Handouts for Math 703/703 for AY 20-21

Undergraduate Handouts from my Math 554/555 classes:

1. Functions and Sets
2. A Rigorous Axiomatic Approach to the Real Numbers   (with chart solutions)   (includes sup (lub) and inf (glb) of sets)
3. Sup/Inf (of sets) Properties Summary
4. Limit Superior (lim sup) and Limit Inferior (lim inf) of sequence.
5. Introduction To Topology   (with chart solutions)   Beware: some definitions differ (but are equivalent to) our book's defintions.
6. Countability    (from Bartle and Sherbert: Section 1.3, Appendix B, The Uncountability of ℝ)
7. Cantor Set

Metric Spaces:

1. Metric Space Basics Defs
2. Function Spaces
3. Compactness
4. Stone-Weierstrass Theorems   (tex file)
5. Equivalence Relations
6. Connectedness

Complex Analysis:

1. Logarithm Functions
2. Isolated Singularities of Holomorphic Functions