## Math 675: Linear Analysis

Instructor: Anton Lukyanenko

Email: alukyane@gmu.edu

## Class Times

Mondays-Wednesdays 5:55-7:10 in Exploratory Hall 4106. Class will be mostly lecture-based, but with some time devoted to group-based problem sessions and student presentations.

## About the Course

The goal of the course is to understand, at a deeper level, the geometry and topology of Euclidean space, and to extend this understanding to Banach spaces: infinite vector spaces with a Euclidean-like structure. This will allow us to interpret functionals such as integration or the Fourier transform as functions between Banach spaces, and to discuss limits and maximal values in this broader context.

On a more applied level, the course will cover content tested by the Linear Analysis preliminary exam.

## Book

We will use the traditional "Introductory Real Analysis" by Kolmogorov and Fomin (ISBN 0-486-61226-0).

## Homework and LaTeX Resources

Homework will be due each Wednesday, and limited to two pages of typed text, and graded for both correctness and style (e.g. succinctness, clarity, overall look). LaTeX is highly recommended:

ShareLaTeX: a good typesetting environment.

LaTeX guide

Detexify: a way to look up tex symbols