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 (Summer 2024)
Useful Resources
- Dr Peyam YouTube Channel
- Topology Playlist
- Real Analysis Playlist
- Analysis 1 – Website
- Analysis 2 – Website
Lecture Notes
Note: The notes will be frequently updated. Please refresh your webpage so that you have the most up-to-date version of the notes.
| 1 | Aug 19 | Metric Spaces and Topology |
| 2 | Aug 20 | Continuity and Connectedness |
| 3 | Aug 21 | Compactness and Uniform Convergence |
| 4 | Aug 22 | Arzela-Ascoli Theorem |
| 5 | Aug 23 | Applications to ODE |
| 6 | Aug 26 | Banach Spaces and Derivatives |
| 7 | Aug 27 | Implicit Function Theorem |
| 8 | Aug 28 | Riemann Integration |
| 9 | Aug 29 | Measure Theory |
| 10 | Aug 30 | Lebesgue Integral |
Recitation Problems
| Recitation 1 | Aug 20 | Solutions |
| Recitation 2 | Aug 21 | Solutions |
| Recitation 3 | Aug 22 | Solutions |
| Recitation 4 | Aug 23 | Solutions |
| Recitation 5 | Aug 26 | Solutions |
| Recitation 6 | Aug 28 | Solutions |
| Recitation 7 | Aug 29 | Solutions |
| Recitation 8 | Aug 30 | Solutions |
| Recitation 9 | Never | Solutions |
| Recitation 10 | Never | Solutions |