Course literature: Gerald B. Folland: "Real Analysis" (2nd edition). ISBN: 0-471-31716-0, and lecture notes.
Some notes for the course. (To save paper, please try to AVOID PRINTING these notes! I hope that you will be able to read it on your computer or ipad screen instead... The notes should be thought of mainly as a source of reference.)
Examination: Three assignments will be given during the course. For each assignment one can get 0-100 points (0-120 on the 3rd). To pass one has to submit solutions to all three assignments, have at least 20 points on each of them and at least 100 points altogether.
assignment 1 (due Feb 18, 10.15).
assignment 2 (due March 13, 10.15).
assignment 3 (due April 29, 10.15).
Preliminary plan:
1. Sums and integrals
2. Measure and integration theory (~ Folland Ch. 1.1-1.3)
3. Measure and integration theory (~ Folland Ch. 2.1-2.3 and 2.5-2.7)
4. Measure and integration theory (~ Folland Ch. 3.1-3, 6.1-2, 7.1-3)
5. Fourier analysis (~ Folland Ch. 8.2, 8.3)
6. Fourier analysis (~ Folland Ch. 8.2, 8.3, 8.6)
7. PROBLEM DISCUSSION
8. Fourier analysis
9. Special functions and asymptotic expansions
10. Special functions and asymptotic expansions
11. Special functions and asymptotic expansions
12. Special functions and asymptotic expansions
13. PROBLEM DISCUSSION
14. Distribution theory (~ Folland Ch. 9.1-2)
15. Distribution theory (~ Folland Ch. 9.1-2)
16. Distribution theory; Sobolev spaces (~ Folland Ch. 9.2-3)
17. Sobolev spaces (~ Folland Ch. 9.3)
18. Dynamical systems: some examples; continued fractions and the Gauss map.
(~ Ch. 3 in Einsiedler and Ward: "Ergodic theory with a view towards Number Theory")
19. Dynamical systems: some more examples.
20. PROBLEM DISCUSSION
Andreas Strömbergsson, Room Å14134, Tel. (018) 4713221, e-mail: astrombe@math.uu.se