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2
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0answers
42 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 ...
2
votes
0answers
44 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
113 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
65 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 ...
5
votes
0answers
42 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
28 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 ...
14
votes
3answers
330 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
37 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
28 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
0answers
10 views

Standards for publishing research on Global Optimization

I needed to search for the global minimum of a function of 24 variables. I did this using the NMinimize feature in Mathematica, and it allows one to do this using Differential-Evolution, ...
0
votes
1answer
50 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
353 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 ...
0
votes
0answers
29 views

Pseudo-monotone operators research paper question

Hi I just want to know if anyone can see how the result (2.34) is obtained in the following research paper http://caa.epfl.ch/publications/9-Boccardo-Dacorogna1984.pdf. Thanks, I know that it is a ...
2
votes
0answers
63 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 ...
0
votes
0answers
15 views

algorithm for traversing a fractal in a “maximally ordered” way

consider a multidimensional fractal that can be "traversed" in an arbitrary order. is there an algorithm for traversing a fractal in a "maximally ordered" way? in other words the algorithm has ...
0
votes
0answers
42 views

How are theorems developed/evolved? How would have a mathematician like Cauchy thought about the following theorem?

I am not sure if i can ask this question over her but the other day i was studying this theorem If $\epsilon = \beta_1 \beta_2 ...... \beta_r$ where the $\beta's$ are 2- cycles, then r is even. The ...
3
votes
2answers
148 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
133 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 ...
76
votes
18answers
7k 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
52 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. ...
3
votes
2answers
141 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
94 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
308 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
674 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 ...
2
votes
0answers
123 views

As a high school student(living in India), how do i go about doing research and writing a research paper?

I am currently a high school junior living in India and have already taken Differential Calculus and will be finishing Integral Calculus in 2 months time. I am interested in doing some research and ...
4
votes
0answers
138 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 ...
3
votes
2answers
51 views

Generating points from a standard Gaussian

I'm new to Gaussian distributions and I'm trying to generate say, $ N$ points from a $ M$ dimensional standard gaussian. What does this mean? How would I do this in matlab?
0
votes
2answers
104 views

Best Line Graph Plotting Software for Display Board

I want to make some line graphs which will be put up on a Display Board in a exhibition So I want to make them eye catching .. Which are the best free available softwares?? Please help.
1
vote
0answers
73 views

Research paper Journal

I am a high school student and want to submit a research paper to a journal. I know that most journals are very hard to be published for the first time. Can anyone suggest me journals which publish ...
2
votes
1answer
115 views

Tataru and Koch Paper “Well posedness of the Navier- Stokes Equation”

Hi I wonder if someone can help me with some inequalities ( [9] in the paper) of this research paper [1]. Suppose $\Pi$ is the Leray operator, this is an operator define as it follows: $\Pi(f)= ...
0
votes
0answers
30 views

Game in a joint-stock company

I would like to compare myself with you on work experience that I'm living these days: In a joint-stock company there are three teams of managers who manage all offices, each team has five directors, ...
1
vote
1answer
49 views

Choosing strategies to maximize ones payoff and minimize others payoff

In game theory, the aim of every player is to pick strategies that maximizes their payoff. This is done irrespective of the payoff of others. But in real life competitions, there arises a secondary ...
10
votes
1answer
467 views

Research in differential geometry

I am an 3rd year undergrad interested in mathematics and theoretical physics. I have been reading some classical differential geometry books and I want to pursue this subject further. I have three ...
3
votes
0answers
62 views

A challenging non homogenous fractional inequality.

The following problem is a challenging generalization of several difficult inequalities, where none of the usual methods used in inequalities seems to work. I would like to know if someone has a ...
0
votes
0answers
65 views

Numerical Error in Computation - What Are the Students' Expected to Know?

I'm going to conduct an educational research about math undergraduates' conceptions about "numerical error." So I'm making a list of items I think someone with a BSc in mathematics is expected to know ...
33
votes
3answers
1k views

A generalization of IMO 1983 problem 6

Note: This question has a bounty that will expire in just a few days. Let $a,b,c$ and $d$ be the lengths of the sides of a quadrilateral. Show that $$ab^2(b-c)+bc^2(c-d)+cd^2(d-a)+da^2(a-b)\ge 0$$ ...
1
vote
0answers
76 views

What resources are available for undegraduate research?

I'm reading Landman's Ramsey theory on the integers, from the preface: The student needs not to be intimidated by the words "Ramsey theory", thinking that the subject matter is too deep and ...
3
votes
3answers
318 views

New kind of identities?

I found a new kind of identities which are half logic and half algebraic while working on a proof of NP-completeness. They are like this: $$ \frac{a+mb}{n+m} < \frac{a}{n} \iff b < ...
1
vote
1answer
456 views

How much room is there for original mathematics research?

Should more universities and colleges offer degrees in mathematical research? I am in the process of incorporating a non-profit college and I am considering offering a degree in mathematical ...