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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
The next homework will be due on October 31.

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