175: The exam is this Monday, Dec. 15, from 8:00 to 10:00 at the usual place.

275: The exam is this Monday, Dec. 15, from 10:30 to 12:30 at the usual place.

It is cumulative, although emphasis is put in the material covered after the second test.

You can use books, notes, etc as before.

Bring your own pens, pencils, calculators, AND PAPER. I won’t have extra paper if you don’t bring enough, and the margins of the exam won’t suffice. Mark with your name every single page you turn in.

See you Monday. Good luck!

Update [Dec. 22/08]:

Here is the exam for Calculus II – 175, and here are the solutions. (Silly typo in the solution of problem 4 corrected.)

I will be in my office on December 19 from about 11 until about 1, in case you want to stop by and pick up your test.

I won’t be on campus until the Spring term. I’ll post my new office hours soon, in case you want to stop by and pick up your test once I’m back. I’ll keep the exams and homework sets I still have through the Spring term, and you can collect them at any time during office hours. Whatever remains once the term is over, I will then discard.

[…] mentioned in problem 6 of the Fall 2008 Calculus III final exam, a function is a harmonic conjugate of iff is defined on , $v_x$ and $v_y$ exist, and the […]

(As I pointed out in a comment) yes, partial Woodinness is common in arguments in inner model theory. Accordingly, you obtain determinacy results addressing specific pointclasses (typically, well beyond projective). To illustrate this, let me "randomly" highlight two examples: See here for $\Sigma^1_2$-Woodin cardinals and, more generally, the noti […]

I am not sure which statement you heard as the "Ultimate $L$ axiom," but I will assume it is the following version: There is a proper class of Woodin cardinals, and for all sentences $\varphi$ that hold in $V$, there is a universally Baire set $A\subseteq{\mathbb R}$ such that, letting $\theta=\Theta^{L(A,{\mathbb R})}$, we have that $HOD^{L(A,{\ma […]

A Wadge initial segment (of $\mathcal P(\mathbb R)$) is a subset $\Gamma$ of $\mathcal P(\mathbb R)$ such that whenever $A\in\Gamma$ and $B\le_W A$, where $\le_W$ denotes Wadge reducibility, then $B\in\Gamma$. Note that if $\Gamma\subseteq\mathcal P(\mathbb R)$ and $L(\Gamma,\mathbb R)\models \Gamma=\mathcal P(\mathbb R)$, then $\Gamma$ is a Wadge initial se […]

Craig: For a while, there was some research on improving bounds on the number of variables or degree of unsolvable Diophantine equations. Unfortunately, I never got around to cataloging the known results in any systematic way, so all I can offer is some pointers to relevant references, but I am not sure of what the current records are. Perhaps the first pape […]

Yes. Consider, for instance, Conway's base 13 function $c$, or any function that is everywhere discontinuous and has range $\mathbb R$ in every interval. Pick continuous bijections $f_n:\mathbb R\to(-1/n,1/n)$ for $n\in\mathbb N^+$. Pick a strictly decreasing sequence $(x_n)_{n\ge1}$ converging to $0$. Define $f$ by setting $f(x)=0$ if $x=0$ or $\pm x_n […]

One way we formalize this "limitation" idea is via interpretative power. John Steel describes this approach carefully in several places, so you may want to read what he says, in particular at Solomon Feferman, Harvey M. Friedman, Penelope Maddy, and John R. Steel. Does mathematics need new axioms?, The Bulletin of Symbolic Logic, 6 (4), (2000), 401 […]

"There are" examples of discontinuous homomorphisms between Banach algebras. However, the quotes are there because the question is independent of the usual axioms of set theory. I quote from the introduction to W. Hugh Woodin, "A discontinuous homomorphism from $C(X)$ without CH", J. London Math. Soc. (2) 48 (1993), no. 2, 299-315, MR1231 […]

This is Hausdorff's formula. Recall that $\tau^\lambda$ is the cardinality of the set ${}^\lambda\tau$ of functions $f\!:\lambda\to\tau$, and that $\kappa^+$ is regular for all $\kappa$. Now, there are two possibilities: If $\alpha\ge\tau$, then $2^\alpha\le\tau^\alpha\le(2^\alpha)^\alpha=2^\alpha$, so $\tau^\alpha=2^\alpha$. In particular, if $\alpha\g […]

Fix a model $M$ of a theory for which it makes sense to talk about $\omega$ ($M$ does not need to be a model of set theory, it could even be simply an ordered set with a minimum in which every element has an immediate successor and every element other than the minimum has an immediate predecessor; in this case we could identify $\omega^M$ with $M$ itself). W […]

The study of finite choice axioms is quite interesting. Besides the reference given in Asaf's answer, there are a few papers covering this topic in detail. If you can track it down, I suggest you read MR0360275 (50 #12725) Reviewed. Conway, J. H. Effective implications between the "finite'' choice axioms. In Cambridge Summer School in Mat […]

[…] mentioned in problem 6 of the Fall 2008 Calculus III final exam, a function is a harmonic conjugate of iff is defined on , $v_x$ and $v_y$ exist, and the […]