Math 422 -- Spring 2015

Abstract Algebra
Emory University


Lecture Room:	W304 MSC
Lecture Time:	TuTh 10:00-11:15
Final Exam:	W May 6, 8-10:30am
Lecturer:	David Zureick-Brown
Office:	W430 MSC
Phone:	(608) 616-0153
Email:	dzb@mathcs.emory.edu

Text:	``Galois theory", Ian Stewart
Office Hours:	W11:30-12:15 (in W430)
	W3-3:34 (in E408)

About this course.

Ring theory: factor rings, Euclidean domains, polynomials over fields and over the integers, maximal ideals in rings, quotient fields.
Field extensions: simple extensions, algebraic and transcendental numbers, the degree of an extension, normality and separability, finite fields.
The Galois group: Normal closure, the Galois correspondence, soluble and simple groups, ruler and compass constructions, solution of equations by radicals.
Additional topics:transcendental degree, the general polynomial equation, the general Galois group, calculating the Galois group, the regular $n$-gon, quadratic and cyclotomic fields, the fundamental theorem of algebra.

Course details

This class will meet 28 times, and we will cover more or less the entire textbook. Additionally, the expectation is that, in addition to the weekly written homework, you will read every word of the textbook and additional notes.

Grading policy

The midterm dates below are tenative (and may be adjusted if the pace of the course is adjusted), but the date of the final exam is set in stone; make your summer travel plans accordingly. If you have a conflict with the final exam (e.g., another final) please let me know ASAP.

Homework	40%	(Bi-weekly, due Thursdays, 5pm)
Midterm	30%	(Th, March 26)
Final Exam	30%	(W May 6, 8-10:30am, W304)

Calculators, notes, and textbooks are not allowed in exams or quizzes.

The final letter grades will be curved, but the following table gives a lower bound on your grade:

85%	A
70%	B
55%	C

Homework

There will be homework assigned roughly every week, due on every other Tuesday at 5pm (in my mailbox). There will be many simple problems, checking your understanding of the definitions, that will be collected and graded for completness but not correctness. Most weeks there will be a number of proofs assigned. You are expected to write them up very carefully.

3-6 of problems will be carefully graded, and you will receive an additional 20 for completing the assignment. Homework assignments will typically be worth 100 points (20 for completeness, and 80 for graded problems).

The homework assignments are available at this link, and will be updated after each lecture.

Plagarism Policy

Remember that copying another student's work is a violation of the Honor Code and will be treated as such. If you must leave class during an exam for any reason, please leave all of your belongings (including your ~~handheld supercomputer~~ phone!).

For homework: you are free to consult any sources (animate or inanimate) while doing your homework (working in groups is encouraged!), but if you use anything (or anyone) other than your class notes or the texts listed above, you should say so on your homework -- please state at the end of every problem any sources used.

On the other hand, you are expected to make an honest attempt to do every problem on your own before consulting other sources. Remember that copying another student's work is a violation of the Honor Code and will be treated as such.

A good rule of thumb to avoid plagarism is the following -- when doing the final write up of a problem, do not have any text books, web pages, or classmate's write up in front of you. If you get stuck when writing up an assignment, go back and look again; just make sure that you organize the mathematics in your head before writing a proof rather than copying a solution from some source. This is a generous homework policy. Please do not abuse it.

Overloads

Ken Mandelberg handles all overloads for the department. To request an overload you must complete the form here and have it signed by your PACE or major advisor.