| | The Beauty of Math
Anthony wrote:I am reading many physics books lately and the
equations in them are all so interesting...the beauty of a
powerful equation. So I am wondering...I want to get back
into math again...etc.
I feel that there are many topics of great interest in the
mathematics behind physics, but I am sure that you already
know that the scope of all physics and all maths is vast,
and recognise that the time a person is able to spend
studying is finite.
So that after receiving a general grounding in both, (which
you sound as if you might have already), most people find it
more rewarding to chase after a limited number of topics,
going after depth of understanding rather than covering many
When one is a young student, maths and physics can seem more
like work than fun, and in my case at least, came low-down
on a list after a women, booze, making money, eating well
and generally having plenty of entertainment. Another
disadvantage I experienced at university was that I spent a
lot of time studying topics which somebody else thought I
ought to know, and less following the interests that I found
most stimulating. I am sure that many other students have a
Married life, a reasonable income, responsibilities, and the
requirement to only drink moderately, meant that the things
I had been chasing after were readily available, and
increased abstinence allowed "the little grey cells" to
Thus I have been able to dip into cosmology, quantum physics
(and how this affects gravitational theory), bits of number
theory, conundrums, history of mathematics and in fact
anything that interests me or takes my fancy, and have much
enjoyed the process so far.
The lack of time constriction and the stimulus afforded by
the freedom to follow my own whim has made this a much more
satisfying form of study from my point of view.
So in a nutshell, I believe that mature study has much to
recommend it, and I would like to encourage you with your
interest in the mathematics behind physics, recommending
that you start by selecting just a few topics - those which
are both achievable and of most interest to you.
Other thoughts: (forgive me if these don't quite match up to
what you were thinking about).
1) "It Must Be Beautiful" (Great equations of Modern
Science) is a series of easy to read essays edited by Graham
Farmelo which you might enjoy.
2) "The New Physics" a series of much more technical and
mathematical essays on quantum and relativity theories
edited by Paul Davies (Prof of Theoretical Physics)
I got a shock at my own ignorance when I started back, and
found that CALCULUS - James Stewart, had lots of examples
with practical applications, got to grips with the
mathematics behind natural processes and reminded me in a
straightforward way about the solution of differential
equations, methods of integration and other things I was a
bit rusty on. If you are beyond this you might find the
calculus of variations of more interest.
Although they do not usually cover the mathematical theory
in any depth, the range of ideas covered by a popular
authors in physics and maths may stimulate you to select and
follow up one topic or another. Some of these authors will
be available in a decent sized public library: -
Physics: Alan H Guth, Lee Smolin, Richard Feynman, John
Gribbin, Martin Rees, Paul Davies,
and a range of books on black holes, inflation and the
accelerated expansion of the universe, relativity, special
and general, the early universe etc
Maths: William Dunham, Martin Gardiner, Paul J Nahin, Albert
H Beiler, and a range of books on Chaos theory, Riemann's
Zeta Function, Games theory, probability of whatever else
You could let us all know how you are getting on and about
any interesting discoveries you have made by posting here.
Also, you have a good chance of getting help if you should
ever get stuck as the total range of knowledge within all
the subscribers to a newsgroup, is substantial.
I'm sure we all wish you good luck - Ian Hutcheson