April 21st, 2010, 02:56 AM
Are any of the members who use the physics forum actual physicists/applied mathematicians?
Just interested to know. If you are what field do you research?
I was going to put this in the general discussion forum, but didn't think I'd get too many replies from the Physics forum.
I am not, I did electronic engineering at university, and now i fix computers for a living.
i build audio devices as a hobby. I read a lot of physics/politics/philosophy books that 99% of people i know find "boring", hence why i like to visit the forum: To find new things to learn about and test what i have learned discussing with others.
Ive also had some help with devices i build.
I would also be interested to hear from anyone who is actually earning a living off being a physicist!
You didnt say if you were a physicist or not.
I'm not a physicist yet. I'm hoping to do a postgrad this year to specialise in QFT and string theory etc. After that I want to do a PhD...
... and win the Nobel Prize
what university? I was at Glasgow.
April 21st, 2010, 11:43 AM
There are at least a couple of real mathematicians, not applied mathematicians, here who also have an interest in physics.Originally Posted by sox
I'm at Strathclyde at the moment. I applied to Glasgow though.
April 21st, 2010, 12:31 PM
What do you research?There are at least a couple of real mathematicians, not applied mathematicians, here who also have an interest in physics.
Out of interest, in mathematics is their a rivalry between pure maths and applied maths? It's just I noticed you used the term "real mathematicians"
April 21st, 2010, 01:31 PM
I am retired.
My experience with quite a few applied mathematicians is that they lack capability in just two areas -- mathematics and applications.
I find theoretical physicists and theoretical engineers are much better at applying mathematics than are so-called applied mathematicians.
Too many specifics on background and research areas make it way to easy to establish identities, and that can reault in nuisances.
May one ask in what field of mathematics that you did your research in?
Analysis
I see.
Do you ?
Mathematics is traditionally divided into 3 areas -- analysis, algebra and topology
But those divisions are not clearcut and there are areas that do not fit neatly in any of the three. Mathematics is in fact a huge and interconnected field of study. That is what makes it interesting.
Combinoatorics is often lumped in with algebra
Geometry is spread round. Algebraic geometry is not only often included under algebra, but in fact most modern approaches to algebra are based on algebraic geometry.
Differential geometry, might be included under analysis, since it is closely related to analytical questions particularly those associated with partial differential equations.
But algebraic and differential geometry are also closely related, and that ties algebra and analysis closely together in that regard.
On the other hand questions of algebraic geometry and differential geometry often involve issues of topology. Moreover, topology at an advanced level quite often means algebraic topology, which in turn sometimes involves differential topology, which is again closely related to differential geometry, and algebraic geometry.
Analysis is a large field that includes real analysis, complex analysis, differential equations and functional analysis. Functional analysis is critical to most areas of analysis and makes essential use of both topology and algebra. It includes the theories of topological vector spaces, Fourier analysis, and distributions which are essential to a modern understanding of differential equations. Differential equations are central to topics in differential geometry. Also, Fourier analysis now includes the non-abelian cases that result from the study irreducible unitary representations of Lie groups, and analysis on manifolds that are the quotient of a Lie group by a discrete group, which in turn involves both algebra and differential geometry.
Many current problems in mathematics result from questions that arise in physics. That ties a great deal of mathematics to theoretical physics. But there is a huge difference in the perspective and rigor of a mathematician as opposed to the viewpoint of a theoretical physicist. Mathematicians have made contributions to physics (e.g. Newton, Riemann, Cartan, Poincare, Noether, Bott) and some physicists have been important to mathematics (e.g. Witten, Stokes)
In short, as I hope this very brief sketch shows, mathematics is a very large subject, Which has many interrelated pieces, and attempts to classify it and to classify mathematicians usually fall short of the mark.
The reason I didn't ask what you did more specifically, was that I thought it might be too personal.
However, your reply reminded me of a question that I've had for some time. What is the difference between calculus and analysis?
Calculus is the most elementary part of analysis.
What you see in a class called "Calculus" is typically that part of analysis that was developed by Newton, in a relatively non-rigorous form. So you might say that it is analysi as the subject stood in about the year 1700.
You the subject done again in somewhat greater generality and with rigor in an introductory class with a title something like "Introduction to Real Analysis", which would typically cover the theory of integration, throught at least the Lebesque integral indifferential calculus in
, and perhaps some other topics like elementary Fourier Analysis.
Analysis might be described as "on beyond calculus".
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