Final syllabus
- Chapter 1 and 2: While not explicitly part of the syllabus, this material is used and taken for granted in this course.
- Chapter 3: Sections 1–5. Section 3.6 might be useful for context in Sec. 4.8.
- Chapter 4: Sections 1–10 (but not the section on Abel's theorem in Sec. 4.4),
- Chapter 5: Sections 1–5. Apart from Sec. 5.5, this should be familiar from MAT1125. If you have not taken that course, or need a brushing-up, consult the textbook.
- Chapter 6: Sections 1–2 and Sec. 3–4 of this note (corresponding to 6.7–6.8 in Spaces, but in Euclidean space).
- Chapter 7: Sections 1 and 3–8. You might want to consult Ch. 1 of my note on measure and integration, which emphasises what I find most important. In particular, Sec. 1.8 is a much simplified version of Spaces' Sec. 7.8.
- Chapter 8: Sections 1–4. You do not need a detailed understanding of this material; consult Ch. 2 of my note on measure and integration to get an overview.
Supplementary material
If you are looking for alternative textbooks to Lindstrøm's Spaces, I can recommend the following:
- W. Rudin. Principles of mathematical analysis. Starts very basic, but still covers a substantial part of our syllabus. Available from the Internet Archive.
- T.W. Körner. A companion to analysis. Covers parts of Ch. 1–6. Starts at a somewhat lower lever, and is more detailed and verbose than Spaces.
- R. G. Bartle. The Elements Of Integration And Lebesgue Measure. A great, quite compact, introduction to measure and integration theory. Covers most of Chapters 7 and 8. Available from the Internet Archive.