Calendar of Events:

Feb 15: Euler's formula, infinite series, power and danger of mathematical infinite

Feb 17: (1.3) root 2 irrational, number systems, axiom of completeness

Feb 19: (1.3, 1.4) props of sup, NIP

Feb 22: (1.4) density of Q, root 2 exists

Feb 24: (1.4) countability

Feb 26: no class (winter carnival) Cantor's diagonalization argument, Cantor's Theorem (optional)

Feb 29: (2.2) Limiit of a sequence

Mar 2: (2.3) Algebraic Limit Theorem

Mar 4: (2.4) Order Limt Theorem, MCT

Mar 7: (2.4) MCT and series of positive terms (p-test)

Mar 9: (2.5) Subsequences and Bolzano-Weierstrass

Mar 11: (2.6) Cauchy Criterion and Series (historical moment on Cauchy with Grace and Gabe)

Mar 14: (2.7) Series, rearrangements

Mar 16: (3.1, 3.2) more rearrangements, Cantor Set, intro to topology (historical moment on Cantor with Noel and Alvaro)

Mar 18: (3.3) open and closed sets

First pledged assignment covering chapters 1, 2, and 3 .

Mar 21: compact sets

Mar 23: Dirichlet function, functional limits (historical moment on Dirichlet Will and Jonah)

Mar 25: Functional limits, epsilon-delta and sequential versions

Mar 28--April 1; spring break

Apr 4: Sequential limits, ctd, continuous functions

Apr 6: More on continuous functions, preservation of compactness, extreme-value theorem

Apr 8 : Uniform continuity

Apr 11: Intermediate Value Theorem (historical moment on Bolzano with Trisha and Andrew)

Apr 13: Def of the derivative, AL, Discts derivatives

Apr 15: no class (student spring symposium)

Apr 18: Fermat, Darboux, Cauchy MVT proof

Apr 20: Mean Value Theorem

Apr 22: pt-wise/uniform convergence

Apr 25: uniform convergence and continuity (historical moment on Abel with Blink and Bob)

Apr 27: uniform convergence and differentiation

Apr 29: uniform convegence of series of functions (historical moment on Weierstrass with Brenda and Jigar)

May 2: power series

May 4: Taylor series

Second pledged assignment covering chapters 4, 5, and 6.

May 6: Riemann integral

May 9 : Integrating functions w/ discontinuities (historical moment on Riemann with Leo and Jenkins)

May 11 : Properties of the integral

May 13: Fundamental Theorem of Calculus

May 16: Return to Euler's formual/Assign final projects

Final Exam: Group project with short oral presentation