# Tag Info

## Hot answers tagged teaching

133 votes

### Mathematical games interesting to both you and a 5+-year-old child

One evening at the dinner table, when my oldest daughter was 3 or 4, I was in a teasing mood, and I called her a goose. She didn't want to be a goose, so she refuted the claim, "I am not a goose!" ...
98 votes

### Mathematical games interesting to both you and a 5+-year-old child

The game "Set" seems to fit the bill. It's a card came where there are cards that show images which have four different features, each of which comes in three possibilities: number (1, 2, or 3 ...
73 votes

### Mathematical games interesting to both you and a 5+-year-old child

Another topological game: Sprouts. Rules: The game is played by two players, starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line ...
68 votes
Accepted

### Ideas for introducing Galois theory to advanced high school students

I have now twice taught Galois theory to advanced high school students at PROMYS. This is a six week course, meeting four times a week, for students who already are comfortable with proofs and, in ...
53 votes
Accepted

### Zorn's lemma: old friend or historical relic?

I agree with almost everything in your post. But still, I believe I know why people use Zorn's lemma. My answer. Zorn's lemma encapsulates succinctly many of the consequences of AC via transfinite ...
51 votes
Accepted

### History of $\frac d{dt}\tan^{-1}(t)=\frac 1{1+t^2}$

I now believe that my question (and suggestion that proof $(1)$ should have become standard before Lacroix) relied on the misconception that tangent was easier to differentiate than arctangent. In ...
• 28.8k
49 votes

### Mathematical games interesting to both you and a 5+-year-old child

Knot or not? The topological game involves a projection of a knot, drawn onto paper, such as: Player 1 picks an intersection and assigns a crossing (which segment of the curve is "above" and which "...
46 votes
Accepted

### Is it consistent with ZF that $V \to V^{\ast \ast}$ is always an isomorphism?

No, it’s not consistent. Let $V=k^{(\omega)}$ be the vector space of finite sequences of elements of $k$. Then $V^*$ can be identified with the vector space $k^\omega$ of all sequences, and elements ...
• 30.9k
42 votes

23 votes

### Short papers for undergraduate course on reading scholarly math

I think Calkin and Wilf’s lovely short paper on what is now known as the Calkin-Wilf tree would be suitable. Neil Calkin and Herbert S. Wilf, Recounting the Rationals. The American Mathematical ...

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