Instructor: Andres Caicedo. Contact Information: See here. Time: MWF 10:30-11:45 am. Place: Business, Room 204. Office Hours: Th 3-4:30 (starting Jan. 31), or by appointment (email me a few times/dates you have available).

Text: Calculus (Michael Spivak), fourth edn. Publish or Perish, Inc. Here are some reviews.

If you want an additional text to supplement your reading, I suggest Calculus. Whitman College (David Guichard and others). The text is distributed under a Creative Commons license. It can be downloaded from Whitman’s page. You may also want to consider as an amusing, quick reference, The cartoon guide to Calculus (Larry Gonick).

Contents: The department’s course description reads:

Definitions of limit, derivative and integral. Computation of the derivative, including logarithmic, exponential and trigonometric functions. Applications of the derivative, approximations, optimization, mean value theorem. Fundamental Theorem of Calculus, brief introduction to applications of the integral and to computations of antiderivatives.

We will see some applications, but our emphasis is on understanding the theory. The material to cover is roughly the first 18-and-a-bit chapters of Spivak’s book.

The grade will be decided based on homework, quizzes, and a final exam (20%). The date of the final is Monday, May 13, 12-2 pm. Details of homework and quiz policy will be given in due time.

I post links to supplementary material on Google+. Circle me and let me know if you are interested, and I’ll add you to my Calculus circle.

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Georgii: Let me start with some brief remarks. In a series of three papers: a. Wacław Sierpiński, "Contribution à la théorie des séries divergentes", Comp. Rend. Soc. Sci. Varsovie 3 (1910) 89–93 (in Polish). b. Wacław Sierpiński, "Remarque sur la théorème de Riemann relatif aux séries semi-convergentes", Prac. Mat. Fiz. XXI (1910) 17–20 […]

It is not possible to provide an explicit expression for a non-linear solution. The reason is that (it is a folklore result that) an additive $f:{\mathbb R}\to{\mathbb R}$ is linear iff it is measurable. (This result can be found in a variety of places, it is a standard exercise in measure theory books. As of this writing, there is a short proof here (Intern […]

Stefan, "low" cardinalities do not change by passing from $L({\mathbb R})$ to $L({\mathbb R})[{\mathcal U}]$, so the answer to the second question is that the existence of a nonprincipal ultrafilter does not imply the existence of a Vitali set. More precisely: Assume determinacy in $L({\mathbb R})$. Then $2^\omega/E_0$ is a successor cardinal to ${ […]

Marginalia to a theorem of Silver (see also this link) by Keith I. Devlin and R. B. Jensen, 1975. A humble title and yet, undoubtedly, one of the most important papers of all time in set theory.

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Gödel sentences are by construction $\Pi^0_1$ statements, that is, they have the form "for all $n$ ...", where ... is a recursive statement (think "a statement that a computer can decide"). For instance, the typical Gödel sentence for a system $T$ coming from the second incompleteness theorem says that "for all $n$ that code a proof […]

When I first saw the question, I remembered there was a proof on MO using Ramsey theory, but couldn't remember how the argument went, so I came up with the following, that I first posted as a comment: A cute proof using Schur's theorem: Fix $a$ in your semigroup $S$, and color $n$ and $m$ with the same color whenever $a^n=a^m$. By Schur's theo […]

It depends on what you are doing. I assume by lower level you really mean high level, or general, or 2-digit class. In that case, 54 is general topology, 26 is real functions, 03 is mathematical logic and foundations. "Point-set topology" most likely refers to the stuff in 54, or to the theory of Baire functions, as in 26A21, or to descriptive set […]