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