Questions tagged [motivation]

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

353 questions
0
votes
2 answers

why commutative integral with limit is important in real analysis?

why commutative integral with limit is important in real analysis ? Why $\lim_{n\to\infty }\int f_n=\int \lim_{n\to\infty } f_n $ is important ?
49-49
  • 4,083
  • 3
  • 11
  • 31
0
votes
5 answers

The meaning of probability and random variables

I do understand pure mathematical concepts of probability space and random variables as a (measurable) functions. The question is: what is the real-world meaning of probability and how can we apply the machinery of probability to the real…
Kirill Tsar.
  • 201
  • 1
  • 3
0
votes
0 answers

An idea to teach equation except balance model

I looking for an idea to start teaching the equation of algebra, but not use the balance model. I am looking for a new motivational idea or a pedagogical method to start teaching equations. The link below contains a good context for a balance model,…
Khosrotash
  • 23,025
  • 4
  • 37
  • 74
0
votes
1 answer

What are the motivations and examples of P. Hall Family?

I am reading J. P. Serre's Lie Algebras and Lie Groups and here is how a P. Hall Family is defined: I failed to understand the motivations of this definition. Could anyone explain it to me? Also, some simple examples of P. Hall Families will also…
Zuriel
  • 4,855
  • 2
  • 18
  • 42
0
votes
1 answer

Motivation of the Logarithm

Suppose that someone wants to calculate approximately the product of 101,123,958,959,055 and 342,234,234,234,236 without using a computer. Since these numbers are so long, completely carrying out multiplication by hand would take a long time because…
LinearGuy
  • 384
  • 1
  • 14
0
votes
0 answers

Dynamical systems with large number of attractors and their dependence on the parameters?

It is much important to study the attractors in a dynamical system as these indicate how the system behaves once the initial transients are discarded. Also, the study of systems with many numbers of attractors are interesting as the parameters are…
BAYMAX
  • 5,494
  • 4
  • 27
  • 54
0
votes
0 answers

Applications of linear algebra other than Euclidean vector spaces.

A typical example of finite-dimensional vector space is Euclidean space $\mathbb{R}^n$, but there are other type of it. For example, the space of polynomials whose order is less than $n$, the space of solutions of a linear differential equation,…
0
votes
4 answers

What problems can we solve using linear algebra?

I thought that linear algebra is a tool for solving systems of linear equations, but this can be done without most of linear algebra. That is, we just have to know matrix and the gaussian elimination and we don't have to know vector space, linear…
user297841
0
votes
2 answers

Why does linear regression involve the $y$-coordinate error?

When dealing with linear regression, we are concerned about how far away a given point's $y$ component is from the "best fitting line". My question: why do we choose the $y$ component instead of the $x$ one, or, better still, the length of the…
0
votes
1 answer

Why solving the cubic is important?

Why people in sixteenth century (or the people now ) interested in solving the cubic? There were (I think) no number theoretic or relation to science that time, and the only impression I get from reading books is that they did it to one-up other…
0
votes
1 answer

motivation behind antisymmetry axiom on partially ordered sets

why does any partially ordered need to be antisymmetric? why can't there be 2 elements in a poset with different values but order-wise have the same order priority? what's the motivation for this? Does it even make sense to think of order without…
0
votes
1 answer

Providing motivation for the importance of the concept of a 'basis'.

In a few situations, I found myself being asked by younger students why the concepts of a basis was important. First, in the concept of linear spaces, it's easy to explain that having a basis allows us to describe the spaces with a relatively small…
YoTengoUnLCD
  • 12,844
  • 3
  • 35
  • 89
0
votes
3 answers

Purpose of a vector space

I am currently studying linear algebra and I've seen what vector spaces are, but I can't seem to understand what their purpose is. What do they allow us to do?
Mathphilo
  • 78
  • 1
  • 10
0
votes
0 answers

Motivation For Tensor Product of R-Modules

I have recently learned about tensor products of modules,specifically the material in Dummit and Foote chapter 10 section 4. My understanding is that the construction of tensor spaces is important because they are a natural staging area for…
user3281410
  • 960
  • 8
  • 23
0
votes
2 answers

Interpretation of condition on positive random variable

Let $W$ be a random variable such that $\mathbb{P}(W > 0) = 1$ and $\mathbb{E}(W) = 1$. Is there an interpretation or motivation for the condition $$\mathbb{E}(W \log (W) ) < c$$ where $c \in (0,\infty)$ is a positive constant? Perhaps if we…
x_Y_z
  • 283
  • 1
  • 7
1 2 3
23
24