# Tag Info

### Interesting things you learned while grading?

I once asked students to find the derivative of $x^x$ (with respect to $x$). One student figured that if the exponent were a constant then the answer would be $xx^{x-1}$ which is to say $x^x$, while ...

### What are some recent, interesting, accessible pieces of mathematics

Perhaps: The discovery a year ago in 2015 of a new tiling of the plane by a convex polygonal tile, found by Mann, McLoud, and Von Derau (the latter of whom was an undergraduate at the time of the ...
Accepted

### Quote to show students don't have to fear making mistakes

Johann Wolfgang von Goethe: "By seeking and blundering we learn." Original German, 1825. Albert Einstein: "Anyone who has never made a mistake has never tried anything new." (However, attribution to ...
Accepted

### Big list of "interesting" abstract vector spaces

Here are some more examples: $C[a,b]$, the set of continuous real-valued functions on an interval $[a,b]$. This abstract vector space has some very nice properties that make it very good for a first-...
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### Interesting things you learned while grading?

Possibly not what you're looking for, but: the things I've learned while grading are mostly pedagogical, not new mathematical facts (in fact, teaching at a community college as I do, I'm not sure that'...
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### Quote to show students don't have to fear making mistakes

"I have not failed. I've just found 10,000 ways that won't work." "Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time." "Many of life's ...

### Where can I find public repositories of past math exams?

Quite a few universities publicly post the math exams their faculty write: UC Berkeley hosts an archive of their past exams, sorted by course. University of Michigan hosts past exams for some ...

### Quote to show students don't have to fear making mistakes

“There is no man,” he began, “however wise, who has not at some period of his youth said things, or lived in a way the consciousness of which is so unpleasant to him in later life that he would ...
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### Quote to show students don't have to fear making mistakes

There was a post over at academia where somebody essentially said that after starting by investigating other people's mistakes: Eventually I got better — I started making my own mistakes. ...

### List of realistic extremum problems

Some example types: Minimizing potential energy of any realistic physical system. Examples: 0D: The point where a rolling ball/flowing water might* come to rest (*might not, if momentum carries it ...
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### List of realistic extremum problems

Here are some optimization problems that were harder than a simple homework problem: Given the pavillion angle of a diamond, what crown angle produces optimal light return? What percentage of the ...
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### What are some recent, interesting, accessible pieces of mathematics

The 2016 result about Unexpected biases in the distribution of consecutive primes. This is really pretty simple to understand - the distribution of primes had been supposed to be unconditionally ...
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### Quote to show students don't have to fear making mistakes

Mistakes Allow Thinking to Happen
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### Good Examples of Questions to have Students Ponder Over Without Paper

A possibility, requiring one definition: What is a tiling of the plane with an infinite supply of congruent copies of a single tile (technically, a monohedral tiling). This can go as deep as you'd ...

### Examples of informal explanations that cause misconceptions

A point (say, in $\mathbb{R}^n$) is a vector. Vectors and points are really no different. They are both $n$-tuples in $\mathbb{R}^n$. The difference between two points (in $\mathbb{R}^n$) is a vector,...

### Interesting things you learned while grading?

Reading the answer posted by Daniel R Collins reminded me of something else I learned while marking student work. Not exactly something mathematical, more something about constructing math exams. I ...