Questions tagged [research]

For questions on the process and the impact of mathematical research, its accessibility to (new) researchers and its applicability in various fields. Do not use this tag just because your question is related to research you are doing.

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Essay Topic On Functional Analysis.

I am an IB student in year 12, I need to do a 4000-5000 word article that focuses on a particular topic however, I need some ideas to write about in my extended essay, I know some functional analysis(...
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1answer
24 views

Publication process and article formats [closed]

I have a few doubts about the publication process and article formats. Suppose that I have developed a new technique to interpret phenomena that were investigated previously using standard methods. ...
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26 views

Research,Thesis: Is it valued or devalued to create a name for a notion when thinking it doesn't have a general name?

Is it valued or devalued (by a jury for example) to create a name for a notion when thinking it doesn't have a general name ? For example , i'm working on sets E such that : E is uncountable , ...
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64 views

Pre-requisites for joining Math Ph.D program [closed]

I entered M.Sc. math course with a dream of doing Ph.D. My grades were really good in B.Sc. course and I got in really good college for M.Sc. course. I was under impression that my basics are really ...
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36 views

Research topics in combinatorics for high school students.

I'm a 12th grade high school students. I was looking for some research stuff from combinatorics within my capabilities. My background: I am introduced to olympiad mathematics. So I am introduced to ...
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62 views

If I am not going to be a professor, how can I continue mathematics research after graduation? [closed]

My goal for after graduation is to have some activities in which I keep up with both my interest in computer science and all things engineering, as well as my interest in pure mathematics. One or the ...
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154 views

Prove that there exists at least a form $g\left ( a, b, c \right )\pm f\left ( a, b, c \right )\left ( a- b \right )\left ( b- c \right )$ of $H$

With nonnegative cyclic polynomial $H$ as form $m\left ( a, b, c \right )\left ( c- 1 \right )\left ( a- 1 \right )+ n\left ( a, b, c \right )$ for $$m\left ( a, b, c \right ), n\left ( a, b, c \right ...
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21 views

Where to find known bounds on expressions?

Example. In a problem I was working on, I had an expression of the form $(1-e^{-\alpha n})^{e^{\beta n }}$. I wanted to find an upper bound $f(\alpha, \beta, n)$ on this that makes it easier to see ...
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24 views

Freeman Dyson classified mathematicians as Birds and Frogs. Can you give some concrete examples how these types differ?

Freemans article can be found here : Freeman's article on Birds and Frogs What is the difference between how a bird and a frog approach mathematics? Are there any textbooks or books in which the ...
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370 views

Need advice or assistance for son who is in prison. His interest is scattering theory.

My name is Dan Cunningham and the letter below is written by my son. I have been sending him text books and looking for answers on the internet to keep his interest up. He has progressed so far on ...
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67 views

How to find research interest?

As a math student, I often get confused about how to find a "research interest," a term that often appears in applications and elsewhere. I think it is almost impossible to pinpoint a single ...
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101 views

What are some possible PhD research areas based on these course pairs? [closed]

Update: This question has been closed by the votes of 5 privileged users because it does not meet stackexchange's guidelines (it is considered off-topic). For questions about choosing a course / ...
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1answer
109 views

How far could you get in Graph Theory, whilst knowing almost nothing about almost all other fields?

Apologies if the content of this post is not mathematical enough and is consequently in the wrong place. For context, I graduated with my masters in mathematics about 8/9 years ago and then went on to ...
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1answer
57 views

I have derived a new formula for π. What should I do with it? [closed]

I mean I know that I should publish it somewhere but have no idea about how to write it in a professional manner and where to publish it. Can anyone guide me?
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61 views

What are the current research areas in Differential Topology?

I am currently in my 4th year of a 5-year BS-MS course. I am majoring in Mathematics and I am quite interested in differential topology and would really appreciate if someone could tell me about ...
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69 views

Any good undergrad analysis research problems? [closed]

I'm looking for some ideas for longer and more research type problems to do in real analysis. The coursework we get is not very demanding and it would be nice to have some longer and harder projects ...
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24 views

Could inverted catenary 'arch' be used to build bridges?

I want to know the difference between catenary applications for bridges. I know that there is something called bridge suspension. But what I want to investigate is bridges that are built using the ...
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27 views

Is Descriptive Complexity dead?

I recently started reading about Descriptive Complexity, the branch of Complexity Theory studying the logic languages needed to express complexity classes. The main milestone in the area seems to be ...
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1answer
48 views

Generalizing topological spaces

I was studying topological spaces having studied metric spaces. I guess the properties of open sets in metric space led into (in terms of open set) definition of Topological spaces. Although there are ...
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1answer
80 views

Help me decide if I'm ready or not for this research topic

so a bit of background info on me. I'm a math grad student. My undergrad classes were mainly math-theory based stuff. I took Number Theory, Intro to Analysis, Intro to Abstract algebra, and such. I ...
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1answer
32 views

How can I rewrite equations with conflicting indices?

I am writing a paper where I have to define theoretical background of the techniques I've used (I'm from the field of Computer Science). However, since I have little mathematical writing background, ...
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3answers
146 views

How is linear algebra used in research? [closed]

I'm currently studying linear algebra with a great deal of attention to its definitions and theorems, but most of the time it seems that the motivation is always in applied or computational ...
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3answers
101 views

Naturalness in mathematics

Why is math so natural to some people? Even trying hard to study with dedication, worrying about ideas and at the same time the technique, nothing for me happens naturally.
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46 views

Open questions in formalization of quantum theory

From time to time I come across the statement that the mathematical formalization of the mathematical instruments, which the quantum theory uses, is not complete yet (admittedly, more often in popular ...
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94 views

Examples of color in mathematical papers

A resource request. Do you have any good examples of color used in a mathematical research paper? One example I've seen is here, in reference to tensor categories: https://arxiv.org/pdf/1612.02762.pdf ...
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55 views

How to read and understand the underlying mathematical concept about Data Programing

I was going through the official paper << https://arxiv.org/pdf/1605.07723.pdf>> Data Programming:Creating Large Training Sets, Quickly and came across ...
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94 views

An easy math paper to read for a high school student?

I am starting to learn about logic and, consequently, about proofs. I already knew that things have to be proven in mathematics, but I did not know that a high school student was able to do it. I ...
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89 views

How to determine your field of research?

This is probably going to be a long post, but its something I've always wanted to know and I believe many could profit from it. How do you determine a field of research? Of course, this question can ...
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1answer
62 views

Research project in graph theory

im a senior computer science student and im really interested in graph theory and in some of its applications. I was wondering if anyone would be down to undergo a research project with me in the ...
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1answer
86 views

Study and research in computational number theory

I am an undergraduate student and i have completed courses like data structures and algorithms , discrete mathematics , elementary number theory (i have studied Burton's book completely), abstract ...
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1answer
66 views

What is the mathematical notation for dependency length calculation algorithm?

I'm doing a computational linguistic research in python programming. I have written an algorithm that calculate dependency length of any sentence, but I won't to describe it in a simple statistical ...
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2answers
88 views

What are the currently conjectures around symmetric group? [closed]

I am asking you this question: What are the currently conjectures around symmetric group on research? Indeed I am interested to work on unsolved problems concerning symmetric or alternating groups. ...
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1answer
94 views

Is there any other controller than PID Controller?

I have been given a Project to search for a controller having better transient response than PID Controller. I searched but I didn't find any research paper on it. All are talking about improving PID'...
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1answer
89 views

Active research on the subject of general topology

I've lately been told that the subject of general topology, like what Hausdorff and Kolmogorov dealt with, is a a dead subject research wise. I have been wondering however whether this is indeed true, ...
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51 views

Climate research and mathematics

I'm not sure if this question belongs here, but I want to try: I Am currently working on my master thesis on the topic differential geometry and wave maps. My plan was to start my PhD studies in this ...
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0answers
38 views

What are the foundational papers of neural networks and how can I find them?

I am researching neural networks and would like to read some of the first papers that established and/or popularized neural networks. Neural networks crosses over between many fields, so I am looking ...
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2answers
67 views

Soft question regarding math theses [closed]

I'm currently in high school and I am wondering about how math papers a formated. In standard literature studies essays, we are told to "come up with" a thesis statement, present it in the ...
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34 views

Construction of $R$-graph semigroup from a directed graph

In the paper https://arxiv.org/pdf/1209.2578.pdf, Krieger is simply defining his notion of $\mathcal{R}$-graph. It is an object $\mathcal{G}_{\mathcal{R}}(\mathfrak{P},\mathcal{E}^-,\mathcal{E}^+)$, ...
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21 views

Construction of $R$-graph from a directed graph

Let $G$ be a finite directed graph with vertex set $V$ and an edge set $E$. In this paper https://arxiv.org/pdf/1209.2578.pdf, another graph is constructed from $G$ called $R$-graph by the following ...
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1answer
158 views

I want to read the 10,000 page paper on Classification of Finite Simple Groups? [closed]

I want to read the entire 10,000 page paper on Classification of Finite Simple Groups, however, I cannot find a copy anywhere on the internet. Math Exchange Question: Can someone please link me to ...
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23 views

Arithmetic Satake Equivalence?

I was wondering if there is an arithmetical analogue for Satake equivalence? I'm looking for a topic to focus on for my thesis, and although I haven't been able to find any arithmetic analogue, I want ...
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30 views

Status of the Kunneth Type Standard Conjecture in the Case of Shimura Varieties?

I am interested in knowing the current status of the Kunneth type standard conjecture in the case of Shimura varieties - I am wanting to focus on this for my thesis, but I want to know if it has ...
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87 views

Open problems in Functions of One Complex Variable?

I am interested in complex variables, and only have knowledge for one variable, not several as of now... Regardless, I want to participate in some research... Do you guys know of any interesting open ...
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74 views

Is information theory out of fashion?

I struggle to find research/PhD projects that use the term "information theory" in their description. I wonder why. Fields that seem to me very related, like representation learning, AI, quantitative ...
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35 views

Reference Request for undergraduate research topics to do with polynomials

I’m an undergraduate and have done several courses on algebra and analysis and I’m looking for some research topics associated with polynomials in general, but that don't require lots of background. ...
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2answers
169 views

Are we still Researching the Foundations of Math?

To my understanding, most of math can be founded in ZFC set theory. And, because of Gödel, we can never really prove the consistency of ZFC and hence mathematics as a whole. My question is, are we ...
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2answers
112 views

Is Competition Problem on Constrained Inequality Relevant in Research?

Many inequality problems on variable $x,y,z$ or $a, b$ come with constraints such as $ab = 1,xyz = 1, x+y+z = 1$. For example, Let $a$ and $b$ be positive real numbers with $a + b = 1$ then prove that ...
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1answer
53 views

On simplifying large exponential equations

I'm working on undergrad research in fractal geometry and have to prove certain functions are decreasing, one of which is $$g(x) = \frac{\left( \frac{2^m-2}{2^m-1}+ \frac{1}{2^m-1}\left(\frac{1}{2^m}...
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53 views

Mathematica legitimacy for research papers

I'm currently working on an undergraduate research project and am close to a paper/poster. A portion of my work involves differentiating a large function, which I did in Mathematica. From there I ...
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46 views

Career in Mathematics as an Electrical Engineer [closed]

I am a university freshman with major in Electrical Engineering. My passion is pure math(topology, group theory etc). During my first semester I noticed that our math classes are not rigorous at all, ...

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