TMA4225 Foundations of analysis: Fall term 2014
Resources
Textbook
The textbook will be McDonald & Weiss: A Course in Real Analysis, second edition.
Other literature
I will add a short list of suitable support literature here.
Notes
Unless otherwise noted, the notes listed here are not part of the syllabus. Their main purpose is to provide a different perspective than the book, especially where I depart from the book.
A quick note on the formats:
- The “screen” version is optimized for screen reading. It has pages of variable length, with a page break between subtopics. It also has a coloured background, so it is not at all suited for printing
- The A5 version is more conventionally formatted (also good for screen reading)
- The “print” version is just the A5 version with two pages per A4 sheet, for easy printing.
| Short title | PDF versions | Remarks |
|---|---|---|
| Sums | screen, A5, print | A different approach to infinite sums Updated 2014-08-12 |
| Compactness | screen, A5, print | Compact subsets of the real line |
| Lebesgue measure | screen, A5, print | Basic properties of Lebesgue measure Updated 2014-09-07, 2014-09-11, and 2014-10-09 |
| Lebesgue integral | screen, A5, print | Definition of the Lebesgue integral Monotone convergence theorem |
| Καραθεοδωρή | screen, A5, print | The general Carathéodory construction of measure (new 2014-10-09) |
| Premeasures | screen, A5, print | Premeasures and the outer measures they induce (updated 2014-10-13) |
| Coin tossing | screen, A5, print | The coin tossing probability space (new 2014-10-13, updated 2014-10-19) This is considered (a cursory) part of the syllabus. |
| Littlewood | screen, A5, print | Littlewood's principles, including Lusin and Egorov's theorems (new 2014-11-09). This is considered part of the syllabus. |
| Differentiability | screen, A5, print | Dini derivatives, Vitali coverings, fundamental theorems of calculus (new 2014-11-02, updated 2014-11-03, 2014-11-09, and 2014-11-10) |