## Math 675: Linear Analysis

Instructor: Anton Lukyanenko

Email: alukyane@gmu.edu

Course Syllabus

## 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.

## Homework

Homework 1: pdf tex

Homework 2: pdf tex

Homework 3: pdf tex

Homework 4: pdf tex

Homework 5: pdf tex

Homework 6: pdf tex

Homework 7: pdf tex

Potential Midterm Questions: pdf tex

Homework 8: pdf tex

Homework 9: pdf tex Mathematica

Homework 10: pdf tex

Homework 11: pdf tex

There will be no further homework.

Potential Final Questions: pdf tex

## Important Dates

September 3: Labor day; no class.

October 8: Fall Recess; class moved to:

October 9: Fake Monday; class held at usual time, even though it's a Tuesday.

October 17: Midterm, covering through Section 14.

November 21: Fall Break; no class.

December 5: Last day of class.

December 17: Final exam, 4:30-7:15 in the usual classroom.

## 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 operators and functionals such as summations, 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

## Approximate Schedule

We will aim to cover two sub-sections per day, as follows:

August

27, 29: 5.1-2, 6.1-2

September

5: 6.3-4

10, 12: 6.5-6, 7.1, 7.4

17, 19: 8.1, 11.1-2, 13.1

24, 26: 13.2-5

October

1, 3: 13.6-14.3

9, 10: 14.4-5, 15.1-2

15, 17: 16.1-2, midterm

22, 24: 16.3-6

29, 31: 16.7-9, 18.1

November

5, 7: 18.2-3, 19.1-2

12, 14: 22.1-3, 23.1

26, 28: 23.4, 24.1-3

December

3, 5: Overflow and Review

17: Final exam, 4:30-7:15pm