HUT / Department of Mathematics / teaching /
Prerequirements: Mat-1.015 Principles of Modern Analysis (ModA) is almost necessary (at least ε and δ should be familiar); Mat-1.140 Principles of Functional Analysis (FAP) helps but you can well do without it.
We recommend you to take the course Mat-1.500 The theory of Martingales (2 credits). after this one, to deepen your learning. That course is lectured in two parts: the first part in Oct'22 -- Nov'20, the second in the beginning of the spring term.
Contents: General analysis: Lebesgue integration, $\L^p$ spaces, measure theory and differentiation. Outside [R2] we shall treate the integration and differentiation of (Banach) vector-valued functions and the weak topologies of Banach spaces.
Lectures: at 2 pm (14--16) on Wednesdays and at 2 pm (14--15) on Fridays,
room U322 (since 2002-9-11);
professor Stig-Olof Londen, U301, p. 451 3035.
Exercises: at 4 pm (16--18) on Wednesdays, room U322 (since 2002-9-18).
research fellow Kalle Mikkola, U313, p. 451 3017 / 040-754 5660. (most easily contacted during or after the exercises or at 3 pm on Fridays, but you may contact or email me on other times too).
Two mid-term examinations: times and locations will be announced at lectures and in the exercise solution papers.
Book: [R2] Walter Rudin: Real And Complex Analysis (third edition; provided by big book stores at around 20 euros). We shall go through chapters 1--3 and 6--8 (and possibly 9) thoroughly and 4 & 5 quickly. (Chapters 4 & 5 are mostly contained in course 1.140 FAP, so if you have not studied FAP, you should work a bit more yourself).
The rest of the book (chapters 10--20) served the course ``Mat-1.151 Complex Analysis'' before year 1998 and serves now as a reference. We may also use partially the book Elliott H. Lieb -- Michael Loss, ``Analysis'', AMS 1997.
The rest of the material: The Finnish speaking students who want to study the course themselves may want to read [R2]:n lukuohjeita. During the course, the exercises and answers will be delivered to the envelope in front of room U313 and to the web (not necessarily simultaneously). You do not get any points from the exercises, but we recommend you to think them yourself anyway.
The oldest material will be moved to the archives in the Optimi room (Y324). The exercises and answer of previous courses (in Finnish) are given in http://www.math.hut.fi/~kmikkola/mat/rea/, in PostScript. Most laser printers do print PostScript (e.g., click the file reav1.ps, save it "reav1.ps" and write "lpr reav1.ps" in the Unix shell); use Ghostview to view them on the screen (often installed in Unix; to Windows it can be downloaded from the web (around 10 MBytes)).