Description:
You will be introduced to algebraic and analytic proofs and reasoning that are used in advanced mathematics. You will analyze the real number system, power series and convergence (absolute, uniform) of sequences and series. You will apply power series to differential equation.

Topical Outline:

1. Topology of The Real Numbers 2. Convergence of Sequences and Subsequences, Cauchy Sequences, Monotonic Sequences 3. Continuity in Metric Spaces; Uniform Continuity 4. Analysis of Differentiation, L'Hospital's Rule and Taylor's Theorem 5. Analysis of Reimann Integration 6. Convergence of Functions: pointise, absolute and uniform

Learning Outcomes:
1. Analyze the real number system topologically
2. Apply advanced algebraic and analytic reasoning and proofs
3. Apply power series, L'Hospital's Rule and the Mean Value Theorem to differential equations
4. Determine and apply uniform continuity of functions and uniform convergence of series