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7
votes
1answer
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 ...
3
votes
1answer
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. ...
1
vote
3answers
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
35
votes
0answers
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: $$u_{n+2}=u_{n+1}+\frac{u_n}{n}$$ $$v_{n+2}=\frac{v_{n+1}}{n}+v_{n}$$ $$u_1=v_1=0$$ ...
5
votes
1answer
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 ...
1
vote
1answer
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 ...
4
votes
1answer
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 ...
10
votes
2answers
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 ...
0
votes
0answers
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 ...
1
vote
0answers
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 ...
0
votes
2answers
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, ...
1
vote
2answers
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 ...
0
votes
1answer
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
6
votes
1answer
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 ...
4
votes
3answers
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 ...
3
votes
0answers
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?
3
votes
4answers
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 ...
2
votes
0answers
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 ...
0
votes
1answer
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: ...
0
votes
2answers
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 ?
113
votes
9answers
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 ...
2
votes
3answers
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 ...
1
vote
0answers
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 ...
6
votes
0answers
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, ...
2
votes
4answers
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. ...
6
votes
1answer
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 ...
3
votes
1answer
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?
5
votes
2answers
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 ...
1
vote
1answer
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 ...
0
votes
1answer
30 views

How to visualize complex domains

I was hoping if someone can help me visualize complex domains. I know how simplex ones like $|z|<1$ or $\text{Re}z < 1$ look like but for the more complicated ones such as $$\text{Im } z < ...
0
votes
0answers
96 views

Are there chain rules for integration possible?

In "A Quotient Rule Integration by Parts Formula" and in "Quotient-Rule-Integration-by-Parts", the authors integrate the product rule of differentiation and the quotient rule of differentiation and ...
2
votes
2answers
217 views

Applications of Linear Algebra in software engineering.

I'm a software engineering and mathematics student, I was searching for disciplines of mathematics that would go well with my engineering degree, and found a lot of people recommended that software ...
2
votes
2answers
42 views

Differentiability implies continuity

This is a but of a more mathematically juvenile question but I'm trying to get all my intuition in order. When taking a limit we can cancel things that might be zero because in taking a limit, we ...
2
votes
2answers
99 views

What's the mathematics behind 3D modelling? [closed]

I'm highly interested about 3D modelling in software, and I know that it has some deep mathematics behind it too. I would like to learn what specific topics are behind it mathematically. As long as I ...
1
vote
1answer
92 views

Why do we call “comprehension” and “regularity” to the axiom schemas in Set Theory?

I have several Set Theory books in my "shelve" but I have found the justification for the names in none. Usually all of them just state something like: "The axiom schema of ...
4
votes
1answer
91 views

Why does the Möbius function take its values so often in $\{0,+1,-1\}$?

The Möbius function of a locally finite poset $P$ is defined on its intervals $[x,y] \subseteq P$ recursively by $$\mu([x,x])=1$$ $$\forall x < y : \mu([x,y])=-\sum_{x \leq z < y} \mu([x,z])$$ ...
4
votes
3answers
94 views

What kind of mathematics do I need to know to understand virtual reality very well? [closed]

In my life I want to develop the virtual reality industry and I wanted to know what kind of mathematics will help me get there, I'm sure that every mathematical subject is helpful, but I mean ...
4
votes
1answer
173 views

What subfields use computers the most and least? (soft question)

What areas within research mathematics use computer programming (not including $\LaTeX$) the most and least? What programming languages are most commonly used in those fields?
4
votes
2answers
64 views

Looking for details on historical math anecdote

My memory is very sketchy here so bear with me. A fairly prominent 19th or 20th century mathematician was captured by a military force, probably invaders. He claimed that he was just a civilian, a ...
2
votes
0answers
78 views

What are some topics of advanced number theory every young geometers should know? (soft question)

By "advanced number theory", I mean topics like arithmetic/Diophantine geometry, modular/automorphic forms and Shimura varieties. I'm interested in derived/non-commutative algebraic geometry, some ...
4
votes
2answers
65 views

How can one determine if a function should have parenthesis around their argument?

I have noticed that there are a select few functions that are acceptable if their argument is not in parenthesis. For example, here are a few functions I noted do not require an arguement: Trig or ...
4
votes
0answers
117 views

Why is recursion theory suffering from terminological bloat?

Several questions on MSE in recent months and most recently this one have made me feel that recursion theory is suffering from terminology bloat. Why have so many synonyms for "recursive" and ...
2
votes
1answer
48 views

Linear algebra MOOCs

I am a statistics student studying a module of linear algebra at the undergrad level. I was looking for MOOCs that might help me. I tried saylor which meets my syllabus but I cannot find videos for ...
4
votes
2answers
90 views

Collective name for algebraic structures

I am doing a thesis about various algebraic structures, primarely about groups, rings and modules (with maybe hint of algebras). However always having type out ALL of them constantly gets very tedious ...
0
votes
1answer
99 views

Question about Bachelor thesis and future lectures. [closed]

I just finished my exams one day ago but lectures will already reassume in less than two weeks. I currently finished my 5th semester and will therefore tackle my last semester of my bachelors. But I'm ...
0
votes
0answers
35 views

Is there a specific name for these methods of summation?

When calculating summation of series I use these methods ; Ex: Method One $$U_r=\frac{1}{(r-1)r(r+1)(r+2)}$$ $$U_r=\frac{1}{(r-1)r(r+1)(r+2)}\left[\frac{(r+2)-(r-1)}{3}\right]$$ Then ...
4
votes
2answers
129 views

Is category theory ambiguous? or it just is the case for beginners? [closed]

First of all, I have to say that I'm not going to offend anyone/anything here; I just need some clarification/studying tips about category theory. I'm totally new in category theory and this happens ...
0
votes
0answers
56 views

Several options using Black-Scholes equation(s)

Could someone provide me some information about the modelling of several options at the same time by using Black-Scholes (probably coupled) equations? Any reference to papers and/or books shall be ...