Mathematics 381 :  Topics in Mathematics:  Galois Theory
Spring 2017
Introduction
Professor:        Jeff Johannes                                    Section 1    MWF    12:30 - 1:20p    Sturges 103
Office:            South 326A
Telephone:      245-5403
Office Hours:    Monday 11:30a - 12:20p, Tuesday 8:00 - 9:00p, Wednesday 11:30a - 12:20p, Thursday 10:15 - 11:15a, Friday 1:30 - 2:20p, and by appointment or visit
IM:                    JohannesOhrs
Web-page:        http://www.geneseo.edu/~johannes

Textbook
Galois Theory, Fourth Edition, Ian Stewart
Our Errata
Comments to student questions, George Bergman

Course Description
In this course we will explore the question of solvability of polynomials.  We will consider finding and permuting roots from Galois’ original historical perspective.  Along the way we will settle some of the classical construction problems and see the power of applying seemingly theoretical ideas to the more practical question of finding roots of polynomials. Prerequisite:  Math. 330.

Course Outline
I Background and field extensions
II Galois Correspondence
III Examples and Applications

Course Summary
Much like Galois himself, we will be heavily driven by examples.  We will consider how permutation of roots allows us to understand polynomials and discover ways to solve them.  We will see a deep connection among factoring, permutations of roots, and extensions of number systems.

Learning Outcomes
Upon successful completion students will be able to
Explain how modern algebra grew out of Galois’ permutations of roots of polynomials.
Analyse particular polynomials – compute their Galois groups and assess their solvability by radicals.

Your grade in this course will be based upon your performance on four problem sets, one take home exam and one oral final exam.  The weight assigned to each is designated below:
Problem sets (4)          10% each
Take home exam          25%
Oral final exam           25%
Class presentation(s)   10%

Problem Sets
The four problem sets will be due on 6 February, 27 February, 3 April, and 24 April.  The assignments will be finalised no later than the Wednesday before they are due.

Class Presentation(s)
Class presentations will be evaluated however we agree to evaluate them.

Take-home Exam
On 3 March in class you will be given your take home exam related to course material included in the first two problem sets.  It will be due on 6 March at the beginning of class.

Oral Final Exam
Sometime after our last class, each student will present a discussion about topics overviewing the course.  Details will be discussed after spring break.  Probably will occur Thursday 4 May, 12N-2:30p.

Feedback
Occasionally you will be given anonymous feedback forms.  Please use them to share any thoughts or concerns for how the course is running.  Remember, the sooner you tell me your concerns, the more I can do about them.  I have also created a web-site which accepts anonymous comments.  If we have not yet discussed this in class, please encourage me to create a class code.  This site may also be accessed via our course page on a link entitled anonymous feedback.  Of course, you are always welcome to approach me outside of class to discuss these issues as well.