MTH 407, Real Analysis I
Updated 06/06/2011
1. Foundations
Positive integers and sets
Integers
Rational numbers
Real numbers
Complex numbers
Cardinal numbers
2. Basic Topology
3. Sequences and Series
Convergence of sequences
Convergence of series
Absolute convergence
Selected tests for convergence
4. Power series
Radius of convergence
Uniform convergence
Term by term integration
Term by term differentiation
Taylor's Theorem with Remainder
Generalized binomial coefficients
Binomial series
5. Continuity
6. The Derivative
7. The Riemann-Stieltges Integral
8. Optional topics as time permits
Proof of the "axiom" of completeness
Wallis' product formula for pi
Intervals of convergence for binomial series
Space filling curves
The devil's staircase
Fourier Series