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0answers
39 views

Recent advancement in Haar measure

From my personal interest I have studied Haar Measure and the related concept of group theory on my own. However due to the lack of an authoritative source it is not getting possible for me to know ...
0
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0answers
21 views

Interesting/emerging research topics in mathematical modelling? [closed]

I get the privilege of doing an undergrad research project next year, and I've decided to go in an applied/computational maths route. The problem is, I have no idea where to start and despite looking ...
3
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0answers
65 views

Are there any modern mathematicians whose research interest is in “Probability Theory”?

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
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1answer
32 views

Redundant proof in Math paper

Recently, I read a published math paper and I found that in the excessive argument in the proof of one of its theorem. In fact, in my opinion, the redundant part is not even correct, because it ...
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0answers
53 views

Next book in in learning Analytic Number Theory

I have just finished the book "Tom M. Apostol - Introduction to Analytic Number Theory". My aim is to reach to graduate level to do research, especially on Rationality/Irrationality and Algebraic/...
4
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0answers
213 views

Research: Looking for a sequence that produce variation's of Pascal's triangle

Prologue I am an undergraduate so if my terminology or approach seem inappropriate/confusing please explain in the comments. I created a notation where $$F(0 \rightarrow n,x) = [\hspace{1mm}F(0 ,...
0
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1answer
43 views

What are some applied math projects/research Ideas that i could do over the summer

I am a high school senior and before I leave for college I want to learn the process of doing applied mathematics. I am having trouble with coming up with ideas. I know through multivariate/vector ...
0
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0answers
35 views

Relating fibonnaci sequence, lucas numbers and golden ratio to make a research question?

I am planning to write a high school level maths essay of approximately 4000 words. I do find Fibonacci sequence, Lucas numbers and Golden ratio amazing and want to research further on them, the thing ...
0
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0answers
21 views

Differentiating a Unique Multi-variable Function

I found this interesting property during my research were $\beta$ is some function of x and the a,e,n are all dependent on x; If $\frac{d \hspace{1pt} \beta(a,e,n)}{dx}=\beta(a+\phi,e,n)+\beta(a,e+\...
2
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1answer
81 views

Pure mathematics research [closed]

What can a first year mathematics undergraduate, who wants to pursue research in pure mathematics, learn in 67 days that will help him in the future?
0
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2answers
36 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
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1answer
32 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
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0answers
85 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
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1answer
53 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
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0answers
27 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
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0answers
70 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
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0answers
58 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
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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
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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
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0answers
37 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 H^...
4
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2answers
134 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
193 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
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1answer
125 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
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1answer
306 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
50 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
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0answers
50 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
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0answers
15 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
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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. $\|A_{n}c_{n}\|_{\...
0
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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
51 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
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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 n)...
2
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0answers
18 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
139 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
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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
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1answer
82 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} \{||Y-DX||_F^2\...
1
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2answers
106 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
129 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
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0answers
125 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
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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
237 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
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0answers
72 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
408 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
453 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
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2answers
134 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 boson,......
0
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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
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1answer
85 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
113 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 ...