Over the next few months I will be organising a read-along of Walter Rudin’s Principles of Mathematical Analysis (AKA Baby Rudin).
Goal: To understand metric spaces, the nicest type of topological space.
Expected prior knowledge: Elementary calculus (of one variable). Elementary linear algebra. Experience with proofs. A significant amount of patience.
Topics to cover: Construction of $ \mathbb{R} $ in detail. Topology of $ \mathbb{R}^n $. Sequences
and series in $\mathbb{R}^n $. Continuity of real functions. Differentiation and theorems in calculus.
Riemann integration. Function spaces. Power series and special functions. (Roughly speaking we will
be covering the material in the University courses MATHS 332 and the first half of MATHS 333.)
Book: Baby Rudin is available in the UoA library at call numbers 515 R91 and 515.8 R91. Editions after the first edition have many corrections. See also some companion notes and errata here. I will upload a scanned PDF copy of the relevant reading each week. However, I will delete it after a week so the blog does not get copyright-pinged.
Format: I hope to start on Monday evening next week (the 1st of April). I shall post weekly (or more often) suggested reading, problems and perhaps additional notes here. I will set up some kind of discussion software up on here so that we can discuss and ask questions; otherwise my uni email address is not really a secret, so if someone emails me with comments or notes than I will be happy to put them up here either under their name or anonymously. In addition, if there is enough interest it may be productive to set up a weekly physical meeting time somewhere with a whiteboard:- not to do reading or to work through the problems, but to discuss particular difficulties and generally catch up.
Further steps: I am hoping to conduct a further read-along of either Rudin’s Real and Complex Analysis, or a multivariable analysis book like Munkres’ Analysis on Manifolds, after completing the first nine chapters of PoMA.
| Week | ||
|---|---|---|
| 1 | 1 April to 7 April | Chapter 1: axioms for $ \mathbb{R} $ |
| 2 | 8 April to 14 April | Chapter 1: existence of $ \mathbb{R} $ |
| 3 | 15 April to 21 April | Chapter 2: set-theoretic preliminaries |
| 4,5 | 22 April to 5 May | Chapter 2: baby topology |
| Meetup 1, agenda |
