September 2: Course info. (docx version)

September 4: Irrational numbers and cuts. (docx version)

September 9: Proving the existence of sqrt(2). (docx version)

September 11: More about cuts. (docx version)

September 14: Proving the Least Element Principle. (docx version)

September 16: Proving the Principle of Induction. The Least Upper Bound Principle. (docx version)

September 18: Proving the Least Upper Bound Property. Other consequences of the completeness of R. The countability of Q and the uncountability of R. (docx version)

September 21: Quantifiers. (docx version)

September 23: Negating propositions with quantifiers. (docx version)

September 25: Algebraic and Order Limit Laws. (docx version)

September 28: The Monotone Convergence Theorem. (no notes available)

September 30: The Bolzano-Weierstrass Theorem. (docx version)

October 2: The Cauchy Criterion. (docx version)

October 5: Infinite Series. (docx version)

October 7: Infinite Series (concluded). The Cantor Set (docx version)

October 9: Open and Closed Sets. (docx version)

October 14: Open and Closed Sets (concluded). (docx version)

October 16: Compact Sets. (docx version)

October 19: Compact Sets (concluded). Review. (docx version)

October 21: Review. (docx version)

October 26: Functional limits. (docx version)

October 28: Combinations of continuous functions. (docx version)

October 30: Combinations of continuous functions (concluded). (docx version)

November 2: Continuous functions on compact sets. (docx version)

November 4: Intermediate Value Theorem. (docx version)

November 6: Intermediate Value Theorem (concluded). (docx version)

November 9: The derivative. (docx version)

November 13: The mean value theorem. (docx version)

November 16: Sequences of functions and uniform convergence. (docx version)

November 18: Sequences of functions and uniform convergence (concluded). Uniform convergence and differentiation. (docx version)

November 20: Uniform convergence and differentiation (concluded). Series of functions. (docx version)

November 23: Power series. (docx version)

November 25: Power series (concluded). (docx version)

November 30: Definition of the integral. (docx version)

December 2: Definition of the integral (concluded). (docx version)

December 4: Integrating discontinuous functions. (docx version)

December 7: Properties of integration. (docx version)

December 9: The Fundamental Theorem of the Calculus. (docx version)

December 11: The Fundamental Theorem of the Calculus. (docx version)

December 14: The extended Riemann integral. (docx version)