Lecture: MWF 11:00-11:50, Engineering E105.

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 the classical questions of doubling the cube, trisecting the angle and squaring the circle are impossible to solve. There are many exciting open questions in Galois theory and it is one of my favorite topics for research. For the most part we will follow the Course syllabus.

Prerequisite: Math 566 or permission of professor.

Text: Abstract Algebra (Second Edition), by Dummit and Foote, John Wiley and Sons, mostly Chapters 10-14, plus handouts.

Grading: The course grades will be computed approximately as follows.
40% Homework; 25% Final; 15% Midterm; 10% Recitation; 10% Project.

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 writing proofs. Homework is divided into easy, medium, and difficult problems; depending on your plans for graduate study, you may choose to hand in either the easy or the difficult problems, along with the medium problems. Homework is due every week (we will vote on the day). 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 a midterm given in class on Monday, March 8.
There will be a final examination on Friday May 14 in E105 from 9:10-11:10.

Recitation:
There will be a recitation from 6-7 pm on every third Tuesday. Location TBA. The purpose of the recitation is for everyone to present interesting homework problems and to describe their project. The recitation will also make up for several classes which will be canceled. In particular, there will be no class on Wednesday March 10 and Friday March 12.

Project:
This is an opportunity for everyone to learn about a different cool topic not covered in class. It is also a good opportunity to develop more skills at writing and speaking on mathematics. Detailed information on projects

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.