The first thing to say is that this is not the same as the question about interesting mathematical mistakes. I am interested about the type of false beliefs that many intelligent p …

It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortun …

I'm ashamed to admit it, but I don't think I've ever been able to genuinely motivate the definition of a topological space in an undergraduate course. Clearly, the definition disti …

Kind of an odd question, perhaps, so I apologize in advance if it is inappropriate for this forum. I've never taken a mathematics course since high school, and didn't complete coll …

Since this forum is densely populated with algebraists, I think I'll ask it here. I'm teaching intermediate level algebra this semester and I'd like to entertain my students with …

What are the most important applications outside of mathematics of each of the major fields of mathematics? For concreteness, let's divide up mathematics according to arxiv mathema …

(Added an epilogue) I started a job as a TA, and it requires me to take a five sessions workshop about better teaching in which we have to present a 10 minutes lecture (micro-teac …

Related: question #879, Most interesting mathematics mistake. But the intent of this question is more pedagogical. In many branches of mathematics, it seems to me that a good cou …

Hope this question is fine. Nakayama's lemma http://en.wikipedia.org/wiki/Nakayama_lemma#Statement is mentioned in the majority of books on algebraic geometry that treat varieties. …

I was helping a student study for a functional analysis exam and the question came up as to when, in practice, one needs to consider the Banach space $L^p$ for some value of $p$ ot …

How does a depressed graduate student go about recovering his enthusiasm for the subject and the question at hand? Edit: I am not that grad student; it is a very talented friend o …

Dear members, Way back in the stone age when I was an undergraduate (the mid 90's), the internet was a germinal thing and that consisted of not much more than e-mail, ftp and the …

I am trying to prepare a "mathematics talk" for five year olds from my daughter's elementary school. I have given many mathematics talks in my life but this one feels very tough to …

Greetings all, I have often heard that it would be good if we as a community did more in the way of mathematics outreach: more to explain what it is we do to the community at large …

Even professors in academic departments other than mathematics---never mind other educated people---do not know that such a field as mathematics exists. Once a professor of medici …