Office: South 326A

Telephone: 245-5403

Office Hours: Monday 1:30 - 2:20p, Tuesday 8:00 - 9:00p, Wednesday 4:00 - 5:00p, Thursday 4:00 - 5:00p, Friday 3:00 - 4:00p (may cancel occasionally) and by appointment or visit

Email Address: Johannes@Geneseo.edu

IM: JohannesOhrs

Web-page: http://www.geneseo.edu/~johannes

Textbook

Errata, George Bergman

Additional exercises, George Bergman

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 (or 319).

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.

Grading

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 30%

Oral Final exam 30%

Homework

The four problem sets will be due on 6 February, 27 February, 2 April, and 23 April. The assignments will be finalised no later than the Wednesday before they are due.

Take-home Exam

On 2 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 5 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.

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.

Academic Dishonesty

While working on homework with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. The Student Academic Dishonesty Policy and Procedures will be followed should incidents of academic dishonesty occur.

Disability Accommodations

SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional or learning disabilities. Students should consult with the Director in the Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin, tbuggieh@geneseo.edu) and their individual faculty regarding any needed accommodations as early as possible in the semester.

Religious Holidays

It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work. You are responsible for notifying me no later than January 30 of plans to observe the holiday.

Philosophy

Since this course has a 300-level prerequisite of theoretical mathematics, I find it reasonable to assume that all students taking this class are interested in pursuing graduate study in mathematics. Therefore I will attempt to run this course as an emulation of a graduate school course. In particular, you may notice fewer evaluations in the course, and fewer checks. You have more responsibility for your own motivation and your own understanding. You may also notice a challenging (to me) attempt on my part to be less "nurturing", and for you to learn material on your own, with my skipping sections for outside reading and similar. The good habits you have developed of working with other students are now even more important than before, as are your skills at reading and learning materials from a text. For those who know me, this course should be a divergence from our prior experiences. Please know that this is intentional.