# Tagged Questions

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

68 views

### “Lifting” fibres of morphism of arithmetic schemes to get rid of “nongeometric” ramification

This is a soft question and really a request for pointers towards a certain rigorous formulation of geometric intuition I've had for some "arithmetic schemes". I'm looking for ideas and key references ...
58 views

### On motivation, focus and mental state [closed]

I have a bit of a meta-question, but first let me give you some background. I used to be a very inquisitive kid, interested a many disciplines, in particular mathematics, computer science and physics. ...
103 views

### Are the assertions “$2 + 2$ equals $4$” and “$2 +2$ is $4$” identical

Are the assertions "$2 + 2$ equals $4$" and "$2 +2$ is $4$" identical? Or is this a linguistic, psychological or murky philosophical thing rather than a mathematical thing
575 views

### Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them?

Benoit Cloitre offered two 'mirror sequences', which allow to compute $\pi$ and $e$ in similar ways: $$u_{n+2}=u_{n+1}+\frac{u_n}{n}$$ $$v_{n+2}=\frac{v_{n+1}}{n}+v_{n}$$ $$u_1=v_1=0$$ ...
61 views

### Nested Radicals and Continued Fractions

Is there some interconnection between these two topics? A sort of classification of the possibile types of nested radicals and maybe some way (hopefully bijective, in some sense) to pass from a ...
32 views

### What is the difference between the notions of travelling wave, solitary wave and soliton?

There are three notions I recently heard often: travelling wave solitary wave soliton I am not very familiar with these notions so my question is, what are the differences between these three ...
94 views

### Will Homotopy Type Theory ever be as accessible as traditional Set Theory?

At the moment, Homotopy Type Theory is barely accessible to undergraduates, and only the most advanced or most gifted could have a decent chance of grasping it at a workable level without mountains of ...
529 views

### Why are invariants of knots and manifolds important or useful?

It is easy to define invariants that completely classify knots; however, this is computationally infeasible, so is it computationally efficient invariants that are important? Why? Do mathematicians ...
58 views

### Name of this Sum

I have come across this sum on a sheet of paper but I have no idea what it is, so if someone recognizes it could they tell me what it regards? Note: I have only the formula and not any other ...
100 views

### Is all of mathematics invented? [closed]

I know this question has potential to be down voted by many users, but this strikes my mind. Can the mathematics we have today solve some problems around us? Is there something still left to be ...
91 views

### Interesting real life applications of elementary mathematics

If you teach mathematics to future highschool teachers, you often feel that they are bored because what they learn at university does not have much to do with what they will have to teach in school, ...
92 views

### How do I explain Erdos-Szekeres theorem to a child?

So,a $5$th grader yesterday asked me to explain the Erdos- Szekeres Theorem to him.He is not too proficient with series and so having problem to understand my explanation.How do I simply explain it to ...
59 views

### If I Wikipedia every topic in Discrete Structures, will I be ok without a textbook? [closed]

My Discrete Structures class doesn't have a textbook, and it only has lecture notes, and I am so confused and can't do any of the homework problems except by googling and the TAs are not helpful ...
36 views

### Are there any (differential) geometries of interest which cannot be formulated as Cartan geometries?

Cartan geometry is a generalization of Klein's Erlangen program. For every homogeneous model space, we have a corresponding type of Cartan geometry obtained by "rolling without sliding" the model ...
44 views

### Can I just make this function up?

The Lambert W function was made to solve the problem $xe^x=k$ for $x$, which is given as $x=W(k)$. Could I just make a function $x=F(k)$ which solves $x\cos(x)=k$? Even though the solution has an ...
59 views

### Basic formality when considering random numbers

Suppose we are interested in randomly picking numbers in the interval $[0,1]$ with the uniform distribution. If I want to write a mathematical text about this, it can be done by saying that $X$ is a ...
69 views

### solve $ax^3+by^3+cz^3+dx^2y+ex^2z+fxy^2+gxz^2+hy^2z+iyz^2=0$ for all triplets $(x,y,z)$.

let $x,y,z$ be any 3 positive integers. If for all $x,y,z$, we have : $$ax^3+by^3+cz^3+dx^2y+ex^2z+fxy^2+gxz^2+hy^2z+iyz^2=0$$ What can be said about the integral coefficients $a,b,c,e,f,g,h,i$? I ...
55 views

### Where do they study Riemannian Geometry in Europe? [closed]

I would like to satisfy this curiosity. Which are the European universities that pay more attention and efforts in to research in Riemannian Geometry?
140 views

### What's the best way for an engineer to learn “real” math?

I'm an electrical/computer engineering student and have taken fair number of engineering math courses. In addition to Calc 1/2/3 (differential, integral and multivariable respectfully), I've also ...
40 views

### Why only a handful of distinct mathematical constants appears in most applications?

Is there some theoretical reasoning behind the fact that the same numbers ($\pi$, $e$, $\gamma$, etc) appear again and again in every application in every field of Mathematics? Most people just ...
38 views

### Abstraction and/or concreteness - What should be emphasized

Alexandar Grothendieck was probably a mathematician focusing on theory developement and abstraction much much more than focusing on concrete examples and/or problems. In his biography, he wrote: ...
44 views

### How to prove that Lebesgue outer measure is monotone?

It is very clear that if $A \subset B$ then $m^*(A)\leq m^*(B)$. But how to prove it ? Most of the books says that it is obvious. But what is the proof ?
9k views

### What's the point in being a “skeptical” learner [closed]

I have a big problem: When I read any mathematical text I'm very skeptical. I feel the need to check every detail of proofs and I ask myself very dumb questions like the following: "is the map well ...
48 views

### In measure theory $\emptyset$ and $\{a\}$ are considered as intervals . Why?

I recently started self learning measure theory. While reading a note , I came across this , In measure theory $\emptyset$ (empty set) and $\{a\}$ (singleton set) are considered as intervals . Why ...
25 views

### An enquiry on subtraction of inequalities

Let $f(x)$ and $g(x)$ be nonconstant functions such that $1<f(x)<g(x)$. If $f(x) < h(x)$ for all $x$, and we suppose that $g(x) \geq M$, does it follow that ...
128 views

### Why so many 'multi-part' definitions, as opposed to 'unified' ones?

Many definitions consist of multiple parts: an equivalence relation is symmetric AND reflexive AND transitive; a topology is closed over finite intersections AND over arbitrary unions; etc. However, ...
205 views

### Does one need to learn set theory before learning category theory?

I am having a course in Algebraic Topology and learning some basic category theory. But I only have a very limited understanding of basic set theory. I have no idea what is ZFC, and stuff like that. ...
97 views

### Can I take Linear Algebra without having learned Vector Calculus?

I need to take Linear Algebra to progress in my major and the course has Calculus III listed as a prerequisite. I've already taken Calculus III and passed with a C, although I didn't learn the ...
76 views

### What do mathematicians mean by “mild condition”?

On some papers you read online you will find theorems dabbled with: "Under a relatively mild condition, ...." What do mathematicians mean by this and what are some examples of correct usage?
93 views

### Powerful applications of linear algebra?

I'd like to see some neat, elegant applications of linear algebra. I'm a undergraduate student but I don't want to prevent people from posting things just because I won't understand them, but if it's ...
21 views

### Example of series of functions that converges uniformly but whose series of uniform norms does not converge

Analysis two is a very heavy exam, and many people try it thousands of times. Thus, I still have friends to help about that, and today I have been asked, "What do I do when investigating the ...
30 views