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0
votes
2answers
33 views

Probability of a number in the real line

I have read that the probability to pick a rational number in the real line is null. My problem is: If $S$ is a dense set in the real line, what is the probability to pick an element of $S$? There ...
1
vote
1answer
30 views

What means to publish views/ideas are used, instead of blogs, among mathematicians today?

My question is motivated by the feeling that some mathematics blogs publish less and less over time. Are there other communication means which are used now instead with a similar role, or is it ...
5
votes
0answers
78 views

Are there any brand new areas of math where a high schooler could contribute?

I am a high schooler who really likes math, and I am interested in pursuing it in my undergraduate years. I have a basic facility with proofs, and I am currently exploring several different areas of ...
2
votes
1answer
48 views

Writing preliminary results in research papers

Suppose we want to put $10$ basic results in the preliminary section of a mathematical researh paper, without proof, but only with reference. It could be done in following way: Theorem 1: If $G$ ...
0
votes
0answers
25 views

What is the name of the identity: (2a)!=(a!*Γ(a-1/2) 4^a)/√π?

I just derived'(2a)!=(a!*Γ(a-1/2) 4^a)/√π'. My teacher has asked me to do some research over it. So my first question is. What is the name of this identity? Could it be a pi identity (if that is ...
1
vote
0answers
68 views

Where to show my work on integrals?

I am not sure if Mathematics Stack Exchange allows this kind of questions. But I do think there are some who can guide me through this. I am working on Indefinite Integrals for quite a long time and ...
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?
0
votes
1answer
55 views

Why do people say that some problem is hard when they do not actually prove it?

I have read many times in different papers something like the following (I do not remember the exact words though): "The problem is nonlinear non-convex programming problem which is hard to ...
0
votes
0answers
39 views

List of Interesting African Mathematics Blogs

Title says it all: looking for info on any Mathematics blogs that are either contributed to by bloggers on the African continent, or have an African continent focus (for example someone living outside ...
1
vote
0answers
36 views

Multiplication of Matrices in a Hilbert Space

So I was having a discussion with a friend as follows: Let $\mathcal H$ be a Hilbert space. Let $\mathcal H^{\otimes n} = \mathcal H \otimes \mathcal H \otimes \cdots \otimes \mathcal H$. $\mathcal ...
4
votes
2answers
130 views

Suggestions for research in Group Theory

(This is about a help for not to lose interest from Group Theory. Dear Group Theorist or Algebraist please help; if question is not clear, give suggestions.) (1) Few days before, I came across a ...
2
votes
2answers
180 views

Looking for fast text-books [closed]

I'm in a bit of a rut. I find myself quite old (20 - old man) and I don't even know high school math properly. And yet I can actually conduct original research (proof: rediscovered a famous theorem in ...
0
votes
1answer
119 views

Questions wrong or theorems useless because hypothesis impossible [closed]

Consider the following question: The area of a right triangle with integral sides is 5. What is twice its area? The answer is 10. But on closer inspection, there is no such right triangle. What can ...
17
votes
1answer
293 views

Errors in math research papers [duplicate]

Have there been cases of errors in math papers, that were undetected for so long, that they caused subsequent errors in research, citing those papers. ie: errors getting propagated along. My ...
0
votes
1answer
49 views

Current Research Using Sieve Methods

I've been learning various basics of Sieve Methods in Analytic Number Theory, and I'm wondering what are some uses of these methods in current research? Not famous, unsolved problems, but areas of ...
0
votes
0answers
48 views

Background Needed for Research in Algebra

I was wondering how much background knowledge is needed to do research in some subfield of algebra. I am currently working on an application for a summer research program, and I need to choose a ...
1
vote
0answers
14 views

Which research groups use stochastic processes and/or stochastic differential equations in computer graphics/vision?

Some research groups use stochastic differential equations for mathematical image processing. Which research groups do use stochastic processes in general and/or stochastic differential equations in ...
0
votes
1answer
28 views

Specific Example of a bounded operator on $\ell^{p}$

Let $p\in (1,\infty)$. To construct a counter example in some other context, I am seeking a bounded sequence $(A_{n})$ of operators in $B(\ell^{p})$ with the following property. ...
0
votes
0answers
27 views

Homomorphisms of quantum spaces

Suppose we have a look at the Hopf $*$-algebra $U_q(sl(2))$ and the Hopf $*$-algebra $A_q(\widetilde{S}^3)$ introduced in the paper: http://arxiv.org/pdf/q-alg/9605017v1.pdf. I want to find a relation ...
0
votes
1answer
50 views

How to find out leading research articles in a specific area? [closed]

If one needs to find out the leading research articles and most cited or influential research articles in a specific area of mathematics, let's say, fractals, chaos and non-linear dynamics what that ...
0
votes
0answers
20 views

Modules and generators

I found the following formulation: The module $N$ canonically isomorphic to the $A$-module with generator $v$ and the relations: $$R_jv=0,\ \ L_jv=v\ \ \ (1\leq j\leq n)$$ $$G_jv=0\ \ \ (2\leq j\leq ...
2
votes
0answers
17 views

Changing Notation in Direct Quote

Tried asking this on Academia.SE but the mathjax doesn't render. Direct quote: "...the estimator for the expected logarithmic return, $\hat{\mu} \equiv [\sum_1^n X_k]/h$, will have the properties ...
2
votes
1answer
119 views

Are there any big controversies in contemporary mathematical research?

Are there any big controversies in contemporary mathematical research? Other domains contain big controversial research topics (for example string theory in physics). The specific nature of ...
1
vote
1answer
25 views

Problem understanding how a linear equation is simplified

Using this paper as a reference (Section IV.C, page 4318), We have the following objective function which we wish to minimize with respect to $D \in \mathbb R^{n \times K}$ ($X \in \mathbb R^{K \times ...
3
votes
1answer
80 views

A question about Singular Value Decompositon(SVD)

Using this paper as a reference (Section IV.C, page 4318), We have the following objective function which we wish to minimize with respect to $D \in \mathbb R^{n \times K}$: $$\min_{D} ...
1
vote
2answers
105 views

Non-academic mathematics development? [closed]

How do you see non-academic mathematics? I have an impression that the academy has still a quite significant prestige and is thought to be the safe-guard for "real science". That is, to verify that ...
6
votes
2answers
125 views

How do I show that $ \sin x, \cos x$ really are in $ [-1,1]$ using series notion?

I'm sorry to ask this question , but should ask it may help me to know more about series theory , It is well known that $\cos x $ and $\sin x$ are represented by alternative series which hard ...
1
vote
2answers
44 views

How do I show $(a+b)^K=\sum _{n=0}^K \binom{K}{n} b^n a^{K-n} $ without using recurrence?

We already know that we can represent this binomial as the following: $$(a+b)^K=\sum _{n=0}^K \binom{K}{n} b^n a^{K-n};$$ where $\binom{K}{n} = \frac{K!}{n! (K-n)!}$ My question here is :How do I ...
3
votes
0answers
119 views

Imagination in Mathematics

I am currently reading the book "An Essay on the Psychology of Invention in the Mathematical Field" by Jacques Hadamard, and one chapter in particular seem very interesting to me. Hadamard discusses ...
4
votes
1answer
236 views

How do I prove that there is no other :$k=9,12,18$ for which this fails :$\sigma^k(114) \equiv 0\mod 6 $?

let $\sigma(n)$ be the sum of divisors for a positive integer for example : $$\sigma(6)=1+2+3+6=12$$ . I have performed some calculations in wolfram alpha about the sum divisors of this number: ...
4
votes
1answer
235 views

How can you confirm that a problem is open?

I was reading an article on Wikipedia and I came across a list of two problems which they asserted to be open, but without citation. I have looked through some literature but not all, as I am afraid I ...
4
votes
0answers
67 views

Research Strategy Question [closed]

I am a third year math phd student who is just beginning research and I have a question about doing research in general. I would like to work on some projects on my own on the side. I started ...
1
vote
2answers
391 views

Am I too old to reach to the point of a ground-breaking research and achieve it? [duplicate]

I am sorry if I am posting this question here; I thought that since I am looking for historical evidences of successful people in mathematics, so may not this question be an opinion-based one. And ...
5
votes
4answers
448 views

Is there any published research on the value of finding new proofs for old theorems?

There have been many conjectures in history of mathematics that some of them after passing long journey have resulted in lengthy and high-level-math proofs. Perelman's proof on the Poincare's ...
1
vote
2answers
129 views

What is the latest work being done in the field of Mathematics? 6/8/2015 [closed]

Young mathematics enthusiast here. I'm very curious to know what the top research is in the field of pure mathematics. Physics seems to take all the glory with quarks, then gravitons, Higgs ...
0
votes
2answers
91 views

Other way show that $\zeta(-2)=(-\frac{1}{12})\mod 2$? [closed]

Lemma: We knew that for any integer $a$ : ${a}^{p}=a \mod p$. Then $1^p=1\mod p ,2^p=2\mod p ,3^p=3\mod p , \ \dots,\ n^p=n\mod p $. Just to sum each term by term RHS and LHS we will get the ...
-1
votes
1answer
84 views

How we can deal with this equation $a^{n}+b^n=c^{n}$ if it was gaven to have solutions in primes numbers not integers numbers ? . [closed]

How we can deal with this equation $a^{n}+b^n=c^{n}$ if it was gaven to have solutions in primes numbers not integers numbers ? . note: $a, b, c $ are primes . Is there someone give us a reason ...
1
vote
1answer
110 views

Researching in Mathematics [closed]

I am presently pursuing Engineering, but I want to make my career in the field of mathematics. How do I come to know of the specific topic in math in which I would like to research, in which I would ...
4
votes
0answers
201 views

Original Research Topics for High School Student [closed]

I'm a grade 12 student interested in Number Theory, Graph Theory and Combinatorics and I am currently looking for ideas for an original research project/paper in mathematics. I was hoping that someone ...
2
votes
1answer
155 views

Applied/Numerical Linear Algebra-Suggestions for Project [closed]

I am looking for suggestions for a research project in applied/numerical linear algebra. As far as requirements, there really aren't any except that the topic has to tie in somehow with numerical ...
47
votes
6answers
2k views

What to answer when people ask what I do in mathematics

This is not really a math question, but I think that every mathematician and student in math (specially pure) struggles with this at some point. Inevitably at some point when we're talking with ...
2
votes
1answer
86 views

Shall I include my inventions in book or first publish them in some journal?

Dear and respected all. Today I am not going to post any problem right now but would like to get suggestion on the following matter. I do not know what step shall I take. I need your valuable ...
1
vote
1answer
94 views

Solving a Derivation of a $2\times2$ Matrix

I am currently doing some research and am working on the following problem: Given $DT_2(R)$ where $DT_2(R)$ is the upper triangular matrix with the diagonal being the same element. Determine all ...
7
votes
0answers
95 views

Are there any disagreements among mathematicians? [closed]

I would like to know if there is any genuine disagreement among mathematicians. By this I don't mean disagreement over convention (e.g. Should a ring contain $1$?). Formally, I mean is there a ...
6
votes
1answer
161 views

Books or texts on singularity theory [closed]

So a friend is doing his PhD in maths (algebraic topology) and his advisor wants him to publish something on singularities (of which, as fas as I understand, he knows next to nothing). I want to give ...
1
vote
2answers
202 views

Little, unknown, English or French research journals with good mathematics

In this article by Gian-Carlo Rota, you can read: "I bought a copy of Frederick Riesz' Collected Papers as soon as the big thick heavy oversize volume was published. [...] It was clear that ...
2
votes
4answers
208 views

Research Projects for 7th Grade Students

I'm going to define some math research projects for 7th grade students. The projects can be both purely mathematical and interdisciplinary. By the way, the students can write simple Pascal codes. I ...
89
votes
5answers
4k views

“Advice to young mathematicians”

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the ...
7
votes
0answers
244 views

Minimal “sumset basis” in the discrete linear space $F_2^n$

Let's $$ C\subseteq F^n_2, $$ $$ 2C=C+C=\{\bar\alpha+\bar\beta\ | \bar\alpha,\bar\beta\in C\}. $$ I need to find $C$ such that $2C=F_2^n$ and $|C|$ is minimal. I have found the following ...
3
votes
1answer
39 views

Proving monotonicity of continuous linear functional

Hi I am interested in resolving the following problem from the bottom of page 147 from a paper I am revising: Given a function $$a: \Omega \times \mathbb{R} \times \mathbb{R}^{N} \rightarrow ...