Which area to choose as a research area that has a lot of applications in everyday life.
Research an area that you struggle to understand but still find interesting. You grow and you have the push to expand your horizons.
You can work to develop an optimization technique, or can improve other optimization technique. You can get mat-lab coding for reference from http://www.mathworks.in/matlabcentral/fileexchange
Thanking You.
I feel it depends many areas are surely useful as u are good at computational mathematics fluid mechanics may be good for you but as a discrete mathematics man i would nothing in this world works without discrete mathematics as computer also uses it to solving complex network problems too graph theory plays a role
I think that pretty much depends on your interest. Biology is an area of increasing mathematical usage.
Mathematical Physics no doubt.
"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better."
---Paul Dirac, The Evolution of the Physicist's Picture of Nature, Scientific American (1963)
"The measure of greatness in a scientific idea is the extent to which it stimulates thought and opens up new lines of research."
--- The scientific work of Georges Lemaître (1968), P.A.M. Dirac, Commentarii (The Pontifical Academy of Science), vol 2, 11, p.1-18.
"Just by studying mathematics we can hope to make a guess at the kind of mathematics that will come into the physics of the future. A good many people are working on the mathematical basis of quantum theory, trying to understand the theory better and to make it more powerful and more beautiful. If someone can hit on the right lines along which to make this development, it may lead to a future advance in which people will first discover the equations and then, after examining them, gradually learn how to apply them."
---Paul Dirac, The Evolution of the Physicist's Picture of Nature, Scientific American (1963).
Mathematics is the language of science. In my point of view Engineering is the best field of mathematics, because it goes directly to application.
Dear Birajdar, Every area in Mathematics is good for research. Do not think about the area. See what you are good at, select the problem and work on it.
I think you can choose one of the mathematics fields and develop it to a higher level,this is one of the great attributes of math that allows you to make progress in this field.
I can give you an example,we have fourier transform, laplace transform and z-transform,these are tools that control engineers use them in many cases for modeling and solving problems. but as you know they have little difference in fact,but each of them has its effect in science.
Hi, for Patrial differantial eq., Analytical Math., etc. http://www.wolfram.com/mathematica/
No direct answer, just to offer an example:
My MS advisor is a Ph.d of applied math. His Ph.D. thesis was to develop a scheme to solve a shock way problem. He then became a faculty in Aeronautical/Astronautical Eng. He devoted himself in using ENO, WENO and many TVD schemes in solving shock/vortex interation. By chance, he simulated a problem of extracorporeal shock wave lithotripsy (ESWL). With successful results, he group a team with a post Doc specialized in missile guidance, a MD, a Ph.D. student from EE, a pos Doc with expertise of image processing, and some Ph.D. and MS students from Astronautical eng. He not only did the simulation, but also experiments and medcal/physiology.
The story tells me that it is the interest+ability+opportinuity+team+continuous learning that make my advisor different.
If I were to be in school right now studying mathematics (not Physics), I would focus on differential equations. Everything in real life changes in complex ways over time, and differential equations are a good way to model this. Hence there should be a lot of room for interesting research and applications.
The classical area like set theory logic and number theory is quite interesting. There are many problems that still unsolved this day in classical area like perfect cuboid problem, ABC conjecture (someone says it has been solved by Japanese mathematician but no one else on earth understand his solution ._.), and many of them.
Big Data Analytics is the emerging field that requires lots of mathematical and computational knowledge. Suitable for researchers....!
I think the best application of mathematics and open research area in OPERATIONS RESEARCH, BIO-INFORMATICS or any other solution optimization field.
Nowadays, Mathematical Biology (i.e., biological system like control modelling in epidemiology, epi-ecological system etc.,) is an emerging field of research area in Mathematics.
How about the long oversight knot theory? It has a chance to strongly influence both physics and biology, maybe even more. Like the graph theory, it was also sleeping nearly 200 years before its today's rapid development.
"Modern Mathematics in the Light of the Fields Medals" by Michael Monastyrsky is full of leading-edge ideas
Instead of searching actual topic you may try to find the successful author with
the topic that you like, read his papers and try to extend his work.
I am partial to combinatorics. The concepts and methods are relatively easy to grasp, and it has many applications in various fields like algebra, algebraic geometry, statistical mechanics, probability and statistics, computational biology, theoretical computer science, etc.
Mathematical description of Turbulence,but above all the topic YOU like!
An interesting field of research area is Optimal Control in Engineering applications.
Research an area that you struggle to understand but still find interesting. You grow and you have the push to expand your horizons.
Please specify first your interest,suppose do you want to study analysis,algebra?,...........then after some body may tell the specfic area so study so ther may be again scholars, with deep knowledge in analysis area, or algebra .defnitly they will help you.
Gunvant,
Virtually all - likely all - of mathematics ends up having real life applications (although often totally unexpectedly so. If you're not convinced, may I recommend "Modern Mathematics in the Light of the Fields Medals" by Michael Monastyrsky. You might also want to check out Max Tegmark's excellent "Our Mathematical Universe".)
Maybe a way forward would be to choose a sub-field beforehand (such as financial math, economic modeling, mathematical physics ... ) and proceed from there ?
Also- a key determinant question has to be, how good are you really at math ?
There are 6 "Millennium problems" still begging for an answer. Although very easy to state and to grasp, their solution is fiendishly difficult and many mathematicians have ruined their lives seeking for solutions in vain (some have been lucky and made it their life's work to find a solution to either a Millenium problem - Grigori Perelman - or to another difficult problem (e.g. Andrew Wiles), and some less so (e.g., the continuum hypothesis is still an unresolved issue, with some arguing that it's provable/disprovable and others not so sure)
“To the scientific mind, all knowledge is an answer to a question. Without questions there cannot be any scientific knowledge. Nothing is obvious. Nothing is given. Everything is constructed.”
Gaston Bachelard, 1938
You can't make a good research without having interest. So it's better to find an area best on your interest.
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