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