Dept)

** 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:
- Compute the invariant factors and elementary divisors of a finitely generated module over a PID.
- Compute the tensor product of two modules.
- Write down bases for extension fields.
- Compute the Galois group of a finite extension
of fields.
- Deduce information related to a field extension
such as the number and relative degrees of its subextensions from its
Galois group.
- Compute the splitting fields of polynomials of
small degree and will build an understanding of the general case.
- Discern if a polynomial's roots are exressible
in terms of radicals by considering the Galois group of the splitting
field of the polynomial.
- 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:

- Homework 70%
- Cumulative Final Exam 30%

The standard grading scale will be used

- A >= 90
- B >= 80
- C >= 70
- D >= 60
- F < 50

### 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.