Lecture 2: Cantor's Theory of Cardinality (Size)

Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property

Lecture 4: The Characterization of the Real Numbers

Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value

Lecture 6: The Uncountabality of the Real Numbers

Lecture 7: Convergent Sequences of Real Numbers

Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences

Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem (18.100A)

Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series (18.100A)

Lecture 11: Absolute Convergence and the Comparison Test for Series (18.100A)

Lecture 12: The Ratio, Root, and Alternating Series Tests (18.100A)

Lecture 13: Limits of Functions (18.100A)

Lecture 14: Limits of Functions in Terms of Sequences and Continuity (18.100A)

Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function (18.100A)

Lecture 16: The Min/Max Theorem and Bolzano's Intermediate Value Theorem (18.100A)

Lecture 17: Uniform Continuity and the Definition of the Derivative (18.100A)

Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function (18.100A)

Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem (18.100A)

Lecture 20: Taylor's Theorem and the Definition of Riemann Sums (18.100A)

Lecture 21: The Riemann Integral of a Continuous Function (18.100A)

Lecture 22: Fundamental Theorem of Calculus, Integration by Parts, and Change of Variable Formula (18.100A)