The advanced calculus course should include a rigorous theoretical treatment of:

    • Sequences and series
    • Continuity
    • Limits of functions
    • Uniform continuity
    • Differentiation
    • Taylor's theorem
    • Lim sups and lim infs
    • Riemann integration
    • Basic methods of mathematical proofs, including epsilon-delta proofs, proof by contradiction, and mathematical  induction.