## Tagged Questions

3k views

### How to write popular mathematics well?

Recently, some classmates and I were lamenting the fact that our classmates in other disciplines had almost no conception of what we did, despite the large mathematics population a …
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### What should we teach to liberal arts students who will take only one math course?

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 …
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### Seeking a Geometric Proof of a Generalized Alternating Series' Convergence

Let $z \in \mathbb{C} \backslash \lbrace 1 \rbrace$ with $|z| = 1$. We consider the following infinite series, which necessarily converges: S(z) := \sum_{n = 1}^{\infty}\frac{z^n …
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### How should one present curl and divergence in an undergraduate multivariable calculus class?

I am a TA for a multivariable calculus class this semester. I have also TA'd this course a few times in the past. Every time I teach this course, I am never quite sure how I should …
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### How misleading is it to regard $\frac{dy}{dx}$ as a fraction?

I am teaching Calc I, for the first time, and I haven't seriously revisited the subject in quite some time. An interesting pedagogy question came up: How misleading is it to regard …
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### Is a continuos and injective mapping from circle to a jordan curve is surjective ? [closed]

Is a continuos and injective mapping from circle to a jordan curve is surjective ?
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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 …
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### One-step problems in geometry

I'm collecting advanced exercises in geometry. Ideally, each exercise should be solved by one trick and this trick should be useful elsewhere (say it gives an essential idea in som …
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### Is x*tan(x) integrable in elementary functions?

Dear All, I'm teaching Calculus and my students asked me to calculate the integral of x*tan(x). I spent quite a lot of effort to do this, but I'm now even not sure if the integra …
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### LU decomosition for ill-condition matrixes

hi.. i have a matrix like this: { 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, …
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### What can we do to raise awareness of reciprocity laws? [closed]

The study of reciprocity laws is a centerpiece of modern mathematics. Of the last ten Fields Medalists, two of them (Ngô Bảo Châu and Laurent Lafforgue) were awarded Fields Medals …
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### Interesting and Accessible Topics in Graph Theory

This summer, I will be teaching an introductory course in graph theory to talented high school seniors. The intent of the course is not to establish proficiency in graph theory, pe …
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### Are there any books that take a ‘theorems as problems’ approach?

Are there any books that present theorems as problems? To be more specific, a book on elementary group theory might have written: "Thereom: Each group has exactly one identity" and …
Let $f(x,y)$ be a a real valued function on an open subset of $\mathbf{R}^2$ with continuous partial derivatives $\frac{\partial^2 f}{\partial x^2}$ and \$\frac{\partial^2}{\partial …