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