Topics
# Topics Covered in Math 501

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We will cover most of the material (excluding Chapter 10) in the text
* Principles of Mathematical Analysis, Third Edition, *
by Walter Rudin.

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The book is only a guide. The objective is to strengthen your
understanding of real analysis as much as possible. It does not
matter whether we cover every single topic. I will certainly skip
some topics, and I may at times inject material that is not in the book.

- Chapter 1. The Real and Complex Number Systems

- Chapter 2. Basic Topology

- Chapter 3. Numerical Sequences and Series

- Chapter 4. Continuity

- Chapter 5. Differentiation

- Chapter 6. The Riemann-Stieltjes Integral

- Chapter 7. Sequences and Series of Functions

- Chapter 8. Some Special Functions

- Chapter 9. Functions of Several Variables

- Chapter 11. The Lebesgue Theory

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