# Tagged Questions

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

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### Natural Analysis: a possible new field?

I have studied real analysis for two years now, yet I often find that when applying it, (say to finding a path of shortest time) I often have to get solutions without closed forms (i.e. defined point ...
787 views

### How do I go about doing math as a hobby?

want to study math as a hobby. I find it very interesting, but I made a lot of twists and turns in college which lead me on a different path. Plus, I'm not really sure I'm gifted enough to hack it at ...
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### A way to describe the following triplet

so first of all the tittle I think is very poor, so I apologize about that. I am working on a homework set for homology, and when I computed the image of a boundary map I got this: $(a-b,2b-c,2c)$ ...
135 views

This semester I'm taking advanced calculus and in the sources list, the lecturer recommends on "An introduction to analysis-by w. wade" and "Advanced calculus by Edwards". Both of them cost around 100 ...
67 views

### Is there a strategy to switching $\infty$ limits to $-\infty$ limits?

I asked recently in this question how to use the definition of $$e:= \lim_{x\to\infty}\left( 1+\frac1x \right)^x$$ to show that $$\lim_{x\to -\infty}\left( 1+\frac1x \right)^x = e.$$ A helpful ...
32 views

### Why does $\sum_{j,k\geq 0}\frac{(j+k)a^{j+k}}{j!k!}=\sum_{l=0}^\infty \frac{l(2a)^l}{l!}$?

I notice that $$\sum_{j,k\geq 0}\frac{(j+k)a^{j+k}}{j!k!}=2ae^{2a} = \sum_{l=0}^\infty \frac{l(2a)^l}{l!}.$$ Is there a simple intuitive explanation why these two should have the same sum, or is it ...
127 views

### Can you give me a good alternative to Rotman's Group Theory book?

I've been trying to learn out of Rotman's book "An Introduction To The Theory of Groups" for the last few months, and it's rough going. I've been studying Chapters 7, 10, and 11 in particular, and he'...
2k views

### Interesting Topics to Give a Seminar On?

So recently I've been attending seminars for the graduate students (and VAP's) at my local university, and after yesterday's seminar, the professor asked if I would like to give a seminar next quarter;...
302 views

### Proving Equality of 2 Functions

I have a general question, illustrated by a specific example. The general question is how to methodically prove that two functions are equal. Much like trying to prove an "if-and-only-if" statement (...
63 views

### SOLVED — Equal or Equivalent Inequalities?

Suppose I have two inequalities: $2ab \leq a^{2} + b^{2}$ $0 \leq a^{2} + b^{2} - 2ab$ Now, obviously these inequalities are just rearrangements of one another. The question I have is: do I say ...
77 views

### Is it acceptable to use the shorthand “PDEs” in the title of a paper?

If I write a paper, is it acceptable for me to use a title like "analysis of PDEs related to blah blah blah" instead of "analysis of partial differential equations related to blah blah blah"? I ...
762 views

### Why do people write stochastic differential equations in differential form?

I am trying to teach myself about stochastic differential equations. In several accounts I've read, the author defines an SDE as an integral equation, in which at least one integral is a stochastic ...
257 views

### Real life applications of Maass wave forms

Explaining my work on Maass wave forms to friends and family (all non-mathematician) typically earns me blank faces. So I wonder whether there is some good example to explain their meaning to laymen. ...
541 views

### Resource for low level maths explained in high level perspectives

I would really never ask a question about resources, noting that it is a soft-question, unless I thought it was very difficult to find elsewhere, and I have looked. Furthermore, I believe that this ...
554 views

### I need tips for increasing concentration for math study

Any tips for increasing concentration? I find it difficult to concentrate for looong periods at a time, after having taken a long break from mathematics. Before I could sit for hours and do ...
833 views

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### Trying to teach supremum and infimum.

I'm helping out my former calculus teacher as a volunteer calculus advisor, and I have under my supervision 5 students. They've already had an exam and... well, they failed. I read their exams and I ...
335 views

### Mathematics for Graduate Political Science

I'm preparing to attend graduate school for political science here in Canada and I'm having something of a crisis. Midway through my degree program I chose to drop my first love (English) to focus on ...
147 views

### Is there a 'Mathematics wiki' analogous to 'String theory wiki'?

I came across this site and am wondering if there is a similar page for Mathematics or its sub-areas. Would be very nice if there is one such site which provides 'canonical' references for each sub ...