In these three courses students are expected to learn the fundamental tools needed to work in the general field of analysis. This sequence will cover 3 main topics:

• I. Measure and Integration (includes Lebesgue measure and Lebesgue integral).
• II. Topological spaces (includes metric spaces).
• III. Basic Functional Analysis (includes L^p spaces).

The following syllabus is tentative. Nevertheless it should give you a reasonable idea of what is ahead.
The course will be divided in 9 chapters as follows: <

1. Basics: [R] Ch. 1, 2; [F] Ch. 0.
2. Metric spaces: [R ] Ch. 7.
3. Measures (Lebesgue measure): [R] Ch.3, 11; [F] Ch. 1.
4. Integration (Lebesgue integral): [R] Ch. 4, 11; [F] Ch. 2.
5. Differentiation and Integration: [R] Ch. 5, 11; [F] Ch. 3.
6. Topological spaces: [R] Ch. 8, 9; [F] Ch. 4.
7. Functional analysis: [R] Ch. 10; [F] Ch. 5.
8. L^p spaces: [R] Ch. 6; [F] Ch. 6. <
9. Selected topics: Radon measures ([F] Ch. 7); Elements of Fourier Analysis ([F] Ch. 8); Elements of Distribution Theory ([F] Ch. 9).

Texts:
Real Analysis, Folland, 2nd Edition (required)[F].
Real Analysis, Royden, 3rd Edition (required)[R].

Reserve List:
Real Analysis, Folland, 2nd Edition.
Real Analysis, Royden, 3rd Edition.
Real and Abstract Analysis, Hewitt & Stromberg.
Real and Complex Analysis, Rudin.
Functional Analysis, Rudin.

Prerequisite: MATH 426 or equivalent.