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-4
votes
0answers
71 views

How to help a postgraduate student to write a book [on hold]

How to help a person who has already completed her post-graduation but has also secured a result much weaker than her expected result during the completion of graduation,for writing a higher secondary ...
2
votes
0answers
60 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
vote
1answer
30 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
203 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: ...
3
votes
1answer
196 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 ...
5
votes
0answers
51 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
votes
0answers
29 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, ...
1
vote
2answers
44 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 ...
0
votes
2answers
315 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
407 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
votes
0answers
176 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
votes
1answer
59 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
19 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
vote
2answers
90 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
81 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
78 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 ...
0
votes
0answers
15 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 & ...
2
votes
1answer
72 views

Researching in Mathematics

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
15 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
votes
0answers
14 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 ...
1
vote
0answers
41 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
votes
0answers
108 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 ...
9
votes
1answer
132 views

Mathematical Research seems daunting [closed]

Suppose you are a research mathematician. I imagine your problems are generally unlike the problems of fellow scientists in the physical sciences, because you deal with proofs, and proofs demand ...
2
votes
1answer
61 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 ...
45
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
74 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
91 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
94 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
89 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 ...
0
votes
1answer
74 views

Choosing a Project Topic.

I am a undergraduate student and recently i have been assigned to project (one of courses). But i have to choose my own topic. I want to work in the field of ...
2
votes
2answers
189 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
145 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 ...
74
votes
5answers
3k 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
233 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
37 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 ...
6
votes
1answer
108 views

Open access peer reviewed math journals

I would like to have a list of existing open access, peer reviewed Mathematics journals, like the Electronic Journal of Probability. I have difficulties to find such a list on the Web. Thank you.
2
votes
2answers
114 views

Applied mathematics commonly needed in the following industries

I was just wondering if anyone could shed more light on specific topics in applied mathematics or other skills (programming, etc) commonly used in the following industries: oil and gas, ...
0
votes
1answer
40 views

How can you find Patrick Flandrin's source codes in his TF publication?

I am reading his publication Elements de Traitement du Signal but I cannot find his sources codes such as files change.m, sousech.m, ... Some his TF codes are here, and probably, he is about these ...
8
votes
8answers
578 views

Mathematical breakthroughs [closed]

When I read about mathematical history I hear of breakthroughs. For example, Cartesian geometry, Newton/Leibniz Calculus, and so on. My question is this: What are some recent epoch-making ...
0
votes
2answers
68 views

Are there particular techniques to find the general formula for an arithmetic function, neither multiplicative nor additive?

I was reading about the Euler phi function and the sigma function when I began to wonder how on earth one gets to the general formula for an arithmetic function. I'm not considering trivial formulae ...
0
votes
1answer
322 views

Parabola investigation

Edit 4: I added the below picture for clarity I'm trying to figure out how to find the angle between the red line and the blue line, but I have no idea how to start. (I have a feeling that this ...
4
votes
1answer
100 views

Research in Mathematics (Formalities vs. Results)

This question is intended to solve an internal dilemma I have been having lately. I assume that most of those who have gone through the process of mathematical research have, at some point, considered ...
7
votes
1answer
248 views

Which hot math research fields became insignificant later on?

In history (for last 150 years), which math research fields were hot (popular) at their time , but whose results became insignificant (almost useless) later on? The reason I ask this question is ...
1
vote
2answers
116 views

Do mathematics researchers regularly solve problems like this?

I'm not sure that this is the right exchange for this question. It asks about the possibilities of research in mathematics and computer science. Extended Background I am very interested in ...
2
votes
0answers
41 views

Is ODE theory useful for developing numerical solvers for ODEs?

I will be doing research in developing numerical solvers for ODEs. I was wondering if knowledge of ODE theory will be useful and if so in what ways. I am asking because, I am inclined to take a ...
3
votes
1answer
134 views

What are the big issues in modern graph theory?

This is inspired by the similar question on modern set theory. I've read through the open problems in graph theory on Wikipedia's list of unsolved problems in mathematics, but what I'm looking for is ...
4
votes
1answer
91 views

Starting research in Algebraic Geometry.

Let us suppose someone knows most of the concepts from Algebraic Geometry texts like Hartshorne. What papers should he start reading to quickly start getting a feel for research? I find myself at ...
2
votes
0answers
49 views

Research: what can I do next if the solution is too long

Sorry for this vague question. Here is my circumstance: I have tried to formulate a problem with an equation, and it is a optimization problem. So I just go ahead, and use mathematica to take the ...
0
votes
0answers
186 views

Is the Annals of Global Analysis and Geometry a good journal?

I hope I'm not out of place asking such a question here. Anyway, I'll soon have my first real paper published in the Springer journal titled "Annals of Global Analysis and Geometry." Since I don't ...
0
votes
2answers
206 views

Open Problems for High School Students

I am a homeschooled rising senior in high school, and I would like to research an open problem in mathematics. I have taken a number of undergraduate-level mathematics courses, including ...