MTHT 530 Analysis for Teachers II
Key Concepts
You should be comfortable with all of the key definitions.
You should be able to state and apply all of the key results.
You should be able to sketch the proof of the key results marked with (*).
Review KeyConcepts
- least upper bounds
- Completeness of R
- limits
- continuity
Key Theorems
- Nested Interval Theorem (*)
- Intermediate Value Theorem (*)
- Bounding Theorem (*)
- Extreme Value Theorem (*)
Sequences
KeyConcepts
- sequences, covergence and divergence
- monotone sequences
Key Theorems
- Monotone Covergence Theorem (*)
- f is continuous at a if and only if f(a_n)->f(a) for every sequence
a_n->a (*)
- Bolzano-Weierstrass Theorem (*)
Last Updated 1/11/06