The Beauty of Math

"PD" <[Only registered users see links. ]> wrote in message
news:1107192506.935956.83830@f14g2000cwb.googlegro ups.com...

I think you are full of shit, draper.
Androcles.

"PD" <[Only registered users see links. ]> wrote in message
news:1107196775.868722.146450@c13g2000cwb.googlegr oups.com...

Crap answer.

Androcles.

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.

Hi Anthony,

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
topics superficially.

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
similar experience.

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
return.

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
interests you.

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

"Androcles" <[Only registered users see links. ]> wrote in message
news:L_sLd.32941$[Only registered users see links. ].blueyonder.co.u k...

Androcles, you really should make an appointment with a psychiatrist.
Your personality disorder is getting to be pretty fierce now.

Franz

"Androcles" <[Only registered users see links. ]> wrote in message
news:RVsLd.32902$[Only registered users see links. ].blueyonder.co.u k...
says the guy who can't spell. but of course the maths is more important. you
guys are so enigmatic. i hope you sort things out cos after all you're both
educated people.

kind regards,
Mo0dy

Mo0dy wrote:
are
years
later, I
these
like
else
Any
like
like
box
won't
when
unless
You
important. you
you're both

I'm not sure how you came to THAT conclusion.

Anthony:


The textbook, ``Geometry, Particles and Fields'', by Bjorn Felsager
(Springer-Verlag) would be ideal for what you want. Depending upon what
you've studied previously and how rusty you are with that material, you
might need to supplement the book with some additional material. According
to the preface, the textbook presupposes a basic knowledge of calculus at
the level of multiple integrals and classical physics, including classical
mechanics, special relativity and electrodynamics. I would add quantum
mechanics to the list. In any case, those will be necessary prerequisites
whatever you do.

The book contains the basic mathematical and conceptual foundations
of modern physics in modern language. Topics include differential forms,
exterior calculus, noether's theorem(s), basic field theory including
things like solitons and instantons and a great many more topics, too
numerous to mention. It doesn't contain general relativity, per se,
but contains the underlying tensor analysis needed to understand
curvature more generally.

If you have the prerequisite background, then what is in the textbook is
exactly what you are seeking and it sounds like you have a substantial
fraction of that background. Good luck.

"Mo0dy" <[Only registered users see links. ]> wrote in message
news:KayLd.21716$[Only registered users see links. ].blueyonder.co.u k...

Draper forgot that education is more about thinking than parotting what
he reads
in a book.
I defined a clock that would emit one pulse of light once per swing of
the
pendulum, and said that was 1 Hz.
According to Draper, if the pendulum slows down to one swing every 2
seconds,
the frequency rises to 2 Hz.
Maybe you can straighten his arse out, I can't.
Androcles.

"Androcles" <[Only registered users see links. ]> wrote in message
news:gvzLd.22009$[Only registered users see links. ].blueyonder.co.u k...
truly gobsmacked..Galileo must be spinning in his grave.

"Mo0dy" <[Only registered users see links. ]> wrote in message
news:1HALd.35558$[Only registered users see links. ].blueyonder.co.u k...

He has to be groaning, that's for sure.
The pedulum swings and hits a microswitch, just like opening a fridge
door.
The swing is once once per second, as measured by the clock, no matter
how
fast or slow the clock is running.
If by some OTHER clock the rate is 2 Hz, then the original clock must
have recorded 2 seconds.
Draper is hung up on his intuitive notion of universal time, and insists
2.0 Hz means the original clock recorded 0.5 seconds from f = 1/t.

The problem came up when I showed Einstein was making no sense.
[Only registered users see links. ]

and said tau = 0.5 seconds (the moving clock runs slow), so we must
1 tick per 2 seconds.

This threw Draper into a tizzy, but
2 seconds t - time gives f = 1/2 = 0.5 Hz,
but two seconds tau-time is two cycles (or flashes) seen in one second
t-time,
or 2 Hz.

Thus according to Einstein, 0.5 Hz = 2Hz.
Draper is miffed because I refuse to withdraw the page, but he doesn;t
know how count to two.

Androcles