Questions tagged [motivation]
For questions about the motivation behind mathematical concepts and results. These are often "why" questions.
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What is the identity of this zeta function?
There are a Riemann zeta function, a Hurwitz zeta function, and many different types of zeta functions. However, I saw the zeta function below in a Japanese blog.
$$\zeta(s)=\frac{1}{1-2^{1-s}}\sum_{m=...
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The meaning/motivation of "generator" of a $C_0$ semigroup
I am currently studying $C_0$ semigroups and have come across the term infinitisimal generator. Now I'm just wondering why it's called a generator and what it generates? Can we get to the semi-flow $T$...
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Why are prime ideals proper?
As children we all learn this erroneous definition of a prime number: “a number $n\in \Bbb N$ is prime iff it’s only divided by one and itself”. Well that’s fine until the teacher asked us for ...
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Why is studying upper bounds for $|I_\delta(\mathcal P,\mathcal L)|$ useful?
A natural problem in incidence geometry is counting the number of incidences of points and lines. For example, if $\mathcal P$ is a collection of points in $\Bbb R^d$, and $\mathcal L$ is a collection ...
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Motivation behind the defination of scalar multiplication of a Vectorspace over a field
In school, we studied physical notations, such as forces, velocities, and accelerations involving both magnitude and direction. We also called any such entity involving magnitude and direction a "...
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What is the motivation of topos theory?
What is the motivation of topos theory?
https://www.youtube.com/watch?v=gKYpvyQPhZo&list=PL4FD0wu2mjWM3ZSxXBj4LRNsNKWZYaT7k&index=1
So from my understanding, the motivation of a topos is to ...
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Did the Descartes-Euler conjecture influence Poincaré's theory of homology?
What is the Descartes-Euler Conjecture?
all simply-connected polyhedra with simply-connected faces are Eulerian $V-E+F=2$.
Additional explanation: The lemma which was falsified by the ring-shaped ...
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Back to basics: Why do we care about symmetry of functions?
I am teaching a high school class on basic properties of functions, and like to motivate each of the properties with an example of why we even care to look at these properties. E.g. monotonicity ...
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Most natural definition of a product of smooth manifolds with a smooth manifold structure.
In this question,I want to ask and clarify(for myself) some points regarding the definition of product manifolds,so that I can appreciate the definition better.
The definition of any product structure(...
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Defiition of discrete/continous random variables and motivation of them. [closed]
I'm a first year math degree student and I'm taking a probability course. We defined what a random variable is and when it is discrete/continuous, but the professor didn't explain in a rigorous way ...
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Understanding the theorem of Cellular Homology through intuition.
When we start reading cellular homology,we begin with this basic but important theorem:
Theorem: Let $X$ be a CW-complex and $X^m$ denote the $m$-th skeleton of its CW structure.Then we have the ...
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When does $-(-v)=v$ not hold?
I am going through some simple questions in Axler's Linear Algebra Done Right and for each I'm trying to come up with "motivation" for why these things must be proved.
Examples:
We want to ...
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The physical motivation of simplex
I read that homology, cohomology, and simplex emerged due to physical motivation on our country's blog. However, I cannot attach a link because my country is not an English-speaking country. For ...
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Why we consider the dual space when defining tensors
My question is very simple: A type $(m,n)$ tensor is an element of $V^{\otimes m}\otimes (V^*)^{\otimes n}$. Is there a reason/motivation, beyond more general definitions, to consider the dual space ...
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Motivation about "Analysis Situs"
I read Poincaré's paper called Analysis Situs. And here's the thing about chain complex.
(Page 104 in this file)
That being given, let ${ε}^q_{i,j}$ be a number which is equal to zero if ${a}^{q−1}...
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