### Instructor

Jonathan Goodman, goodman@cims.nyu.edu, 212-998-3326room 529 Warren Weaver Hall

office hours: 4 to 6 pm Tuesdays or by appointment

### Summary

This is a first class in abstract algebra for undergraduate math majors or others interested in high level undergraduate algebra. The class will cover the basic topics of abstract groups and rings, but with many concrete examples. Much of the discussion of groups will use groups of matrices as examples. In particular, we will discuss linear algebra in finite fields, which are used now in cryptography and coding. Examples of rings include rings of algebraic integers and polynomials.

Much of the class is devoted to formulating axioms that capture the algebraic structures common to important examples. There is heavy emphasis on abstract reasoning and mathematical proof. There will be weekly homework assignments that involve writing proofs and working out examples.

There is a tentative week by week syllabus here.

### Prerequisites

The most important prerequisite is linear algebra. Students also should have completed Calculus III. It would be helpful to have taken a class that emphasizes mathematical proof, such as Analysis I.

### Grading

The grade will be based on weekly homework assignments as well as one midterm and a final exam.

### Text

* Algebra* (second edition), by Michael Artin

### Communication

Out of class communication will be through a class page on the NYU Blackboard system. Registered students can access the site through their home.nyu.edu account. This page will have a message board where class announcements will be posted and students can communicate with each other about homework assignments or other matters. Students also will be able to check grades there.