# 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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### find the number of distinct values of $z=\cos(\frac{p}{q}(\pi+4\pi k)) +i \cdot \sin(\frac{p}{q}(\pi+4\pi k))$ [closed]

So, I want to actually find and prove the number of distinct values of $$\cos(\frac{p}{q}(\pi+4\pi k)) +i \cdot \sin(\frac{p}{q}(\pi+4\pi k)),$$ with $\frac{p}{q} \in \mathbb{Q}$.
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### Analytic works versus synthetic works in mathematical research

With the purpose to clarify my ideas about terminology I would like to ask in Mathematics Stack Exchange what is the difference of two verbal expressions: when a professional mathematician understands ...
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### Process after solving a problem

I think I may be on the verge of solving a previously unsolved problem. It is not a hugely interesting or revolutionary problem. However, I was wondering if there would be something I should do after ...
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### ranking and reputation of a math paper?

Say I found a math paper X and that X was published in a journal Y, before taking it seriously, how would I usually go about judging the quality of the journal or its reputation ? in a fast way.
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### Difficulty with Complex Computation in Proof on Ford Spheres

I am reading a paper on arXiv taking the idea of Ford circles and putting it into three dimensions, but am having difficulty with the following lemma, at a very basic level. Most of the details aren't ...
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### Publishing Research Papers on Mathematical Software Packages

I have written some LaTeX package for Mathematics. It involves substantial work. In general only a person having good knowledge of Mathematics and TeX could develop such things. There are other ...
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### Preparing for Research Course while at Budapeset Semesters in Mathematics

I am a current math undergrad who's going to be attending Budapest Semesters in mathematics this summer and possibly fall. I am looking to get into the research course they offer as I've done research ...
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### How to group using percentiles?

I'm trying to understand this research below that I added: The outcome variable was categorized using percentiles to Mild, Moderate, and Severe in the Symptom Severity Scale (SSS). The three ...
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### Looking for notes/books on the Laplace Transform that uses 0- as shorthand notation.

I have been reading the Linear Physical Systems Analysis website located at https://lpsa.swarthmore.edu/LaplaceXform/FwdLaplace/LaplaceXform.html . The first equation on that website involves a ...
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### name/applications for this surface?

If you have a space of bounded killing flow lines in 3-space say spanning points $p$ and $p'$ s.t. the flow vanishes at these points and the boundary, maps the boundary to itself (boundary is a ...
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### What topics in mathematics have no or very little research done about them, so far? [closed]

This is a bit of a soft and subjective question, but can someone give me some examples of mathematical topics or areas which have no or very little research done about them? I love reading math texts ...
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### Helix with mixed handedness

I'm currently interested in the mathematics and the mechanism of chirality inversion that could take place in (regular/irregular) helices, for which it possesses both left- and right-handed sections. ...
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### Has there been any mathematical research on redundancy in axiom sets?

This is a bit of a soft question, but has there been any significant research on redundancy in axiom sets? Let me explain what I mean. I know that a few papers deal with proving that a particular ...
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### How do you know when trying to find a proof/counterexample isn't worth it?

This is quite a general question... apologies if it is too general; I'm just wondering if anyone has any useful tips or advice. As part my final year university project I've made an algebriac/...
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### Is it okay to utilize a mixed sampling technique (Probability and Non-Probability Sampling)?

I am conducting a research with a descriptive correlation design. And I have rationalized that the best sampling procedure to apply in my study context is a combination of a probability and non-...
1 vote
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### Closed form of $\sum\limits_{m=0}^\infty \frac{(a)_m\text B_p(b+m,c-b)z^m}{m!}$ with the Incomplete Beta function.

This question comes from related “sum of incomplete gamma function” problems. Also,there are many research papers trying to make the Hypergeometric Incomplete. Here is one confluent example from ...
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### Suggestion of topics in General Topology for PhD interview

I got shortlisted for PhD admission .I've to prepare a presentation as a part of my interview.My research interest is General Topology. I've studied Munkre's topology upto Chapter 8. Please suggest me ...
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### Is mathematics a deductive science?

As it was discussed, for instance, in answers to this MSE question, formal mathematical proofs are deductive in nature. The question I am interested in is: What is the nature of mathematics at the ...
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### Axiomatic combinatorics

I'm curious about combinatorial analysis. I have some questions about this topic because when I think of combinatorics I recall some technics to solve problems but that's all. I'm curious at a ...
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### New/up-and-coming/lesser known mathematical topics [closed]

Having spent a lot of time with popular science, I am generally exposed to topics that are either very well-developed (like calculus) or have a very rich history (like geometry). Authors tend to avoid ...
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### Is there is any name of the adjacence matrix constructed in such way?

I have constructed an adjacence matrix for a non-conjugate graph of a generalized quaternion group.In this matrix if two elements which are conjugate to each other are operated gives "0" ...
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### How are contributions to mathematics reviewed/published? [closed]

Let's say you're a hobbyist who's seemingly found a novel identity/solution/method or other general contribution to some field of mathematics. What you don't know however is: If you're actually the ...
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### Help with writing research proposal about topological divisor of zero

I have completed my M.Sc. and I want to do Ph.D. I am very much interested in Banach Algebras and the topic that has got my attention is Topological divisors of zero. I would like to study properties ...
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### What are some interesting problems in the intersection of Diophantine Approx and Algebraic Geometry?

I am a first year graduate student and I am eager to work on irrationality/transcendental proofs of specific numbers like Euler's constant gamma. Because backgrounds for Elliptic Curves include very ...
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### Ergodic Theory and Euler-Mascheroni Constant

Originally posted on mathoverflow but didn't get an answer. I am highly interested in doing research on proving irrationality of some specific numbers like Euler-Mascheroni Constant or ζ(5). A ...
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### What are some good math research topics for high schoolers?

I'm a junior in HS and I have an interest in math. I wanted to pursue some research in math but I have trouble deciding which subject since there's so many. I know calculus (I took Calc AB, learned ...
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### Analysis Research Devolved into a Weird Combinatorics Problem

I was doing research in Analysis and it somehow all devolved into some weird type of combinatorics optimization problem. The problem is that I don't know anything about combinatorics. For the progress ...
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### Why Algebra has continuing research while for something like Calculus, there is none.

Why does the nature of algebra provide such a vast amount of research to be conducted with so many new discoveries while something like calculus is essentially complete. Is there a good reason as to ...
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### Any interensting math to be done on Pyraminx?

to start I am not sure if this is the right SE to be posting this so feel free to tell me if I should take it down or change tags. Now to proceed to the core of my question. I am thinking about my ...
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### Summarising a Research Paper

I thought to put this out to the community. I am an Undergraduate student summarising maths papers, firstly to get to grips with reading mathematical research and collecting a body of interesting ...
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I had previously asked a question on mathstack exchange (Conjecture on The Generalized Carmichael Numbers) concerning with a conjecture I had discovered. I worked on the problem for a long time and ...
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### Graduate Real Analysis research based question- Completion of the real numbers

I am currently a graduate student taking a real analysis independent study class. This is my first time taking real analysis, as I did not take it as an undergraduate. I am working on a research ...
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### Find $g(x,y,z);p(x,y,z)\ge 0$ so that $f(x,y,z):=x\cdot g(x,y,z)+p(x,y,z)$

We have the following fact: (I don't remember where I read it, but there is.) If $f(x)$ is which is non-negative for $x\ge 0,$ then $f(x)=g(x)+x\cdot h(x),$ where $g(x)$ and $h(x)$ are SOS. So I ...
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### 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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### 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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### 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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### 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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1 vote
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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