Calendar of Events:

Sep 9: introduction to infinity, Euler's sum

Sep 11: (1.3) root 2 irrational, number systems, axiom of completeness

Sep 13: (1.3, 1.4) props of sup, Nested Interval Property

Sep 16: (1.4) density of Q, root 2 exists

Sep 18: (1.5) countability, R is uncountable

Sep 20: (1.6) Cantor's Theorem

Sep 23: (2.2) limit of a sequence

Sep 25: (2.3) Algebraic Limit Theorem

Sep 27: (2.4) Order Limt Theorem, Monoton Convergence Theorem

Sep 30: (2.4) MCT and series of positive terms (p-test)

Oct 2: (2.5) subsequences and the Bolzano-Weierstrass Theorem

Oct 4: (2.6, 2.7) Cauchy Criterion and series (Historical moment on Cauchy with Sean and Joselyn)

Oct 7: (2.7) more on infinite series

Oct 9: (2.7) rearrangements, Cantor Set (Historical moment on Cantor with Olivia and Olivia)

Oct 11: TBD

Oct 14: (3.2) open and closed sets

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

Oct 16: (3.3) compact sets

Oct 18: (4.1, 4.2) Dirichlet function, functional limits (Historical moment on Dirichlet with Gebre and Soyibu)

Oct 21: fall break

Oct 23: (4.2) Functional limits, epsilon-delta and sequential versions

Oct 25: (4.3) sequential limits, ctd, continuous functions

Oct 28: (4.4) preservation of compactness, extreme-value theorem, uniform continuity

Oct 30: (4.5) Intermediate Value Theorem (Historical moment on Bolzano with Nick and Tomasso)

Nov 1: (5.1, 5.2) def of the derivative, AL, discontinuous derivatives

Nov 4: (5.2) Fermat's Theorem, Darboux's Theorem, Cauchy's MVT proof (Historical moment on Fermat with Roger and Patrick)

Nov 6: (5.3) Mean Value Theorems

Nov 8: (6.2) pointwise convergence and uniform convergence

Nov 11: (6.2) uniform convergence and continuity (Historical moment on Abel with Eric and Will S)

Nov 13: (6.3) uniform convergence and differentiation

Nov 15: (6.4) uniform convegence of series of functions (Historical moment on Weiestrass with Colin and Nick)

Nov 18: (6.5) power series

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

Nov 20: (6.6) Taylor series (Historical moment on LaGrange with Omar and Alex)

Nov 22: (7.1, 7.2) Riemann integral (Historical moment on Riemann with Sarah and Molly)

Nov 25: (7.3) integrating functions w/ discontinuities (Historical moment on Darboux with Will M and ??)

Nov 27--29: Thanksgiving break. No class.

Dec 2 : (7.4) properties of the Riemann integral

Dec 4: (7.5) Fundamental Theorem of Calculus

Dec 6: (7.5, 8.3) Fundamental Theorem ctd., assign final projects

Final Exam: Group project with short oral presentation