# Tagged Questions

Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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### Importance of Representation Theory

Representation theory is a subject I want to like (it can be fun finding the representations of a group), but it's hard for me to see it as a subject that arises naturally or why it is important. I ...
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### Good Physical Demonstrations of Abstract Mathematics

I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to ...
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### Why can't you add apples and oranges, but you can multiply and divide them?

What is the algebraic difference between arithmetic operations, that prevents entities with different units from being summed or subtracted, but allows them to be multiplied or divided? This looks ...
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### Teenager solves Newton dynamics problem - where is the paper?

From Ottawa Citizen (and all over, really): An Indian-born teenager has won a research award for solving a mathematical problem first posed by Sir Isaac Newton more than 300 years ago that has ...
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### Is learning (theoretical) physics useful/important for a mathematician?

I'm starting to read The Princeton Companion to Mathematics, at the beginning it says: A proper appreciation of pure mathematics requires some knowledge of applied mathematics and theoretical ...
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### What is the meaning of the third derivative of a function at a point

(Originally asked on MO by AJAY.) What is the geometric, physical, or other meaning of the third derivative of a function at a point? If you have interesting things to say about the meaning of the ...
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### Why learn to solve differential equations when computers can do it?

I'm getting started learning engineering math. I'm really interested in physics especially quantum mechanics, and I'm coming from a strong CS background. One question is haunting me. Why do I need ...
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### “Curled-up dimensions”?

I'm a grad student in math, but I don't know as much about physics as I should. I've read a handful of pop expositions of string theory, and they often refer to "curled up dimensions" and I've always ...
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### Is it possible to use physics or other form of non-canonical reasoning to study functions?

It is well-known (see, for example, the books New Horizons in geometry, Maxima and minima without calculus and The Mathematical Mechanic) that it is possible to use some forms of "physical reasoning", ...
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### Why can't you simulate isotropic fluid flow on a square lattice?

There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you ...
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### What mathematical structure models arithmetic with physical units?

In physics we deal with quantities which have a magnitude and a unit type, such as 4m, 9.8 m/s², and so forth. We might represent these as elements of $\Bbb R\times \Bbb Q^n$ (where there are $n$ ...
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### Pure maths vs applied

Is there any point in an aspiring theoretical physicist doing pure math topics such as analysis? (Assuming that he would not be doing them out of pure interest.)
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### Energy norm. Why is it called that way?

Let $\Omega$ be an open subset of $\mathbb{R}^n$. The following $$\lVert u \rVert_{1, 2}^2=\int_{\Omega} \lvert u(x)\rvert^2\, dx + \int_{\Omega} \lvert \nabla u(x)\rvert^2\, dx$$ defines a norm on ...
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### Dirac Delta Function of a Function

I'm trying to show that $$\delta\big(f(x)\big) = \sum_{i}\frac{\delta(x-a_{i})}{\left|{\frac{df}{dx}(a_{i})}\right|}$$ Where $a_{i}$ are the roots of the function $f(x)$. I've tried to proceed by ...
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