Linear Analysis
Math 675-001 (Fall 2024)
This web page will be updated regularly and always contain the latest information on the course.
| Instructor: | Thomas Wanner |
| Office: | Exploratory Hall 4404 |
| E-mail: | twanner@gmu.edu |
| Web Page: | https://math.cos.gmu.edu/~wanner |
| Fax: | (703) 993-1491 |
| Office Hours: | MW 2-3pm, and by appointment |
| Learning Assistant: | TBA |
| Office: | Exploratory Hall 4311 |
| E-mail: | tba@gmu.edu |
| Office Hours: | TBA |
| Prelim Session: | TBA |
| Lectures: | MW 4:30-5:45pm, Exploratory Hall 4106 |
| Prerequisites: | Math 315 and Math 322, or equivalent. |
| Textbook: | There is no required textbook for the course, I will post handwritten lecture notes on Blackboard after every class. |
| While I will draw the material from a variety of sources, the following two texts can be used for supplementary reading: | |
| 📕 E. Kreyszig: Introductory Functional Analysis with Applications, Wiley, 1978. | |
| 📘 A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis, Dover, 1970. |
Important Links
- Detailed syllabus (including notes and recommended books)
- Relevant official GMU policies
Detailed lecture notes, solutions to homework assignments, reading assignments, and additional materials can be found on the Blackboard site for this course. Homework assignments can be found on Gradescope, which is linked through Blackboard as well. Please make sure to check there regularly!
Syllabus
The course introduces basic concepts and techniques of linear functional analysis. These techniques constitute the abstract mathematical framework for solving a variety of applied problems, and applications of the theory will be given throughout the course. In addition to a brief introduction to the necessary topological concepts, the course covers basic Banach and Hilbert space theory, the theory of bounded linear operators between such spaces, as well as the fundamental theorems of functional analysis. A more detailed syllabus can be found here. It will be updated weekly. This course is one of the core courses of the graduate program, and will therefore cover all the topics outline in the Linear Analysis Preliminary Exam Syllabus.
Homework Assignments
Homework problems will be assigned once a week and posted on Gradescope. Some of these assignments will be graded and count towards your homework score. While the remaining ones do not have to be handed in, I do advise everyone strongly to study them and write out the solutions properly. I will post detailed solutions as well as videos discussing the solutions on Blackboard, and you will not benefit from this if you have not made a serious attempt at solving the problems.
Grading Policy
Your final grade in the course will be determined from your performance in the homework assignments, a midterm exam, a final exam, and your attendance and participation in class. Weights for these items will be distributed approximately according to the following schedule:
| Homework | Midterm Exam | Final Exam | Attendance |
|---|---|---|---|
| 50% | 20% | 20% | 10% |
The assignment of your course grade is based on the total course score. The following grading scale may serve as a guideline:
| Letter Grade | A | B | C | D | F |
|---|---|---|---|---|---|
| Score above | 90% | 80% | 70% | 60% | otherwise |
These percentages might change, and any changes will be announced in class.