This repository is home to an ongoing project that was first conceived during my time at Boston College. The goal of this project is for me to organize 4 semesters worth of real analysis notes into one document for my future self. The perfect time to make this a reality was while quarantined during the COVID-19 Pandemic. While these notes are mainly for my personal use, this repository is public. Online course notes are a great resource, and I see no harm in making these notes available to others (even though they may not be of the highest quality). That being said, apologies if these notes aren't helpful! I also am trying to be as pedantic as possible with proofs and examples.
One of the reasons I want to organize all my notes is because they pull from four different courses, and several texts. My goal is for the final product to be a convex combination of various sources, all presented in a approachable manner.
- Rudin, Principles of Mathematical Analysis
- Rudin, Real and Complex Analysis
- Rudin, Functional Analysis
- Tao, Analysis I
- Tao, Analysis II
- Apostol, Mathematical Analysis
- Folland, Real Analysis: Modern Techniques and Their Applications
- Royden and Fitzpatrick, Real Analysis
- Aliprantis, Infinite Dimensional Analysis: A Hitchhiker's Guide
- Munkres, Analysis on Manifolds
- Axler, Measure, Integration, & Real Analysis
- Grafako, Classical Fourier Analysis
- Chpaters 1-7, first semester undergrad course
- Chapters 8-12, second semester undergrad course
- Chapters 12 - 17 , first semester PhD course
- Chapters 18- Beyond, second semester PhD Course, PhD field course in functional analysis
As stated before, I am hoping to make the material as approachable as possible, and stay constant in tone throughout. One of the best ways to learn math is working through a very concise text, drawing your own illustrations, and coming up with your own examples. Unfortunately, people who are very comfortable with formal math take it for granted that students don't know this. Unless you happen to stumble upon this unusually insightful amazon review, a first pass at analysis using Baby Rudin can be torture (mine was at least). I'm trying to create the type of guide I would have wanted when I first learned basic analysis. That means frequent illustrations, digressions about motivation, footnotes, and not-so-concise proofs. Furthermore, I want to treat more advanced topics with this approach as well, because measure theory and functional analysis are not as scary as graduate textbooks make them look.
- Go back to sections marked "FINISH" in red
- Incorporate color to highlight changes from one line to the next in align enviroments
- Cross references figures, results, examples, definitions, etc. using hyperref