# 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 motivation to introduce Tate-cohomology groups?

What is the motivation to introduce Tate-cohomology groups ? Let $G$ be a Galois group and $M$ be a $G-$module. Let $H^n(G,M)$ be usual Galois cohomology. In group cohomology theory, we often ...
70 views

### How to motivate the teaching of differential equations?

I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against ...
1 vote
72 views

### Motivation for presentation of group $G$ in Hungerford’s Abstract Algebra

An immediate consequence of Corollary 9.3 and the First Isomorphism Theorem is that any group $G$ is isomorphic to a quotient group $F/N$, where $G =\langle X\rangle$, $F$ is the free group on $X$ and ...
75 views

### Origins behind different terms for the same thing in Linear Algebra

It seems that there are many terms in linear algebra that have multiple names. For example, unitary and orthogonal both refer to the same general idea, a Hermitian is essentially a self-adjoint matrix,...
1 vote
32 views

### Conditions on open sets in the definition of topological space

The question on the definition of a topological space has been appeared many times on this site, but I was unable to get answer to a natural question which not only I but a new learner of this subject ...
1 vote
59 views

### Motivation (intuition) about a formal group

A (one-dimensional) formal group over $\mathbb{C}$ is a formal power series $F(x,y)\in\mathbb{C}[[x,y]]$ such that $$F(x,y)=x+y + \text{terms of higher order}$$ $$F(x,F(y,z))=F(F(x,y),z))$$ ...
72 views

### Motivation for integrals over differential forms

I am trying to find some sort of motivation as to why we integrate manifold over differential form and why especially does it in some form corresponds to integrating the surface of the area. I have ...
1 vote
183 views

### What is the motivation behind the definition of Cech cohomology?

From Hartshorne's Algebraic Geometry, chapter 3.4: The Cech cohomology of a sheaf topological space wrt an open cover is defined as $\frac{ker(d_{i+1})}{im(d_i)}$, where $d$ is some operator involving ...
240 views

### Why inner automorphisms; why conjugation? Why not closure under other automorphims?

I've been casually reading up on group theory recently, and I want to get a really solid and motivated understanding of where all the definitions we use come from. Notions like the center of a group ...
233 views

### Motivation for representation theory

Next year I have choose a few optative courses from a big list, but syllabi are not available yet, so I have to make a choice based on names only. I am thinking about taking one titled "Groups ...
53 views

### Profinite completion motivation

I have started galois theory recently, and curiosity quickly leads one to the subject of profinite groups. Although I have yet to be comfortable using these, I get what they are and we define them as ...
In the study of algebraic curves,we define intersection number of $F$ and $G$ at a point $p$ to be $I(F\cap G,p)=\dim_K(\mathcal O_p(\mathbb A^2)/\langle F,G\rangle$.But it is a rather unintuitive ...