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0
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1answer
36 views

Connection between Functional Analysis and Quantum Physics [closed]

Hi does anyone have an idea of which specific areas of Functional Analysis and Topology have a strong connection with the study of Quantum Mechanics and Quantum Field Theory? Thanks.
0
votes
0answers
88 views

Research Paper on Math [closed]

I have to write a research paper for American history and it can be about anything so I want to write it about math. The thing is, in order to do so I have to be able to tie it back into American ...
5
votes
0answers
90 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
107 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
45 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 ...
42
votes
6answers
1k views

What to answer when people ask what I do in mathematics [closed]

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
67 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
89 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
92 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
68 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
61 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
185 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
112 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 ...
73
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5answers
2k 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 ...
2
votes
0answers
88 views

Minimal “basis” in $n$ dimensional unit cube

Let's $$ B^n=\{\bar\alpha=(\alpha_1,\alpha_2,\ldots,\alpha_n)|\alpha_i\in \{0,1\}\};~~~~n=1,2,\ldots $$ and let's $$ C\subseteq B^n, $$ $$ S(C)=\{\bar\alpha\oplus\bar\beta\ | \bar\alpha,\bar\beta\in ...
3
votes
1answer
35 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
104 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.
1
vote
1answer
67 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
39 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 ...
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votes
8answers
516 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
66 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
251 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
96 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
208 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
107 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
39 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
110 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
82 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 ...
0
votes
0answers
39 views

Research scopes in Computational Geometry

I have taken a short a course on Computational Geometry and at present I want to do some research works of my own. Can anybody tell me about the research scopes on it? I mean, what are the active ...
2
votes
0answers
47 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
142 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
175 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 ...
2
votes
1answer
81 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
6
votes
1answer
73 views

Is there any relation between Galois solvability and integrability of hamiltonian systems?

Galois theory provides a method and formalism to study solutions of polynomial equations and solvability. Dynamical Hamiltonian systems have a somewhat similar concept of integrability. Since many ...
1
vote
1answer
32 views

Maximization with constraints

How can I find $\lambda_H$ and $\lambda_T$ such that $$\max_{0 \leq \lambda_H , \ \lambda_T \ \leq 1 }\left\{\frac{4.6575342 \times 10^{-4}}{2.1722965 \times 10^{-4} + \lambda_H},\frac{1.0958904 ...
22
votes
4answers
906 views

Book ref. request: “…starting from a mathematically amorphous problem and combining ideas from sources to produce new mathematics…”

I couldn't find Charles Radin's Miles of Tiles at the local university library or the public library, and cannot afford its Amazon price right now. Thus, while sorely disappointed for the moment, I ...
3
votes
0answers
47 views

Linear Algebra progression in our times

I know that Linear Algebra is relatively new branch of Mathematics. I wonder, Is there any significant progress with Linear Algebra in our time? Are there any major questions which haven't solved ...
0
votes
1answer
32 views

statistics confidence level

A survey was carried out to find out if the occurrence of different kinds of natural disasters varies from on part of the town to the other. The town was divided into two as center town and town ...
0
votes
1answer
72 views

Free Vibrations - Simple Harmonic Motion

As an engineering enthusiast I have been practicing with numerous model assignments to see how well I could deal with dynamics if I were in an educational environment. Most problems seem simple to ...
9
votes
2answers
388 views

Could we invent a new number with $|p|=-1$?

We know that how a single definition $i^2=-1$ revolutionized our mathematics and solved many many problems. I wonder whether the definition $|p|=-1$ could have the potential of creating a new ...
2
votes
0answers
97 views

Changing research area in grad school

I'm a PhD student about to close out my third year. My current research area is operator algebras. At the beginning of this semester I completed my qualifying exams (this was accomplished a semester ...
3
votes
2answers
187 views

Why are mathematical results discovered by multiple people independently?

This is a meta question. No this isn't a meta question about site, this is a meta question about maths itself. It has been observed quite a lot of times, that around some point in history,maybe ...
3
votes
1answer
229 views

Is there active research in trigonometry?

One learns trigonometry in high school/secondary school and either forgets it if one continues onto a career less mathematical or, possibly. uses it extensively in their work, as do engineers and ...
90
votes
18answers
9k views

How do you describe your mathematical research in layman's terms?

"You do research in mathematics! Can you explain your research to me?" If you're a research mathematician, and you have any contact with people outside of the mathematics community, I'm sure ...
5
votes
0answers
67 views

Making modular representation theory and cohomology 'compelling' and 'accesible'

I'm currently putting together an application for a dissertation completion fellowship offered through my university. A part of the application includes 500-1000 words describing my dissertation. ...
4
votes
2answers
191 views

Surveys of Current (last 50 years) Mathematics at Graduate / Research level?

I'm wondering if there are any books or broad survey articles that survey current mathematical areas, i.e. mathematics of the last 50 years. Ideally, these would continue in the style of the various ...
0
votes
1answer
99 views

What is the meaning of $(x^2+y^2)^n$? Is this an already known geometric object?

We all know that $x^2+y^2=r^2$ is a circle. What does $(x^2+y^2)^2$ signify? In general, what is $(x^2+y^2)^n$?
3
votes
2answers
596 views

How is research done in universities?

I have searched for some time for the "insider scoop" on how academics operate when it comes to mathematical research (theoretical physics research would also be interesting, but mostly interested ...
20
votes
6answers
827 views

How can a high schooler get more involved in mathematics?

For a high school student interested in majoring in math and learning more about math, what kinds of mathematical research can a student in high school get involved in? How can a high school student ...
6
votes
1answer
185 views

making mathematical conjectures

If a non-mathematician wanted to conjecture something and had strong numerical evidence to support the conjecture, how would he/she go about doing so? Would the mathematical community (a) take it ...