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46 views

Is there a good database with math papers?

I'm trying to do extensive research on the Twin Prime conjecture for one of my undergraduate classes, but I'm having trouble finding the sources. For example, I can only find Polignac's paper in ...
0
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1answer
52 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 ...
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0answers
23 views

What does meant “Uncounditional proof” and why should believe it that is a complet proof?

I have tried many times to understand what it does meant "Uncounditionally proof" but i don't succed , only I think that is the proof which produced from Insufficient conditions and and havn't enough ...
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0answers
31 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 ...
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0answers
32 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 ...
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0answers
34 views

Does a “zero counting” norm exist and, if so, is the following use of it a reasonable approach?

DISCLOSURE: The following question relates to research. If this is an improper place to put this question, or if this is generally improper demeanor, I would welcome correction as I am not very ...
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2answers
122 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
170 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
108 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 ...
13
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0answers
167 views

Errors in math research papers

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
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1answer
46 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
44 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
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
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0answers
18 views

Generators of locally finite part of $U_q(sl(2))$

I want to know the following: If one has the quantum group $U_q(sl(2))$ one can have a look at the locally finite part as introduced in http://arxiv.org/pdf/1307.3642v3.pdf (Definition $3.1$). From ...
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
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0answers
21 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 ...
2
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1answer
101 views

Undergraduate research in group theory? [closed]

I'm a freshman in college currently taking an introductory course in abstract algebra, and find it extremely interesting. I was looking at some research other undergraduates at my school did on group ...
1
vote
1answer
41 views

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

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 ...
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0answers
19 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
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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
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1answer
102 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
79 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} ...
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2answers
99 views

Non-academic mathematics development?

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
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2answers
124 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 ...
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2answers
42 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
114 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 ...
1
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1answer
82 views

Finding conferences and summer/winter schools

I have some funding for travel next term, my colleagues always seem to know of a conference here or there or a workshop in their area. Apart from personal contacts, is there any good web resource for ...
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
227 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
61 views

Research Strategy Question

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 ...
2
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0answers
37 views

Is there a connection between uniform law of large number and Ibragimov's conjecture?

In limit theorems, one of the biggest problem is to give an answer to Ibragimov's conjecture, which states the following: Let $(X_n,n\in\Bbb N)$ be a strictly stationary $\phi$-mixing sequence, ...
2
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2answers
72 views

a theory of transcendental functions?

Lately I've been interested in transcendental functions but as I tried to search for books or articles on the theory of transcendental functions, I only obtained irrelevant results (like calculus ...
1
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2answers
377 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 ...
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4answers
436 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 ...
4
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0answers
182 views

Has this difference equation :$x_{n+1}=Ax^2_{n}-Bx^2_{n-1}$ been studied before?

I posted this problem before in MO but only I would like to know if this difference equation :$$x_{n+1}=Ax^2_{n}-Bx^2_{n-1}$$ where $A(\theta)= \cos(\theta)$ and $B(\theta) =\sin(\theta)$ are ...
2
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1answer
71 views

Outlier detection with robust multiple regression model

I have a set of features (eg, location, income, budget, education) that I use to predict a continuous variable (say, amount spent per day on the internet). I am interested in detecting outliers. I ...
0
votes
1answer
26 views

A theorem about a increasing sequence of operators

I am searching for a theorem of the following form: if $T$ is a (unbounded) self-adjoint operator on a Hilbert space $H$ and $(h_n)_n$ a increasing sequence of bounded Borel functions, which converges ...
1
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2answers
120 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
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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 ...
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1answer
80 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 ? .

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 ...
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0answers
23 views

Research into the application of Jacobi matrices

The general real infinte hermitian Jacobi matrix is written in the form $$ \textbf{$J$}:= \ \left( \begin{array}{cccccc} b_1 & a_1 & 0 & \cdots & 0 & \cdots \\ a_1 & b_2 & ...
1
vote
1answer
99 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 ...
0
votes
1answer
26 views

Ratio laying within the confidence interval still being depicted as having an influence?

I keep seeing this in research papers. The researchers claim that there is a positive correlation between A and B then subsequently show that they odds ratio/sample mean etc. is IN the confidence ...
0
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0answers
18 views

selecting points on a domain which represent the derivative of a function

I'm working on some algorithm part of which entails me to subdivide a domain based on the derivative of a function. Let's just consider the 1D case with a closed and bounded domain $[a,b]$ for a ...
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0answers
52 views

Directed Graph Equivalence Class

Consider the following conversion involving directed graphs. To convert from $\mathcal{G}$ to $\mathcal{G}^u$ (they have the same number of vertices): $V_i \rightarrow V_j$ in $\mathcal{G}^u$ iff ...
5
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0answers
187 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
110 views

Applied/Numerical Linear Algebra-Suggestions for Project

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 ...
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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
84 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 ...