# motivation's questions - English 1answer

234 motivation questions.

### 8 Why is the derivative important? [duplicate]

Derivatives, both ordinary and partial, appear often in my mathematics courses. However, my teachers have never really given a good example of why the derivative is useful. My questions: Other than ...

### 23 Why does the generalised derivative have to be a linear transformation?

I am starting to learn Real Analysis and I have come across the generalised definition of the derivative for higher dimensions. I realise that the derivative being a linear transformation nicely ...

### 13 Motivation of Splines

10 answers, 2.198 views analysis numerical-methods spline motivation
What is the motivation of splines, in particular cubic splines. For example, why does it matter that they have any type of smoothness at the knots.

### 3 What's the Intuition behind divisors?

I am currently studying Algebraic Geometry (by Hartshorne), for the first time, and had attended/am attending to some lectures related to it. (Commutative Algebra, Complex manifolds, ...) As I learn ...

### 36 Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$

13 answers, 1.956 views analysis metric-spaces intuition motivation
This week, I come to the end of the first year analysis, and suffer from a "crisis of motivation." With this question, I want to chase away my thought, "Why is it important to study the general ...

### 18 Why do PDE's seem so unnatural? [closed]

3 answers, 608 views soft-question motivation
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 ...

### 2 How to understand cocategories

$\newcommand\CC{\mathsf{C}}$The notion of a category is well-known. There are multiple equivalent definitions; small categories can be seen as an internal category in $\mathsf{Set}$, that is a couple ...

### 1 What is the motivation of the identity $x\circ(a\circ b)=(((x\circ b)\circ a )\circ b$?

1 answers, 60 views abstract-algebra motivation
A symmetric set (also called an involutary quandle or a kei) is a set $A$ with a binary operation $\circ$ satisfying the following conditions for all $a,b,x\in A$: $a\circ a =a$; $(x\circ a)\circ a=x$...

### 101 Motivation for the rigour of real analysis

I am about to finish my first year of studying mathematics at university and have completed the basic linear algebra/calculus sequence. I have started to look at some real analysis and have really ...

### 1 About study of sub group [closed]

0 answers, 36 views abstract-algebra motivation
Consider the group G(under operation +) i take subset H of G. I proved that H itself become the group( under same operation + )Now how study of H helps us to study the structure of G. In other words ...

### 16 Why is Fourier Analysis effective for studying uniform distributions

On his great expository article about the naturality of the Zeta function in number theory, Tim Gowers makes the following claim: When it comes to the primes, we find that we do not have a good ...

### 3 How does one introduce characteristic classes

How do you introduce or how are you introduced to characteristic classes. I am assuming the student is comfortable with principal bundles and connections on principal bundles.

### 32 Fractional Calculus: Motivation and Foundations.

If this is too broad, I apologise; let's keep it focused on the basics if necessary. What's the motivation and the rigorous foundations behind fractional calculus? It seems very weird & ...

### 5 A good way to explain $\varepsilon$-$\delta$ for chemistry / biology students?

1 answers, 117 views education epsilon-delta motivation
I feel like I have a pretty good way to talk about $\varepsilon$-$\delta$ to physics and engineering students (and possibly students in comp sci). But I am not very sure what I can do for chemistry ...

### 14 Why is the fact that a quotient group is a group relevant?

I'm studying the basics of quotient groups. I understand that if you build a quotient set from cosets of a group and the subgroup you are using to build them is normal then you end up with a group. I ...

### 1 What is a particular and a homogenous solution of a differential equation?

1 answers, 163 views differential-equations motivation
When solving linear nonhomogeneous equations, we deal with two types of solutions: particular homogeneous Why do we have these two types of solutions for differential equations? What does each of ...

### 9 What is the physical meaning of fractional calculus?

What is the physical meaning of the fractional integral and fractional derivative? And many researchers deal with the fractional boundary value problems, and what is the physical background? What ...

### 96 Why study linear algebra?

12 answers, 94.414 views linear-algebra soft-question motivation
Simply as the title says. I've done some research, but still haven't arrived at an answer I am satisfied with. I know the answer varies in different fields, but in general, why would someone study ...

### 2 What is the motivation behind the (metric spaces) definition of an open set?

As far as I know, the standard definition of an open set is that the set $A$ is called open if $A \subseteq X$ for some set X and if $A \cap \partial A=\emptyset$ where $\partial A$ is the set of ...

### 32 What are the applications of continued fractions?

What is the most motivating way to introduce continued fractions? Are there any real life applications of continued fractions?

### 1 How to focus for long hours? [closed]

I'm currently working on my A levels and would like to know about how to focus for longer hours and stay motivated? I'm also working on STEP Support program for entry into Cambridge and would like to ...

### 2 The definition of a subspace in linear algebra

3 answers, 1.268 views linear-algebra definition motivation
I'm trying to learn linear algebra on my own but I am stuck on the definition of a linear subspace. Let's assume I want to find out if $S$ is a subspace of $\mathbb{R}^2$, where $S = [X_1 , X_2]$ ...

### 2 Importance of integral extension

I am studying basic algebraic number theory these days and I am curious if the concept of “integral extension” is important in purely number theoretic sense. Of course, integral extension is a ...

### 3 Motivating Number Theory/Combinatorics questions leading to finite field

3 answers, 190 views number-theory finite-fields motivation
I want to learn about Finite Field, but don't want to learn but by starting from the memorizing the axioms of finite field, I wanna learn it by solving a few problems (good if NT /Combinatorics), ...

Is there anything similar to this (page written by Field Medalist Timothy Gowers) for quadratic reciprocity ? I mean, the link there explains how you can figure out the solution of cubic equation by ...

### 3 Motivation for the study of units in cyclotomic fields beyond Washington's book

1 answers, 127 views number-theory motivation
Right now, I am reading Larry Washington's book "Introduction to Cyclotomic Fields." In Chapter 8 of this book, the unit group of the ring of integers in a cyclotomic field (or its totally real ...

### 3 Motivation for abstractness

2 answers, 146 views education motivation
I'm seeking examples of concepts or theorems in school mathematics that are better understood when we generalize (when we deal with a more abstract concept where the former concept is a special case ...

### 1 Motivation for Abstract Nonsingular Curves

0 answers, 108 views algebraic-geometry motivation
I just got through reading section I.6 in Hartshorne, and I have no idea why anybody would ever have invented these concepts. I agree that what you can do with it is pretty neat, but how would anyone ...

### 12 Different ways to state the motivation of the definition of the product topology

Suppose for every $i\in\mathscr I,$ $X_i$ is a topological space. The product space has as its underlying set the product set $X =\prod \limits_{i\,\in\,\mathscr I} X_i$ and as its open sets product ...

### Why solving the cubic is important?

1 answers, 104 views number-theory polynomials motivation
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 ...

### 2 Definition of Cofibration and Fibration: Motivation, analogy and examples

I tried to understand the definitions of cofibration and fibration through wikipedia. But I didn't get any motivation why such things are important, and through which basic natural question they come? ...

### 3 Understanding the unit/counit of an adjunction

I'm trying to understand adjoint functors better and I have to admit I'm a little bit confused by the idea of the unit/counit of an adjunction. I have written out units, counits and their triangle ...

### 8 A layman's motivation for non-standard analysis and generalised limits

Disclaimer: My apologies for making such a long question. The question is possibly also rather specific, but I hope that (some parts of) it might be useful in general. Background: I have recently ...

### 18 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 ...

### 3 What is the motivation behind the Hilbert Symbol?

The Hilbert Symbol it superficially similar to the Legendre Symbol: it measures whether or not solutions to some polynomial exist. In the case of the Legendre Symbol it was clear for me that it is a ...

### 3 Application of inequality in other math fields

I'm learning inequalities for the first time, and except a paragraph by Paul Zeitz in his book Art and Craft of problem solving, none actually give much motivation of why should I care about ...

### 2 Why are polynomials interesting?

2 answers, 528 views polynomials intuition motivation
I'm learning polynomials (for competitions) the first time, with having a little number theory and combinatorics experience. The difficulty is that I can't understand why polynomials are so ...