Mathematics 421/510

Real Analysis II

Department of Mathematics,  Math undergrad courses,  Math grad courses

Prerequisites:

• For Math 421: Math 420
• For Math 510: Familiarity with the material of Math 420 (roughly chapters 1-3 and §6.1 of Folland or chapters 1-5 and 11 of Royden).

Catalogue No:

• For Math 421: 19307
• For Math 510: 33115

Instructor

Joel Feldman

Text

Other possible references include

• Michael Reed and Barry Simon, Methods of Modern Mathematical Physics, I: Functional Analysis, Academic Press.
• H. L. Royden, Real Analysis, Macmillan.
• Walter Rudin, Real and Complex Analysis, McGraw-Hill.
• Walter Rudin, Functional Analysis, McGraw-Hill.

Topics

1. Point Set Topology (Chapter 4, excluding §4.3 and §4.8).
2. Banach and Hilbert Spaces (Chapter 5, excluding § 5.4).
3. L^p Space (Chapter 6, excluding §6.4 and §6.5).
4. Riesz Representation Theorem (§7.1).
5. Applications
   • Brownian Motion
   • Haar Measure

Grading

• Weekly problem sets, assigned each Wednesday and due the following Wednesday.
• Final exam.

I will post all handouts, problem sets, final grades, etc. on the web here.