Announcements
- 4/22
- The take-home final exam with source is available.
- 3/4
- Here is a copy of the midterm from the last time I taught this class. The book was different, so some of the material won’t overlap with ours. But you can see the structure and degree of difficulty. This is intended to be a straightforward exercise: do you know the essential definitions and theorems, and can you use them to prove some elementary results?
- 2/4
- Here are the promised notes concerning all norms on a finite-dimensional vector space being equivalent.
- 1/15
- Here are the files for a demo Latex solution set.
- HWDemo.tex, the main file with the solutions
- homework.cls, a class file that defines the formatting
- 1/15
- Here is a beginner’s guide to LaTeX. Please read it, even if you have used LaTeX before.
- 1/15
- In this class, you are required to use LaTeX to typeset solutions. If you are new to using LaTeX, I can help. Your first step is to install LaTeX; here are some installation guides.
I didn’t write a guide for Linux; if you are using Linux and need help just let me know.
- 1/15
- We will use Piazza for course-related discussions outside of class time. You’ll need to sign up to start using the service.
Office Hours
Monday | 1:00-2:00 |
Thursday | 10:00-11:00 |
Friday | 9:15-10:15 |
Readings and Homework
Week | Reading | Problems | Due | Solutions |
---|---|---|---|---|
4/19 - 4/25 |
Sections 7.3, 8.1, 8.2 |
Wednesday, |
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4/12 - 4/18 |
Sections 7.2, 7.3 |
Wednesday, |
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4/5- 4/11 |
Sections 6.4, 7.1, 7.2 |
Wednesday, |
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3/29 - 4/4 |
Sections 6.2-6.4 |
Friday, |
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3/22 - 3/28 |
Sections 5.7, 6.1 |
Wednesday, |
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3/8 - 3/21 |
Sections 5.5, 5.6, 5.7 |
Wednesday, |
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3/1 - 3/6 |
Start Chapter 5 |
Wednesday, |
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2/22 - 2/28 |
Chapter 4 |
Wednesday, |
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2/15 - 2/21 |
Chapter 4 |
Wednesday, |
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2/8 - 2/14 |
Finish Chapter 3 |
Wednesday, |
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2/1 - 2/7 |
Chapter 3 |
Wednesday, |
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1/24 - 1/30 |
Chapter 2 |
Wednesday, |
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1/17 - 1/23 |
Secs. 1.1-1.3 |
No Homework |
Lecture Notes
Day | Topic |
---|---|
2/26 | Closed Graph Theorem |
2/26 | Open Mapping Theorem |
2/21-2/23 |
Lebesgue spaces as completions Invertibility |
2/16-2/19 |
The space of bounded operators Completions |
2/14 | Bounded Linear Maps |
2/12 | Continuous (Bounded) Linear Maps |
2/9 | Orthonormal Bases |
2/7 | Orthogonal Decomposition |
2/5 | Inner Prodcuts, Gram-Schmidt |
1/31 | Riesz Lemma |
1/29 | Finite Dimensional Vector Spaces |
1/26 | Equivalent Norms |
1/24 | Normed Vector Spaces |
1/22 | Metric Spaces |
1/19 | Metric Spaces |
1/17 | Linear Algebra |