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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.

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How do you do a literature review when you don't know the name of the concept?

So this is certainly a soft question, but one that I've encountered a lot of times; just check my post history and you'll find a many questions like this. I frequently play around with random ...
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Help coming up with a high school research project

I'm going to be a junior next year, and our school requires us to make a science fair project. I've always been interested in math and am heavily involved in math contests. However, for the past few ...
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1answer
52 views

Best way to find papers in Mathematics by a specific author?

I am a student studying Mathematics. I am looking for papers (in the field of abstract algebra) by a specific author. I wonder if there are standard ways, well-known strategies or methods you ...
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1answer
188 views

Research level algebraic topology

I became very interested in Algebraic Topology more or less recently, and learnt a lot of "classical algebraic topology", including : Hatchers' Book, and more categorical approaches here and there ...
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Is Fractional Calculus an important research topic “in pure mathematics” today?

Being a potential graduate student, I would like to know if fractional calculus is an actively developing research topic in the area of pure mathematics today.
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Statistical test for comparing samples where a subject's performance may be affected by a previous test?

I'm performing a study in which participants are being asked to listen to a changing musical tone and to answer when they detect a change and what they think that change correlates to (based off of ...
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1answer
34 views

Research areas/topics in Resource Allocation.

I want to investigate different models/theories/areas of research for problems in Resource Allocation. In general terms, by 'resource allocation' I mean problems that involve a finite amount of ...
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115 views

Next book in learning Algebraic Number Theory

I have just finished the book Introductory Algebraic Number Theory by Kenneth S. Williams and Saban Alaca. My aim is to reach to graduate level to do research, especially in one or more of the ...
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1answer
33 views

Method for scoring a test in which participants may be able to give more answers than there are questions?

I'm currently performing a study in which participants are being asked to listen to a continuous, changing musical tone and to answer when they detect a change and what they think that change ...
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1answer
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Literature request: Papers by Charles C. Cadogan.

I am looking for three papers on the Collatz Conjecture by Charles C. Cadogan. The Annotated Bibliography lists these three as: "Charles C. Cadogan (2000), The 3x+ 1 problem: towards a solution, ...
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examples for mathematics research [closed]

I am really interested in mathematics and physics, and I know a lot about whats going on in the world of physics. Do you recommend any places where I can also find popular researches in math so I will ...
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Maxwell-Chern-Simons equations: Translating from form language to component form

I am trying to solve the scalar-coupled Maxwell-CS equations, which is written in this form in the differential form language \begin{eqnarray} 0=d(Q_{IJ}\star F^J)+\frac{1}{4}C_{IJK}F^J\wedge F^K \...
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1answer
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Publications in differential geometry [closed]

I am a senior year mathematics undergraduate who is reading "Analysis on manifolds" by Munkres and "topology from a differentiable viewpoint" by Milnor. I would like to know how can I find a simple ...
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2answers
262 views

High School Mathematical Research Project Ideas [closed]

i am currently looking out for some possible topics i could study for my research project in high school. Algebra, trigonometry, Pythagoras’ theorem, geometry, circles and their properties, etc. and ...
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19 views

A question relating to citation of papers.

I am reading a paper: "A geometric setting for the quantum deformation of $GL_n$", how to find some other papers that quoted from this article? I would appreciate it if you could give me some ...
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21 views

Quick question involving Computational Fluid Dynamics

So I'm a high school student with some free time on my hands and I've been trying to learn about the Navier-Stokes equation. Anyway, this set of lecture notes from UCLA is a bit hard to understand. ...
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1answer
71 views

Is it possible to find such a discrete non-cyclic mathematical function?

Is it possible to find such a discrete non-cyclic function with the following features? Let $$f: \mathbb{Z^{+}} \rightarrow \left\{0,1,2 \right\},$$ and for any $n\in\mathbb{Z^{+}},\left\{ f(...
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39 views

Research trends on mean curvature flow

It's been a few months since I've been curious about mean curvature flow and now I'm reading Robert Haslhofer's lecture notes. I like the subject and would like to do research on it, but I know ...
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54 views

Is it possible to prove the following inequalities to be true?

I'm trying to prove the following inequalities are true, but they're a little too complex, is it even possible to prove that they are true? I suspect they are, but unless there is some simple method ...
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Research Suggestion

I am a 10th grader, I am trying to learn smooth manifolds and group theory, our teacher wants us to select a research topic and make a paper about it, (it can be about anything) and I want my paper to ...
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21 views

What are the directions of research in Numerical Optimization?

I have just begun reading in the field of Numerical Optimization. Are people trying to invent new Algorithms? or proving the convergence of Heuristic Algorithms? and what else? What are the tools a ...
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Do any open problems in research mathematics hinge on a solution to an “elementary” integral?

So undergraduates have the calculus tools to write an integral so convoluted it admits no closed-form solution. But most such integrals are uninteresting or already useful even without closed-forms, ...
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2answers
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Actual problems in fractals.

I am preparing a report for student conference on the mathematics. The main objective of a report is to overview history of fractals, both from theoretical and applied viewpoint. The only problem is ...
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58 views

Applications of Stochastic Dynamical Systems in Artificial Intelligence

It is my first post here but I have come to ask a question that will, hopefully, clear the ambiguity I have regarding the subject. A bit of a background about myself - I am a physics undergraduate ...
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1answer
48 views

How do you determine what to define when you are writing a math research paper?

I find that often researchers in math do not define every piece of notation that they use, however, I am not sure what criteria they use to deem that a definition should be left out, or should be ...
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Compute $\lim\limits_{n\to\infty}(x_{n+1}-x_n)$ if $x_n =\sum\limits_{k=1}^{n-1}f(\frac kn)$ and $f$ continuous (but not continuously differentiable)

The following question from Furdui's book (Exercise 1.32. page 6) is an "open problem" : Let $f: [0,1] \to \mathbb{R}$ be a continuous (and not a continuously differentiable) function and let $...
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How to find less-difficult-than famous unsolved problems?

When I was in my high school I studied 14 undergraduate books with almost all their exercises. I am about to begin my undergraduate in mathematics this week. I love to do research in mathematics. I ...
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Searching for the identity of CS sets

I apologize in advance if this question is too surface level. I have heard recently about such mathematical objects as "CS sets". They are defined as sets of natural numbers $a_1,a_2,\ldots,a_n$ such ...
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1answer
1k views

Binomial Coefficients involving Prime Powers Minus 1

I would like to show the following is true; Let $p\in\mathbb{P}, \alpha,n\in\mathbb{N}$. Then $$p^\alpha\mid\sum_{k=1}^{n-1}\binom{(p^\alpha-1)n}{(p^\alpha -1)k}.$$ I've never worked with prime ...
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1answer
46 views

How to compare B Spline Surfaces?

We can define b spline surfaces over a set of points. However, is it possible to compare two set of b-spline surfaces fitted over different set of points ? The objective is to identify if the curves ...
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1answer
75 views

When is it possible to find necessary and sufficient conditions linking two concepts?

Status of this question: The notion I'm after is vague in my mind. I hope someone can clarify whether there is an exact version of the question I'm asking. It seems to me that one of the most ...
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3answers
1k views

How to know when to give up on a ${}$ math problem, which may not have a solution? [closed]

When you're working on problems from textbooks, you know that the problem has a solution, because the author claims that it has. But when you're doing original research, you generally don't know ...
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1answer
91 views

Books/Reference progression for an aspiring graph theorist [closed]

I have just finished a first course in graph theory and finished my undergraduate degree in mathematics. I have two broad questions about research/further study in graph theory. What is the natural ...
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motives in current research

Are motives still studied in current research? Searching various papers I can see that a lot of these works about motives are quite old. I'm interested in arithmetic geometry and i'm also really ...
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1answer
54 views

Research areas in Peano arithmetics

So I recently just finished a course on Peano arithmetics and it's non-standard models. I am very much intrigue by this topic. Hence I am rather curious what are some research areas surrounding PA ...
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How to find a research question and relevant materials [closed]

I am a PhD student working in Spectral Graph Theory. Can anyone please help me solve the following questions: How to find a research question?I contacted my advisor,he says he does not know how to ...
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2answers
190 views

Why are there researchers in PDE theory when we can instead build numerical solvers?

I have a bit of a naive question: Why are there researchers in PDE theory, e.g. people who work on analysis and PDEs, when instead one can spend their research days building numerical solvers to get ...
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Is persistent homology mathematically “interesting”? [closed]

Currently, I am occupying myself with (non-applied perspectives on) Persistent Homology, having a background in non-applied maths (representation theory). After having spent some time on the topic ...
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1answer
40 views

Properties of any structures

Bonjour, I've never made extensive researches in number theory, scared to lost myself, so... I would like to ask you something : Could you help me to find some sources(or anything else) about the ...
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5answers
4k views

Can a chemical engineer become a self-taught mathematician? [closed]

My background covers calculus, analytical geometry, linear algebra, ODEs, numerical methods, statistics. Not to mention all the physics, chemistry and typical chemical engineering subjects. I am ...
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222 views

What's there to do in logic? [closed]

I recently asked a similar question about category theory (it got more interesting answers on MO though, I hope for this one I'll get answers here too), but here I'm going to reduce the scope a little ...
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2answers
103 views

I am looking for an idea research question for a 5000 word essay in Multi Variable Calculus

As part of one of my university courses, Multi-variable Calculus, I need to write a 5000 word essay on an a research question that is on the course. Before telling you what I have as an idea here are ...
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44 views

Intersection of commutative algebra and discrete math [closed]

What are the fields of mathematics where commutative algebra/algebraic geometry and discrete math/combinatorics intersect?
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1answer
256 views

Research in motives and number theory

By what I have seen a modern approach to the study of number theory and arithmetic geometry is by motives, motivic cohomology and something like that. But, what are the applications of motives and ...
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Papers on Tensor factorization

I started reading a few papers on Tensors. Right now I am reading a paper by Chi and Kolda called “On Tensors, Sparsity, and Nonnegative Factorizations”. I passed linear algebra and calculus courses. ...
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Choosing research topic [closed]

I have a PhD in Mathematical Statistics. I have strong background in Statistics and I love programming and modelling, networks and graphs. (I am using mathematica and learning python). Do you have a ...
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28 views

Graph algorithm to find the most likely ancestor of a node

I'm working on the Wikipedia Category Graph (WCG). In the WCG, each article is associated to multiple categories. For example, the article "Lists_of_Israeli_footballers" is linked to multiple ...
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Research in the Discrete Logarithm Problem

I have already taken a course on Abstract algebra and tis implementation in the criprography, among other topics the course focused on the discrete logarithm problem in finite fields. Now, I would ...
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1answer
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Is Algebraic Number Theory still an active research field?

I've took an introductory course on Algebraic Number Theory during my Master's, which I really enjoyed. Now that I'm beginning to think about my PhD area, I wonder if I shouldn't go for something in ...
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53 views

General conditions for the Fixed point property on the Quotient topology

Today in my topology class (undergraduate) we introduced the basics for Fixed Point theory for topological spaces (i.e.Fixed point property, retracts, contractability, etc.) and we were discussing the ...