**Introduction to Abstract Algebra II**

Mathematics 567: Spring 2016

** Lecture:** MWF 12:00-12:50, Engineering E105.

**
Syllabus **

**Course description:**
In this course, we will study modules and Galois theory.
Modules are abstract algebraic structures (developed by Emmy Noether) which generalize vector spaces and abelian groups.
The theory involved is difficult but permeates all areas of mathematics.
Galois theory started with the study of symmetries of polynomials.
It shows that there is no formula for the roots of a general quintic equation.
There are many exciting open questions in Galois theory and it is one of my favorite topics for research.

**Prerequisite:**
Math 566 or permission of professor.

**Text:**
Abstract Algebra (third edition), by Dummit and Foote,
John Wiley and Sons, mostly Chapters 10-14, and also Chapter 18.

**Grading: **The course grades will be computed approximately
as follows.

25% Homework (may include short project); 20% Quiz 1; 20% Quiz 2; 35% Final.

**Homework:**
Homework is the most important part of this class.
It should demonstrate your knowledge of the material,
your investigation of open ended questions, and your skill at proofs.
Homework is due every week, both in a
Homework must be neat, legible, and stapled in order to receive credit.
I encourage you to brainstorm the problems in groups and write up your
solutions independently.

**
Detailed information on homework and exams **

**Examinations:**
There will be two quizzes given in class on Friday 2/19 and Friday 4/1.

There will be a final examination on Wednesday May 11 from 4:10 pm - 6:10 pm.

**Help:** Help is always available if you have trouble with homework
or lecture material. If your comrades can't answer your question,
come ask me! Office hours will be (TBA) or are available by appointment.