For questions about the motivation behind mathematical concepts and results. These are often "why" questions.

# Questions tagged [motivation]

353 questions

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### How to appreciate Riemannian geometry

I'm currently following an introduction to Riemannian geometry i.e. connections, curvature and isometric immersions (the Gauss, Codazi and Ricci equations).
I find the introduction to Riemannian geometry interesting, but whenever I look at some…

abcdef

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### Motivation behind the definition of flat module

Can someone explain what is the motivation behind the definition of a flat module? I saw the definition but I don't really know why it is important to work with these structures.

Jr.

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### Book series like AMS' Student Mathematical Library?

I had the joy of discovering AMS' Student Mathematical Library book series today, and I have been pleasantly surprised by how enticing some of the titles seem: exciting and expositionary, a perfect stepping stone for learning!
I am familar with some…

bzm3r

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### What problems, ideas or questions first got you interested in algebraic geometry?

Obviously, a lot of people are very interested in algebraic geometry. I suppose this means it is a fascinating area. However the few times I have tried to read introductory books and/or articles in the area, I haven't been able to "get it" or even…

goblin GONE

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### Why study cardinals, ordinals and the like?

Why is the study of infinite cardinals, ordinals and the like so prevalent in set theory and logic? What's so interesting about infinite cardinals beyond $\aleph _0 $ and $\mathfrak{c} $? It seems like they're enough for all practical purposes and…

user132181

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### Why is the tensor product constructed in this way?

I've already asked about the definition of tensor product here and now I understand the steps of the construction. I'm just in doubt about the motivation to construct it in that way. Well, if all that we want is to have tuples of vectors that behave…

Gold

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### Why do PDE's seem so unnatural?

First let me preface by saying that I'm highly aware of the fact that plenty a math topic seems unnatural upon first learning. But PDEs seem to have a special place in my "unnatural" category of mathematics. Specifically because I'm comfortabe with…

Zduff

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### What is Representation Theory?

I'm beginning a course that uses representation theory, but I do not really understand what that is about. In the text I am following, I have the following definition:
A representation of the Lie group $G$ on the vector space $V$ is a continuous…

diffGeoLost

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### Fun math for young, bored kids?

For 6 months, I'll be organizing, as part as my volunteer work in an NGO, math classes with small groups (~10 students, aged 16 or 17). These classes are not compulsory, but students willing to stay past the third class must accept to attend all…

Clément

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### Motivation for the study of amoebas.

What was the primary motivation for the study of the amoebas?

Gilles Bonnet

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### How can construction of the gamma function be motivated?

The gamma function extends the factorial function. This can be proved inductively using integration-by-parts.
But if you didn't already know that the gamma function had this property, and you wanted to construct a continuation of factorial a priori,…

spraff

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### Why do we need (the abstract concept of) random variables (in discrete probability models)?

What we defined: Suppose we have a (discrete) probability model $\left(\Omega,P\right)$,
where $P$ is the probability function (at least, that was the way
it was introduced in a course I took; that means only that $\Omega$
is at most countable, that…

MyCatsHat

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### Motivation behind the definition of tangent vectors

I've been reading the book Gauge, Fields, Knots and Gravity by Baez.
A tangent vector at $p \in M$ is defined as function $V$ from $C^{\infty}(M) $ to $\mathbb R$ satisfying the following properties:
$V(f+g)=V(f) + V(g)$.
$V(\alpha f)= \alpha…

Mohan

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### What is the motivation behind the study of sequences?

I was discussing some ideas with my professor and he always says that before you work on something in mathematics, you need to know the motivation for studying/working on it.
A better way to put this would be,
Why were sequences studied and sought…

Non-Being

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### Traveling salesman problem: why visit each city only once?

According to wikipedia, the Traveling Salesman Problem (TSP) is:
Given a list of cities and the distances between each pair of cities,
what is the shortest possible route that visits each city exactly once
and returns to the origin city?
Okay,…

goblin GONE

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