In this course we will follow the book "Spaces - An Introduction to Real Analysis" by Tom L. Lindstr?m.
The second chapter "The Foundation of Calculus" contains important fundamental material that you are expected to know. The material will however not be covered in the lectures, since (most of) it has been covered in earlier courses at UiO. So you are advised to work through it on your own, and make sure you know it well.
We will not be able to cover the entire book, so more specifically the syllabus is the following:
- Chapter 1: Whole chapter.
- Chapter 2: Whole chapter (but not lectured on).
- Chapter 3: 3.1--3.6.
- Chapter 4: 4.1--4.7 (But material similar to 4.10 and 4.11 will be presented in connection with Chapter 10)
- Chapter 5: 5.1--5.5.
- Chapter 6: 6.1--6.5 and 6.7--6.8 (But we we only stated the Implicit Function Theorem in 6.8 in R^n)
- Chapter 10: 10.1--10.4 (the chapter number refers to the compendium that will be made available in due time).