Welcome to the APMA Summer Bridge Program, an exciting Analysis adventure awaits you! This is the webpage for this course, where you can find all the administrative info you need to know. Feel free to e-mail me if you have any other questions.
Syllabus
Summer Bridge Program – Syllabus
Useful Resources
- Dr Peyam YouTube Channel
- Topology Playlist
- Real Analysis Playlist
- Analysis 1 – Website
- Analysis 2 – Website
Lecture Notes
Acknowledgements: The notes are based on the 2017 and 2018 workshops that were led by Bjorn Sandstede. The original notes were typed by Rebecca Santorella and Patrick Liscio, updated by Ross Parker, and revamped by myself.
| 1 | Aug 21 | Metric Spaces and Topology |
| 2 | Aug 22 | Continuity and Connectedness |
| 3 | Aug 23 | Compactness and Uniform Convergence |
| 4 | Aug 24 | Arzela-Ascoli Theorem |
| 5 | Aug 25 | Applications to ODE |
| 6 | Aug 28 | Banach Spaces and Derivatives |
| 7 | Aug 29 | Inverse and Implicit Function Theorems |
| 8 | Aug 30 | Integration and ODE |
| 9 | Aug 31 | Measure Theory |
| 10 | Sep 1 | Lebesgue Integral |
Practice Problems
Note: The practice problems are optional, and you only need to submit them if you want to get feedback on them. You will go over those problems during the recitation sections. The due dates are flexible and you submit your assignments on Gradescope
| Homework 1 | Aug 21 | Solutions |
| Homework 2 | Aug 22 | Solutions |
| Homework 3 | Aug 23 | Solutions |
| Homework 4 | Aug 24 | Solutions |
| Homework 5 | Aug 25 | Solutions |
| Homework 6 | Aug 28 | Solutions |
| Homework 7 | Aug 29 | Solutions |
| Homework 8 | Aug 30 | Solutions |
| Homework 9 | Aug 31 | Solutions |
| Homework 10 | Sep 1 | Solutions |