Lecture Notes for Math 4023, Spring 2000
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Lecture 1: Proofs and Logic
Lecture 2: Methods of Proof
Lecture 3: Methods of Proof, Cont'd
Lecture 4: Methods of Proof, Cont'd
Lecture 5: Review of Set Theory
Lecture 6: Relations
Lecture 7: Functions
Lecture 8: Cardinality
Lecture 9: Integers, Rational Numbers and Algebraic Numbers
Lecture 10: Fields and Ordered Fields
Lecture 11: The Completeness Axiom
Lecture 12: The Completeness Axiom, Cont'd
Lecture 13: The Topology of the Reals
Lecture 14: Compact Sets
Lecture 15: Convergence
Lecture 16: Limit Theorems
Lecture 17: Monotone Sequences and Caucchy Sequences
Lecture 18: Limits of Functions
Lecture 19: Continuous Functions
Lecture 20: Properties of Continous Functions