# Reading Guides for Math 331

Readings for Math 331 are from the textbook Foundations of Analysis, second edition, by David Belding and Kevin Mitchell, supplemented by some web pages about metric spaces. My goal here is to pull out important points from the reading and give my perspective on them, as well as to give some additional information and examples in some cases. I might occasionally record videos of short lectures and include links to them in the posts. I hope to post two or three of these "reading guides" per week throughout the semester. As the semester gets going and things get hectic, the length of the posts will probably decrease. If the class goes remote, the posts will be an important resource for the course, and their lengths should increase—and I will include more videos.

- 01. Irrational Numbers
- 02. Dedekind Cuts
- 03. Least Upper Bounds
- 04. Axioms for $\R$
- 05. Consequences of the axioms
- 06. Heine-Borel and Bolzano-Weirstrass Theorems
- 07. Limits of the form $\ds\lim_{x\to a}f(x)$
- 08. Other Kinds of Limit
- 09. Continuity and Uniform Continuity
- 10. Metric Spaces
- 11. Limits and Continuity in Metric Spaces
- 12. The Derivative
- 13. The Riemann Integral
- 14. Properties of the Integral and the Fundamental Theorems
- 15. Taylor Polynomials
- 16. Sequences and Series of Real Numbers
- 17. Sequences of Functions
- 18. Series of Functions