All blackboards are gone. They were replaced during the break. (So, no chance to use this MathOverflow question on the near future.) Makes me think of T.H. Huxley’s On a Piece of Chalk (see here) and wonder what the equivalent will be in a few decades.

On the plus side, we now have computers and projection equipment on each classroom. I am using this quite a bit in my abstract algebra class. Except that, during the first few weeks, it was more often than not that the keyboard would be locked away.

Annoyed, I called OIT and asked that they please make sure it was unlocked before my class. It worked for a few days. But then, again, I found it locked.

I called again (I was charming, I am sure). So, somebody came to the classroom, looked at me, smiled. And pressed a button, to open the drawer.

Sigh.

(In my defense, the class is at 8:30 in the morning, and I’m supposed to drink less coffee these days. But still.)

(“Thanks. I’m sorry. I’m an idiot.” “Oh, no, no. It is new.” “It is a button.”)

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Have you had a chance to use a tablet+projection to replace the whiteboard? Infinite paper with infinite zoom to add additional comments in the right place is a great tool I use for taking notes, but never had a chance to use in class.

A database of number fields, by Jürgen Klüners and Gunter Malle. (Note this is not the same as the one mentioned in this answer.) The site also provides links to similar databases.

As the other answer indicates, the yes answer to your question is known as the De Bruijn-Erdős theorem. This holds regardless of the size of the graph. The De Bruijn–Erdős theorem is a particular instance of what in combinatorics we call a compactness argument or Rado's selection principle, and its truth can be seen as a consequence of the topological c […]

Every $P_c$ has the size of the reals. For instance, suppose $\sum_n a_n=c$ and start by writing $\mathbb N=A\cup B$ where $\sum_{n\in A}a_n$ converges absolutely (to $a$, say). This is possible because $a_n\to 0$: Let $m_0

Consider a subset $\Omega$ of $\mathbb R$ of size $\aleph_1$ and ordered in type $\omega_1$. (This uses the axiom of choice.) Let $\mathcal F$ be the $\sigma$-algebra generated by the initial segments of $\Omega$ under the well-ordering (so all sets in $\mathcal F$ are countable or co-countable), with the measure that assigns $0$ to the countable sets and $1 […]

You assume $\omega_\alpha\subseteq M$ and $X\in M$ so that $X$ belongs to the transitive collapse of $M$ (because if $\pi$ is the collapsing map, $\pi(X)=\pi[X]=X$. You assume $|M|=\aleph_\alpha$ so that the transitive collapse of $M$ has size $\aleph_\alpha$. Since you also have that this transitive collapse is of the form $L_\beta$ for some $\beta$, it fol […]

No, this is not possible. Dave L. Renfro wrote an excellent historical Essay on nowhere analytic $C^\infty$ functions in two parts (with numerous references). See here: 1 (dated May 9, 2002 6:18 PM), and 2 (dated May 19, 2002 8:29 PM). As indicated in part 1, in Zygmunt Zahorski. Sur l'ensemble des points singuliers d'une fonction d'une variab […]

I don't think you need too much in terms of prerequisites. An excellent reference is MR3616119. Tomkowicz, Grzegorz(PL-CEG2); Wagon, Stan(1-MACA-NDM). The Banach-Tarski paradox. Second edition. With a foreword by Jan Mycielski. Encyclopedia of Mathematics and its Applications, 163. Cambridge University Press, New York, 2016. xviii+348 pp. ISBN: 978-1-10 […]

For the second problem, write $x=-3+x'$ and so on. You have $x'+y'+z'=17$ and $x',\dots$ are nonnegative, a case you know how to solve. You can also solve the first problem this way; now you would set $x=1+x'$, etc.

This is quite hilarious (I sympathize).

Have you had a chance to use a tablet+projection to replace the whiteboard? Infinite paper with infinite zoom to add additional comments in the right place is a great tool I use for taking notes, but never had a chance to use in class.

I haven’t, but I probably should. I’ve heard Hugh Woodin uses this quite effectively teaching precalculus, of all things.