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Which Math Topic Should I choose for Research

  • #1
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2

Main Question or Discussion Point

I am finishing up my undergraduate degree in Mathematics, for my last semester I need to choose a topic of research with a particular professor. I am interested in applied math, mostly mathematical physics but there are certain fields of math that may not seem like they relate to mathematical physics or any applicable field but still do in some way or another. Below I will list a number of research topics that are presented to us. I am hoping maybe or a few people can shed some light on which topics might be interesting in terms of practical use.


-Discrete Markov Chains

-Logical Fallacies

-Polynomial rings and theorem proving in Euclidean geometry

-Selected Solutions of the Navier-Stokes Equations

-Solutions of the nonlinear Schrodinger equation

-Probability of binarity in a section of the sky

-Symmetries in the arbitrary quadrilateral

-The Weibull distribution and its applications

-The Half Normal Distribution

-The Folded Normal Distribution
(note these 2 are closely related where the 1
is a special case of the 2)

-Finding Parameters of a Nonlinear Combination Oliveri

-Taguchi Methods For Design of Experiments (applications and how they differ from
classical DOE designs)
 

Answers and Replies

  • #2
DrClaude
Mentor
7,148
3,281
Below I will list a number of research topics that are presented to us. I am hoping maybe or a few people can shed some light on which topics might be interesting in terms of practical use.
Depends on what you mean by "practical" A few things in there a quite interesting for physicists, and might be considered as "useful" for them, if nor "practical."

As someone who's worked with Bose-Einstein condensates, it is clear that I find "Solutions of the nonlinear Schrodinger equation" very interesting. "Selected Solutions of the Navier-Stokes Equations" is quite applied and could probably be considered "practical."
 
  • #3
StatGuy2000
Education Advisor
1,740
825
To the OP:

As a statistician I personally find the following topics on your list to be of particular interest:

-Discrete Markov Chains

-Probability of binarity in a section of the sky

-The Weibull distribution and its applications

-The Half Normal Distribution

-The Folded Normal Distribution
(note these 2 are closely related where the 1
is a special case of the 2)

-Taguchi Methods For Design of Experiments (applications and how they differ from
classical DOE designs)


Discrete Markov chains have a broad range of scientific applications from physics (where it appears extensively in thermodynamics and statistical mechanics; furthermore, the path integral formulation of quantum mechanics are Markov chains as well), computer science (where it is used in pattern recognition, information theory, speech recognition, and bioinformatics), statistics, economics, among many others.

As someone who is actively involved in the design of experiments, the Taguchi methods are very useful, and are frequently used by engineers, and likely useful for experimental physicists to know as well. The other topics above are all part of probability theory, which all play important roles in both physics and statistics, among other areas.
 
  • #4
Do something of each time. Me, for example, I am an undegraduate major in Physics. I want to study Theorical Biophysics, Astrobiology, Epistemology, Science Communication, I want to do a second college in automotive engineering, and then, in philosophy. Do something of each time. if you are multi-task, you can do two postgraduates at the same time, if you see that will account, do two things. I have a friend of mine, who has a professor that give three different subjects. If you want to do all of this, try to do direct doctoral thesis (here in Brazil, there is this endeavor and it is a law).

If I were you since you like everything (like me, lol). I'll do each thing in each time (if you are acquainted with everything), or if I know something less than some other, I'll do what I more acquainted (I'm a freshman, I enter in 2018.1 in the college hehe).
 
  • #5
I was thinking about to do the two things, Theorical Biophysics and Astrobiology (I want science communication too). Theorical Biophysics because I'm a fan of Biology and I want to do explain the biochemical ou biomechanical reações through the mathematics and Astrobiology I'm fascinated by life since I was a teenager. Do you have any academic advisor? Have you told this to your advisor? Maybe he can answered better than us, and sure, better than me hehe.
 

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