Originally, I started this post to mention the first
few items found through the excellent PhysicsForums.

Then I kept finding more and thought it not worth
the extra trouble of several posts (especially with
so little feed back on each prior post.)

Besides these PhysicsForums included below are:

    Quantum Mechanics web site
    Mark Srednicki's QFT book (615 pages) while it lasts
    Two different Quantum Wikis:  Quiki AND Quantiki

BTW, this is our ONE HUNDDREDTH POST!!!!

Here you go....(--Herb)

PhysicsForums includes many excellent tutorials:
http://www.physicsforums.com/archive/index.php/

For instance, nice short tutorials on Physics and supporting Math:
http://www.physicsforums.com/archive/index.php/t-95535.html

An Example: Matrices and Solutions to Linear Equations
Excllent on matrices including CLEAR definitions of things
like Bra-Ket <A| & |A>, Hermitian, Self-Adjoint, Complex Conjugate etc.
http://www.physicsforums.com/attachment.php?attachmentid=5263&d=1129677866

By the way, 'Bra' is pronounced like a woman's undergarment
despite the fact that Bra-Ket is derived from 'bracket'.

Quantum Mechanics:
A graduate level course by Richard Fitzpatrick
<http://farside.ph.utexas.edu/teaching/qm/lectures/lectures.html>
Nice, online HTML notes that are (on first view) explicit and clear.

Mark Srednicki's QFT book (615 pages in pdf format)
Free and downloadable until it is PUBLISHED.
<http://www.physics.ucsb.edu/~mark/qft.html>
mark@....
<<Preface for Students
Quantum field theory is the basic mathematical language that is used to
describe and analyze the physics of elementary particles. The goal of this
book is to provide a concise, step-by-step introduction to this
subject, one
that covers all the key concepts that are needed to understand the
Standard
Model of elementary particles, and some its proposed extensions.
In order to be prepared to undertake the study of quantum field theory,
you should recognize and understand the following equations: [short
list follows]>>



Welcome to Qwiki!
Qwiki is a quantum physics wiki devoted to the collective creation of
technical content for practicing scientists. Please sign up, browse
around the site, click on the edit links, and contribute something!
http://qwiki.caltech.edu/wiki/Main_Page

Welcome to Quantiki – the free-content WWW resource in quantum
information science that anyone can edit.
Is there something missing? Is there something not-quite right? You
can join Quantiki and improve it.
<http://www.quantiki.org/wiki/index.php/Main_Page>

--- "milongadude" <milongadude@...> wrote:
>
> --- "herbmartin52" <herbmartin@> wrote:
> >
> > --- "milongadude" <milongadude@> wrote:
> > > --- "herbmartin52" <herbmartin@>
> > > wrote:
> >
> > For Differential Equations and Linear Algebra I have been
> > watching the MIT Open Courseware videos which are practically
> > as good as being in the lecture hall.  (Recitations and tutorials
> > are the only things missing.)
> >
>
> Hmmm.. yes, I've had a look at some of these, they're very good!
> Hopefully other universities will follow suit - but as a lecturer
> once said to me, academic staff on the whole are ambivalent about
> this trend, as it allows universities to take a lot of power away
> from them.

There is a push towards this and a few are doing it.
UCSD has that very good QM three semester course online
(great materials, almost great video, but the instructor
is only average -- but at least he tries.)

So many teachers have never been taught to actually TEACH.

> Aha.  The other issue is that it's not always obvious what it is
> you're missing when you don't understand something.  e.g. in QM it's
> common to speak of SO(3) symmetries, etc, etc, but unless you know
> what that refers to, how can you know that the relevant material can
> be learnt in a text on Lie Groups?  And that before looking at Lie
> Groups, you'd better get a good handle on group theory and linear
> algebra? RTR helped in that respect, as it provided a bit of a road
> map.

Yes, I think this and the "guide" idea is pretty much solve
by RTR.  Even Penrose's bad explainations show you what you
need to know to understand the subject.


> Absolutely - that helps a lot.  So read "by topic" instead of "by
> book".  For instance, I found that learning GR (on my own) from a
> single book was virtually impossible - only when I started reading
> various books, and getting different perspectives, did the
> mathematics "sink in".

This is so true that I actually consider "post-it flags" a significant
part of my learning strategy <grin> since I have dozens of books and
papers with one or more such book marks in them that I read in rotation.

This is actually one of the reasons it took me "2 months" to read RTR,
as I actually read several other books and many papers in pararrel
with it.

> > Below was [I cut if for responding in a separate message] one of
> the
> > best overview explanations of Fiber Bundles that I have seen.
> >
>
> Thanks, but please be careful not to read too much into it - it
> wasn't intended to be rigorous.  I probably glossed over some
> important points, and was very loose with what I was saying.  Maybe
> others may be able to correct any mistakes.

Of course not, I praised it as a good overview, something to give an
intuitive understanding and a direction for actually studying the subject.

I had actually worked out most of it, but had I read it (and
recognized its importance) earlier it would have helped a lot.

For instance, I still don't believe (have to finish re-reading to be
sure) that Penrose EVER mentioned WHY he was discussing Moebius strip
bundles -- the main reason being as an example of a NON-trivial bundle
versus the trivial cylinder or how trivial bundles and non-trivials
bundles differ PRACTICALLY.

(By the way, the "Falling Cat" stuff I mentioned elsewhere gets into
this a bit.)

> > You are going to be a great addition to the list since you clearly
> > have some significant mathematical background and also know how to
> > cut to the important points for developing a clear base of
> understanding.
>
> Thank you, but I struggle with new material just as much as anyone,
> and there's plenty in RTR that was new to me.  I hope that people
> won't be too hard on me when I fail to understand something. :-)

No one here is hard on anyone so far.  If you want that you will have
to post in sci.physics <grin>

Someone MIGHT correct you if they think you state something
incorrectly but most of us here just want to learn and want all the
questions AND answers we can share....

> For instance, at my university, GR, QFT, Lie Groups, Manifolds were
> barely mentioned in senior courses - the meaty stuff was left for
> the honours year and beyond. And Strings - forget it! Unfortunately,
> I didn't get that far in science, I needed to get a proper job :-)
> (no offense intended to anyone! :-))  So I have had to make up for
> it on my own.

That seems to be pretty much the norm.  Special Relativity might even
be a FRESHMAN topic at a top university but GR and the rest (except
for QM) are pretty much left to graduate school.

> Right now I'm trying to get my brain around the Standard Model and
> QFT - unfortunately, though RP offers some tantalising glimpses, I
> find I really need to refer to other texts to make sense of what
> he's trying to say.  I've done QM, but QFT is just one of those
> subjects that we didn't touch on at uni.


For light mathematical BUT SIGNIFICANT depth of gauge theories and the
Standard Model I cannot recommend "Deep Down Things" by Bruce A.
Schumm strongly enough.

It includes a significant explanation of Lie Groups at a conceptual
(non-rigorous, non-mathematical) level but clearly tying Lie Groups to
their PRACTICAL meaning in the Standard Model and Gauge Theories.

It is both better than RTR for clarity and worse for narrow coverage.
Schumm is a REAL teacher.

I wonder if anyone has read and can comment on these:

"A Unified Grand Tour of Theoretical Physics", 2nd edition (Paperback)
by Ian D. Lawrie

"An Introduction to General Relativity and Cosmology" by Jerzy
Plebanski, Andrzej Krasinski

--
Herb

--- Francis Fung <fycfung@...> wrote:
>
> Hello! I'm another new member; I've always wanted to
> learn something about GR and QM. Thanks for putting
> this together.

Welcome to you also!

> Regarding your question, I was recently browsing
> through Barnard Schutz's "Geometrical Methods of
> Mathematical Physics", a Cambridge book. I cannot say
> that I have read more than a few bits of it, but it
> seemed quite nice, and the table of contents indicates
> several sections devoted to physics applications of
> fibre bundles. Also, there is a whole chapter on "Lie
> Derivatives and Lie Groups", together with a
> bibliographic note on p. 112 saying that for more
> details on this relationship, one can refer to F.
> Warner, Spivak, and Auslander/MacKenzie (all
> differential geometry texts, the last of which is
> available in a Dover reprint).

I think the book is good too although I didn't buy
it.  I ran across it in a book store and almost
bought it on "impulse" but resisted and for various
reasons later purchased:

"The Geometry of Physics: An Introduction" by Theodore Frankel

Although I like this book too, and have read an appreciable amount of
it, it has occurred to me that purhaps the Schutz book would have been
a better choice.

Anyway, I must resist "buying everything" until I have read more of
what is already in my library and on my computer <sign>

Right now, my focus is on several articles about "Falling Cats" and
"Berry Phase".  (Google for a couple of good, short articles which
include terms like magnetic monopole, bundles, pararrel parking,
connection, and gauge theory.)

Falling Cats
http://philsci-archive.pitt.edu/archive/00000794/00/falling-cats.pdf
Berry's phase and Fine Structure
http://www.quanics.com/alfa137MN6.pdf
Vector Bundles & K-Theory
<http://www.math.cornell.edu/~hatcher/VBKT/VBpage.html>
Fibre Bundles and Gauge Theory  109 pages
Johan Dupont
http://www.math.mcmaster.ca/~ohagans/pdf/fiberbundles.pdf
<http://www.math.mcmaster.ca/~ohagans/index.php?menu=4>

--
Herb

Hello! I'm another new member; I've always wanted to
learn something about GR and QM. Thanks for putting
this together.

Regarding your question, I was recently browsing
through Barnard Schutz's "Geometrical Methods of
Mathematical Physics", a Cambridge book. I cannot say
that I have read more than a few bits of it, but it
seemed quite nice, and the table of contents indicates
several sections devoted to physics applications of
fibre bundles. Also, there is a whole chapter on "Lie
Derivatives and Lie Groups", together with a
bibliographic note on p. 112 saying that for more
details on this relationship, one can refer to F.
Warner, Spivak, and Auslander/MacKenzie (all
differential geometry texts, the last of which is
available in a Dover reprint).

Best wishes,
Francis Fung

--- herbmartin52 <herbmartin@...> wrote:

> What is the relationship between a Lie Derivative,
> commonly
> seen in General Relativity texts, and Lie
> Groups/Algebras?
>
> Is there any significant?
>
>
> New finds in Relativity follow:
>
> Lecture Notes on General Relativity by Matthias Blau
> (185 pages):
>
http://chaos.swarthmore.edu/courses/Phys130_2004/LectureNotes/Blau_Notes.pdf
>
> More stuff:
> http://chaos.swarthmore.edu/courses/Phys130_2004/
>
> --
> Herb Martin
>
>
>
>
>
>


__________________________________________________
Do You Yahoo!?
Tired of spam?  Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

--- In rtrfans@yahoogroups.com, "herbmartin52" <herbmartin@...>
wrote:
>
> --- "milongadude" <milongadude@> wrote:
> > --- "herbmartin52" <herbmartin@>
> > wrote:
>
> > Hi Herb.  I probably know analysis best. It's a very elegant
part of
> > mathematics.
>
> While I know what analysis means, I still find that I
> am unsure of what your expertise would be.  Would that
> just simply be Real and Complex Analysis or something
> beyond these subjects...?
>

Basically stuff based on limits, continuity, convergence etc.. even
going beyond that into metric spaces and the like.  So real and
complex analysis both fit the bill.  But I hesitate to call it
my "area of expertise" - although maths was a major in my science
degree, I can't say I specialised in the subject, as I continued
with EE (and ended up in information technology... go figure).

Analysis is just what I'm most comfortable with, by no means am I
an "expert" - I just tremble less when faced with an analysis
problem than when faced with, say, a number theory problem :-)


> "Visual Complex Analysis" is one of those delightful books
> that cuts through the complexity and makes the truly
> complicated as simple as possible.

I'll be sure to keep an eye out for it, thank you!

>
> For Differential Equations and Linear Algebra I have been
> watching the MIT Open Courseware videos which are practically
> as good as being in the lecture hall.  (Recitations and tutorials
> are the only things missing.)
>

Hmmm.. yes, I've had a look at some of these, they're very good!
Hopefully other universities will follow suit - but as a lecturer
once said to me, academic staff on the whole are ambivalent about
this trend, as it allows universities to take a lot of power away
from them.

>
> > The web, however, is a blessing - there is free material out
there
> > at all levels.  The trouble is trying to find material that is
at
> > the right level: not so easy that you know it all already, and
not
> > so hard that you can't get past the first few paragraphs.
>
> Exactly.  I have gigabytes of PDF,PS,DejaVu, and other format files
> that I have collected over the last six months and page after page
> of links (in OneNote) pointing to the source of those items and
> much more.

Aha.  The other issue is that it's not always obvious what it is
you're missing when you don't understand something.  e.g. in QM it's
common to speak of SO(3) symmetries, etc, etc, but unless you know
what that refers to, how can you know that the relevant material can
be learnt in a text on Lie Groups?  And that before looking at Lie
Groups, you'd better get a good handle on group theory and linear
algebra? RTR helped in that respect, as it provided a bit of a road
map.


>
> One thing that is happening laterly is that I keep finding sources
> that seem clearer than previously found, but must be careful not
> to recommend them TOO enthusiastically because some of this is
> due to my being "ready" to understand the subject, or just a form
> of synergism where this explanation combined with all the others
> I have seen causes a breakthrough.

Agreed.

>
> One method learning I have touted here in earlier messages is
> syntopic reading -- i.e., reading many books on the same subject
> in parallel.
>

Absolutely - that helps a lot.  So read "by topic" instead of "by
book".  For instance, I found that learning GR (on my own) from a
single book was virtually impossible - only when I started reading
various books, and getting different perspectives, did the
mathematics "sink in".


> In my previous posts in the archive here are reviews of these
> sources and others.
>
> Below was [I cut if for responding in a separate message] one of
the
> best overview explanations of Fiber Bundles that I have seen.
>

Thanks, but please be careful not to read too much into it - it
wasn't intended to be rigorous.  I probably glossed over some
important points, and was very loose with what I was saying.  Maybe
others may be able to correct any mistakes.

> You are going to be a great addition to the list since you clearly
> have some significant mathematical background and also know how to
> cut to the important points for developing a clear base of
understanding.

Thank you, but I struggle with new material just as much as anyone,
and there's plenty in RTR that was new to me.  I hope that people
won't be too hard on me when I fail to understand something. :-)

For instance, at my university, GR, QFT, Lie Groups, Manifolds were
barely mentioned in senior courses - the meaty stuff was left for
the honours year and beyond. And Strings - forget it! Unfortunately,
I didn't get that far in science, I needed to get a proper job :-)
(no offense intended to anyone! :-))  So I have had to make up for
it on my own.

Right now I'm trying to get my brain around the Standard Model and
QFT - unfortunately, though RP offers some tantalising glimpses, I
find I really need to refer to other texts to make sense of what
he's trying to say.  I've done QM, but QFT is just one of those
subjects that we didn't touch on at uni.

>
>
> Thanks and again, Welcome aboard.
>

Thank you!

--- "milongadude" <milongadude@...> wrote:
> --- "herbmartin52" <herbmartin@>
> wrote:

> Hi Herb.  I probably know analysis best. It's a very elegant part of
> mathematics.

While I know what analysis means, I still find that I
am unsure of what your expertise would be.  Would that
just simply be Real and Complex Analysis or something
beyond these subjects...?

I have been reading "Visual Complex Analysis" by Needham
(a former student of Penrose, and actually included in the
bibliography I believe -- but I found it separately and
coincidentally.)

"Visual Complex Analysis" is one of those delightful books
that cuts through the complexity and makes the truly
complicated as simple as possible.

You likely know all of this but if you see it in a book
store you definitely should thumb through it and see if
you would enjoy just reading it, or using it if you teach.

> > Apparently, I have about the least amount of formal math
> > and physics (at least of those willing to admit it.)
> >
>
> There are probably *some* benefits to taking some formal courses,
> but I doubt that there's much that can't be learnt at home with a
> text.  Plus, at home, no-one is forcing you to learn material you're
> not interested in, so you can focus. :-)

For Differential Equations and Linear Algebra I have been
watching the MIT Open Courseware videos which are practically
as good as being in the lecture hall.  (Recitations and tutorials
are the only things missing.)

> > > I saw RTR at the bookshop, and was immediately attracted by the

> > Long had I wished for and proclaimed the need for a book which
> would
> > just start at the beginning and explain whatever math and physics
> > needed to understand the subjects of QM, QFT, Particle Physics,
> > and Relativity.


> The sad reality is that there aren't that many lay people with the
> willingness to learn - so there just isn't a market for such books.

Hopefully the success of RTR will encourage others.

Of course this may be the new "most purchased but least read
book".

> The web, however, is a blessing - there is free material out there
> at all levels.  The trouble is trying to find material that is at
> the right level: not so easy that you know it all already, and not
> so hard that you can't get past the first few paragraphs.

Exactly.  I have gigabytes of PDF,PS,DejaVu, and other format files
that I have collected over the last six months and page after page
of links (in OneNote) pointing to the source of those items and
much more.

One thing that is happening laterly is that I keep finding sources
that seem clearer than previously found, but must be careful not
to recommend them TOO enthusiastically because some of this is
due to my being "ready" to understand the subject, or just a form
of synergism where this explanation combined with all the others
I have seen causes a breakthrough.

One method learning I have touted here in earlier messages is
syntopic reading -- i.e., reading many books on the same subject
in parallel.


> I'm impressed.  So I guess you (and RP) ought to be congratulated!

Much of this is due to Penrose -- the rest due to persistence
and an absolute lack of fear in learning.

I have a theory, give me a book or other source by someone
who really knows the subject AND both remembers what was
hard about it when first learning and knows how to explain
things correctly then I can learn anything.

Whether it is true or not, acting as if it is true will make
anyone "smarter".

> > I finished the book in about 2 months, and now have just passed
> > six months since beginning RTR.  Now I am reading and watching
> > videos on
> > Gravitional Waves, Blackholes & Cosmology (with math), Quantum
> > Mechanics, and General Relativity (in general).
>
> I saw some of the "Elegant Universe" episodes just recently. I enjoy
> these types of programs (otherwise I wouldn't watch them!) but they
> are frustrating in that they rarely contain full explanations of
> anything - most of the time it becomes an exercise in hand-waving!

My wife and I enjoyed that show quite a bit.  We watched it before
purchasing RTR and my only disappointments in Elegant Universe were
that it could have kept going and could have added more math.

But, when I say that I am watching and reading these thing I mean
university level courses (QM from UCSD) or graduate courses in
Relativity (Kip Thorne on Gravitational Waves.)

In my previous posts in the archive here are reviews of these
sources and others.

Below was [I cut if for responding in a separate message] one of the
best overview explanations of Fiber Bundles that I have seen.

You are going to be a great addition to the list since you clearly
have some significant mathematical background and also know how to
cut to the important points for developing a clear base of understanding.

[I will likely comment on the following when I have time to think
it through a bit more -- THANKS, and I never pour out kudos without
reason.  I think my comments and questions will go better in a
separate message but what is here seems even more clear than Penrose.]

Thanks and again, Welcome aboard.

--
Herb

--- In rtrfans@yahoogroups.com, "herbmartin52" <herbmartin@...>
wrote:
>
>
> What area(s) of math do you know best?
>

Hi Herb.  I probably know analysis best. It's a very elegant part of
mathematics.  But I'm interested in virtually everything - of late,
it's been number theory, and set theory.  And now, with RTR, I've
been hitting the tensor theory, calculus on manifolds, and lie group
texts again.

>
> Apparently, I have about the least amount of formal math
> and physics (at least of those willing to admit it.)
>

There are probably *some* benefits to taking some formal courses,
but I doubt that there's much that can't be learnt at home with a
text.  Plus, at home, no-one is forcing you to learn material you're
not interested in, so you can focus. :-)

> > I saw RTR at the bookshop, and was immediately attracted by the
fact
> > that it was supposedly a layman's book that did not shy away from
> > mathematics - impossible!, I thought...
>
> Exactly!!!
>
> Long had I wished for and proclaimed the need for a book which
would
> just start at the beginning and explain whatever math and physics
> needed to understand the subjects of QM, QFT, Particle Physics, and
> Relativity.
>

The sad reality is that there aren't that many lay people with the
willingness to learn - so there just isn't a market for such books.
The web, however, is a blessing - there is free material out there
at all levels.  The trouble is trying to find material that is at
the right level: not so easy that you know it all already, and not
so hard that you can't get past the first few paragraphs.


> Personally I love it -- I am also highly critical of the
weaknesses in
> the book but these criticisms amount to very little when compared
to
> the strengths.
>
> I gave it "Five Stars" on Amazon in my review there, but indicated
> that were there "1000 other similar books" it would likely only get
> two.  As the ONLY attempt to do this, it probably deserves six
stars.
>

I think I agree.

> > I was lucky enough to have the mathematics background to follow
(most)
> > of the book this far - however, it's left me with serious doubts
that
> > anyone without the right background could make any sense of
it... it
> > seems most people would agree.
>
> It can be done.  My math was "advanced High School" or at
best "First
> Year College" and this book has brought me a world of success.
(Yes,
> I put in a great deal of work, but the title "Complete GUIDE" was
true
> for me.)

I'm impressed.  So I guess you (and RP) ought to be congratulated!

>
> I finished the book in about 2 months, and now have just passed six
> months since beginning RTR.  Now I am reading and watching videos
on
> Gravitional Waves, Blackholes & Cosmology (with math), Quantum
> Mechanics, and General Relativity (in general).

I saw some of the "Elegant Universe" episodes just recently. I enjoy
these types of programs (otherwise I wouldn't watch them!) but they
are frustrating in that they rarely contain full explanations of
anything - most of the time it becomes an exercise in hand-waving!

>
> Pretty good, since I had to teach myself Differential Equations and
> Tensor Analysis during this period.  Now, I am approaching an
> understanding of MODERN Differential Geometry and Lie
Groups/Algebras.
>

Excellent!

>
> Agreed.  Fiber bundles still present difficulties for me -- not so
> much the "what" but rather the practical "why do we care" or "why
work
> so hard".  I suspect this is mostly just very poor explanations by
> everyone (no criticism of Penrose here especially) since all of the
> resources I have found tend to have the same lack of clarity and
> practical motivation.


I could try to give my take on them... if you like.

Take a manifold of dimension N, and say you want to assign to each
point of the manifold a space of it's own, of dimension M.  Then the
whole setup becomes a fibre bundle, with each point of the base
manifold dim N being associated with a "fibre" dim M.  You probably
know this already.

The obvious question is then: why bother with fibres at all?  Why
not simply define a broader manifold of dimension N+M?  Wouldn't
this be equivalent to the fibre bundle above?  Well, no.  The
difference is that there need be *no* identification between points
on different fibres, whereas in the broader manifold of dim N+M
there IS a natural identification.

For instance: when you go from ordinary fixed 3-D vectors in R^3 to
vectors on manifolds, students get confused.  Why? Because in R^3
you're taught that, if two 3-D vectors have the same components,
then they are in some way equivalent, regardless of where in R^3 the
vector is located.

But we know that in a general 3-dim manifold it's not quite like
that, a vector on one point in the manifold is not necessarily the
same as a vector on another point, even if the components of the
vector are identical.

We need some way of making it clear that the tangent vector space on
one point is a completely different beast to the tangent vector
space on a different point - and cannot be compared.

So how do we express this?  We need to define a structure where each
point in the 3-dim manifold (let's call that the base space) has
it's own 3-D vector space (let's call that the fibre, with each
vector becoming an element or "point" of the fibre).

Then we state that in this structure you can't naturally equate a 3-
D vector on one fibre with another 3-D vector on another fibre (i.e.
that there is no natural identification between points on different
fibres).

But this is what characterises a fibre-bundle, the lack of a natural
identification between points across fibres!

Of course, you're free to *define* your identifications - via
connections -  but these are defined *on* the bundle by you, they
aren't defined *by* the bundle and forced on you.

All of this could also be done with a generalised N+M manifold
instead of an M-dim fibre bundle defined on an N-dim manifold - the
mathematics would work out, and you'd end up with the same result,
but it would be more complicated, and you'd always have to remember
when it's permissible to compare points and when it's not, you'd
need to define what the permissible operations are.

If you talk of a fibre bundle, people automatically know it's not
possible to compare vectors on one fibre with another.  No one will
attempt to, say, differentiate naively by taking the difference
between vectors at two different points.  They will know that one
must first define a connection before we can talk about
differentiation.

--- "susan_jane_fischer" <susan_jane_fischer@...> wrote:
> As per the group's regulations I am posting to introduce myself to
> other members. My name is Susan, and I am currently studying for a
> BSc. degree in physics.

Excellent.  Welcome!

Please excuse the delay in (any of us) posting a welcome,
we really are friendly and helpful to each other but most
here are quite busy with our "other life".


> I came across "Road to Reality" in our department bookstore. I liked
> what I've read so far [Ch. 24 and counting] (excepting the highly
> esoteric and convoluted technical stuff).

You have pretty much beat the "hard parts" so just
keep reading and enjoying the book, especially the
parts that are clear.

Note:  The book RTR is fantastic but it is far from
perfect and not all of the areas are as clearly explained
as others.

> Note: by the way I've just
> completed my first year... so I really can't claim to possess any
> knowledge of the higher-level materials; one reason for me joining
> this group.

Then you are to be especially encouraged, with only
first year math and physics this book is VERY difficult
to complete.  (I know because although I left school
long ago, that WAS about the extent of my math and
physics knowledge.)

> My prof tells me this is what most grad students in
> physics study, so I won't have to worry about most (not all) of this
> material until my final year... YIKES!!! However, it's a good start
> if someone wants to ace their upper-level courses. ;)

True, considering that Penrose reaches Calculus by chapter
six and "complex calculus" (complex analysis) by the seventh,
it is clear that the other chapters on math will take you
far past undergraduate subjects.  String theory and Quantum
Gravity are seldom undergraduate subjects either (except
perhaps in the final year, and then at a fairly light level.)

But also notice that if he 'covers Calculus' in and by chapter
six the coverage must be very sketchy.

Remember this when the going gets rough in some later chapter.

[I actually thought the chapter on calculus was on of the worst
in the book -- having a pretty good understanding of calculus
it was clear to me he was leaving out critical ideas AND not
doing a very good job on the concepts he did cover.]

> I think this is really a wonderful resource for physics students;

Agreed.  I have learned more math and physics due to the
outline and guide provided by Penrose than I would ever have
expect from any other book.


> however, all this abstract material can become really daunting.

Well, "daunting" means 'creating fear', so I would prefer 'become
realy challenging' or perhaps better, 'require a LOT of effort and
determination."

One sig line I have used when asking questions motivated by reading
RTR is:

     "Mathimatically naive, but undaunted."

> That's why, following my senior's advice, I am listing down all the
> major problems I am encountering while I read this work; forums like
> this will make my reading much less cumbersome and more informative.

Good plan.

While I am not (usually) the person to ask for deep math or physics
knowledge, please let us know which areas or questions you have.

Even if I cannot answer your questions directly, I have a huge set of
links and material that I have collected on pratically ever area of
the book.

And, there are several people here who may be able to respond directly
to questions.

Also note that Usenet had groups unders sci.math and sci.physics which
may not be as friendly as this group but which are definitely a good
resource for focused math and physics questions (just ignore the
trolls and nutjobs though.)

> Great site!
> Susan

It will get better with every question you (or any of us) ask or try
to answer so please ask your questions....

No one here will disparage your level of knowledge since no one has
been anything but helpful to me with even less preparation.

Let's help each other....

--
Herb

--- "milongadude" <milongadude@...> wrote:
> Hi All,
> Since the practice here is to write a short intro whenever someone
> joins a group, I'll follow suit.

Not everyone follows the practice but it's a good one.

Welcome!

> I have a BSc in Mathematics, a BE (Hons) in Electrical Engineering,
> and finally a BA in History (yeah, I'm a jack of all trades, but
> really a master of none).

What area(s) of math do you know best?

> I've wanted to do physics and mathematics from childhood, but
> life has taken me in a different direction.
> I haven't lost my interest in these subjects, so I still read plenty
> on them, and have my bookshelves stacked with relevant books.

This probably describes a most of us who are on this list.

Our backgrounds are different of course, but our interests
pretty much match.

Apparently, I have about the least amount of formal math
and physics (at least of those willing to admit it.)

> I saw RTR at the bookshop, and was immediately attracted by the fact
> that it was supposedly a layman's book that did not shy away from
> mathematics - impossible!, I thought...

Exactly!!!

Long had I wished for and proclaimed the need for a book which would
just start at the beginning and explain whatever math and physics
needed to understand the subjects of QM, QFT, Particle Physics, and
Relativity.

> Anyway, I'm about 1/2 way through the book now (ch 22), and thought
> I'd look around on the net to see what others thought of the book.

Personally I love it -- I am also highly critical of the weaknesses in
the book but these criticisms amount to very little when compared to
the strengths.

I gave it "Five Stars" on Amazon in my review there, but indicated
that were there "1000 other similar books" it would likely only get
two.  As the ONLY attempt to do this, it probably deserves six stars.

> I was lucky enough to have the mathematics background to follow (most)
> of the book this far - however, it's left me with serious doubts that
> anyone without the right background could make any sense of it... it
> seems most people would agree.

It can be done.  My math was "advanced High School" or at best "First
Year College" and this book has brought me a world of success.  (Yes,
I put in a great deal of work, but the title "Complete GUIDE" was true
for me.)

I finished the book in about 2 months, and now have just passed six
months since beginning RTR.  Now I am reading and watching videos on
Gravitional Waves, Blackholes & Cosmology (with math), Quantum
Mechanics, and General Relativity (in general).

Pretty good, since I had to teach myself Differential Equations and
Tensor Analysis during this period.  Now, I am approaching an
understanding of MODERN Differential Geometry and Lie Groups/Algebras.

> On the other hand, I doubt anyone
> could have made a better effort of bringing advanced mathematics to
> beginners than Penrose (in a single volume! going from fractions to
> calculus on manifolds, with applications!  most people would have
> thought it impossible...)

It COULD have been better but certainly no one has done that yet.

> However, it's becoming one of my favourites on the subject - alongside
>  Feynman's lectures (BTW, I always wished that Feynman would have
> covered in his lectures stuff like QFT and an in-depth GR, but
> unfortunately he stopped at the 2nd / 3rd year level.  And I wish
> someone would do a "Feynman" on mathematics, just as he did on
physics...)

That would be very exciting.

> To those that are daunted, don't despair!  Some of the material in
> RTR is graduate level stuff - normally you would have to spend 3-4
> years at university before looking at it.

Agreed.  Fiber bundles still present difficulties for me -- not so
much the "what" but rather the practical "why do we care" or "why work
so hard".  I suspect this is mostly just very poor explanations by
everyone (no criticism of Penrose here especially) since all of the
resources I have found tend to have the same lack of clarity and
practical motivation.

> Anyway, hello to everyone!
> Cheers,
> milongadude.

Cheers to you also, and again Welcome!

I have a large set of links on most every RTR topic, many of them
already posted to this groups but if you need anything please ask.

There are a couple of smart people here (who are willing to answer
questions) so you may even get direct help with questions.

--
Herb

Hi All,

Since the practice here is to write a short intro whenever someone
joins a group, I'll follow suit.

I have a BSc in Mathematics, a BE (Hons) in Electrical Engineering,
and finally a BA in History (yeah, I'm a jack of all trades, but
really a master of none).

I've wanted to do physics and mathematics from childhood, but life has
taken me in a different direction.

I haven't lost my interest in these subjects, so I still read plenty
on them, and have my bookshelves stacked with relevant books.

I saw RTR at the bookshop, and was immediately attracted by the fact
that it was supposedly a layman's book that did not shy away from
mathematics - impossible!, I thought...

Anyway, I'm about 1/2 way through the book now (ch 22), and thought
I'd look around on the net to see what others thought of the book.

I was lucky enough to have the mathematics background to follow (most)
of the book this far - however, it's left me with serious doubts that
anyone without the right background could make any sense of it... it
seems most people would agree.  On the other hand, I doubt anyone
could have made a better effort of bringing advanced mathematics to
beginners than Penrose (in a single volume! going from fractions to
calculus on manifolds, with applications!  most people would have
thought it impossible...)

However, it's becoming one of my favourites on the subject - alongside
  Feynman's lectures (BTW, I always wished that Feynman would have
covered in his lectures stuff like QFT and an in-depth GR, but
unfortunately he stopped at the 2nd / 3rd year level.  And I wish
someone would do a "Feynman" on mathematics, just as he did on physics...)

To those that are daunted, don't despair!  Some of the material in
RTR is graduate level stuff - normally you would have to spend 3-4
years at university before looking at it.

Anyway, hello to everyone!

Cheers,

milongadude.

What is the relationship between a Lie Derivative, commonly
seen in General Relativity texts, and Lie Groups/Algebras?

Is there any significant?


New finds in Relativity follow:

Lecture Notes on General Relativity by Matthias Blau (185 pages):
http://chaos.swarthmore.edu/courses/Phys130_2004/LectureNotes/Blau_Notes.pdf

More stuff:
http://chaos.swarthmore.edu/courses/Phys130_2004/

--
Herb Martin

Hi,

As per the group's regulations I am posting to introduce myself to
other members. My name is Susan, and I am currently studying for a
BSc. degree in physics.

I came across "Road to Reality" in our department bookstore. I liked
what I've read so far [Ch. 24 and counting] (excepting the highly
esoteric and convoluted technical stuff). Note: by the way I've just
completed my first year... so I really can't claim to possess any
knowledge of the higher-level materials; one reason for me joining
this group. My prof tells me this is what most grad students in
physics study, so I won't have to worry about most (not all) of this
material until my final year... YIKES!!! However, it's a good start
if someone wants to ace their upper-level courses. ;)

I think this is really a wonderful resource for physics students;
however, all this abstract material can become really daunting.
That's why, following my senior's advice, I am listing down all the
major problems I am encountering while I read this work; forums like
this will make my reading much less cumbersome and more informative.

Great site!

Susan

This intriguing flash demonstration of "Imagining
the Tenth Dimension" was unconvincing to me:

   http://www.tenthdimension.com/flash2.php

...but I am posting it in case you might find it
either amusing or useful.  It takes about 10 minutes
to view.

(My criticism is that after dimension 3 they used versions
of either time or alternate realities/universes as the
model but you might disagree and I would love to hear
if you find it useful.)

Also, since the site was referencing string theory which
they state uses 10 dimensions of space plus 1 of time,
they left out one by counting to 10 while using time for
#4.

--
Herb

On 19/07/2006, at 5:28 AM, herbmartin52 wrote:
>> In other words, the phase space is a cotangent bundle on the
>> configuration space.
>
> I have not seen it written that way, but rather
> as both the tangent bundle and the cotangent bundle
> being structures on the base space and that with
> the proper metrics a connection is available between
> cotangent and tangent bundles OR alternatively that
> they are usually considered dual spaces.

But that's a separate issue right?

I'm saying the phase space is a fiber bundle with the configuration
space as the base.

That's a separate concept from the tangent bundle and the cotangent
bundles being dual (and the metric providing a mapping between the two).

I actually found the description of the phase space as a fiber bundle
helpful in understanding what a fiber bundle *is* - particularly a
tangent bundle.

If we, for a moment, take the phase space to be *velocity* rather
than momentum based (to get around the tangent vs cotangent issue,
which I still haven't internalized) then the phase space seems to be
the example par excellence of a tangent space.

> (I read:) There are alternative definitions where the
> cotangent bundle is defined independently of the
> tangent bundle for those cases where no such metric
> exists.
>
> While I can throw these words around as if they mean
> something (and I can memorize definitions and such),
> the physical and practical meaning of such terms,
> structures, and distinctions still seems like trying
> to grab hold of mist or (the notorious) "nailing jelly
> to a tree."

I think the struggle I'm having is just on what a cotangent space
means geometrically.  The idea of using the cotangent space for
momenta seems like just a hack to get the Poisson bracket to come out
nicely :-)

James

--- In rtrfans@yahoogroups.com, James Tauber <jtauber@...> wrote:
> Doesn't the configuration space just refer to the possible
> *positions* and the phase space the possible positions *and momenta*?

From what I understand this is correct (as long as
we generalize the latter phase space in other contexts
to include observables other than just momentum but
in, as you indicate, definitely in addition to mere
position.)

> In other words, the phase space is a cotangent bundle on the
> configuration space.

I have not seen it written that way, but rather
as both the tangent bundle and the cotangent bundle
being structures on the base space and that with
the proper metrics a connection is available between
cotangent and tangent bundles OR alternatively that
they are usually considered dual spaces.

(I read:) There are alternative definitions where the
cotangent bundle is defined independently of the
tangent bundle for those cases where no such metric
exists.

While I can throw these words around as if they mean
something (and I can memorize definitions and such),
the physical and practical meaning of such terms,
structures, and distinctions still seems like trying
to grab hold of mist or (the notorious) "nailing jelly
to a tree."

> I wondered why the *co*tangent bundle rather than just the tangent
> bundle and found this:
> http://www.lepp.cornell.edu/spr/2002-01/msg0038327.html

I wondered that too, and despite reading the above and
several other sources, the only concrete reason I can
see is given in that reference by Baez concerning the
"natural way to define" the poisson bracket.

>  > Why not the tangent bundle?  Well, it turns out that while
>  > velocity is best thought of as a tangent vector, momentum
>  > is best thought of as a cotangent vector.  One reason is
>  > that there's a natural way to define the Poisson brackets
>  > of smooth functions on a cotangent bundle - but not on a
>  > tangent bundle.

This following hierarchy is a loose first attempt as classification
(although I don't mean to imply that all sibling [etc] nodes are
mutually exclusive):

Fiber bundle
   Vector bundle
     Tangent bundle
     Cotangent bundle
   Principal bundle
     Frame bundle
   Hopf Bundle
   Sphere bundle
   Associated bundle
   Pullback or induced bundle
   Universal bundle

This whole topic remains a gray area for me and any clarification or
references to useful sources is much appreciated.

--
Herb

By the time you finish RTR you realize that Penrose is generally
negative towards String Theory, at least as a total and final theory
of Reality.

While Penrose does cover String theory he does not provide nearly the
level of actual understanding or mathematical reasoning he explained
so well in the other sections of RTR.

I am completely unqualified to have an (informed) opinion concerning
the efficacy of String Theory but it does seem that many very smart
and qualified people share Penrose's doubts, mainly on the grounds
that String theory predicts little, offers no plan for experiment, and
so far seems totally unprovable AND unfalsifiable.

Obviously, there are also some (other) very smart people who think
that the String is the Thing (to research and use for further
understanding.)

And as Penrose shows in his review, the vote by participant and by
papers is something like 2 to 1 in favor of Strings and against other
paths to the road to reality.

But can we understand Strings enough to begin having our own opinion?

Maybe, and we can certainly TRY.  (My own suspicion is that Loop
Quantum Gravity will be a big part of the solution, perhaps WITH
String Theory.)

Introduction to String Theory (from Spain 528 pages)
http://gesalerico.ft.uam.es/paginaspersonales/angeluranga/Lect.pdf

Geometry, Topology and String Theory
by Uday Varadarajan (Thesis 163 pages)
http://zippy.ph.utexas.edu/~udayv/thesis.pdf

Amazing bid by Thiemann to absorb string theory into LQG    .
<http://www.physicsforums.com/archive/index.php/t-13263.html>
LQG -- String: Loop Quantum Gravity Quantization of String Theory I.
Flat Target Space
<http://arxiv.org/hep-th/0401172 >

String Theory Lectures
<http://www.math.duke.edu/computing/Broadcasts/StringTheory.html>

K3 Surfaces and String Duality
<http://arxiv.org/abs/hep-th/9611137>

SUPERSTRINGS! Tutorial
<http://www.sukidog.com/jpierre/strings/tutor.htm>

Special Lecture Series on F-Theory
<http://www.math.duke.edu/computing/Broadcasts/F-Theory.html>

String Coffee Table by Urs Schreiber
<http://golem.ph.utexas.edu/string/archives/urs.html>

Strings 05 Conference July 11-16,2005-talks
<http://www.fields.utoronto.ca/audio/05-06/#strings>

Special Lecture Series on F-Theory
<http://www.math.duke.edu/computing/Broadcasts/F-Theory.html>

Ian Swanson: Tangled Physics: Superstring Theory and the AdS/CFT
Conjecture 4/24/2003
[cable/DSL] [broadband] [56k modem] 36 minutes
Ian Swanson, a graduate student in physics at Caltech, discusses the
quantum field theory is known as the Standard Model of particle
physics, providing the most accurate physical predictions in the
history of science. Physicists must now unite the Standard Model with
the tenets of general relativity, and string theory is arguably the
most promising candidate of the last 50 years.

John Schwarz's "String Theory: Past, Present, and Future" 2/11/2004
[56k modem] [broadband] [cable/DSL] 38 minutes
String theory connects the microscopic quantum world of elementary
particles to the macroscopic world of gravity and geometry. John
Schwarz, Harold Brown Professor of Theoretical Physics at Caltech,
presented this talk with a historical overview of the subject. He also
discusses (without the technical details) some of the problems that
are yet to be overcome.
<http://today.caltech.edu/theater/results.tcl?query_string=quantum>

Conference: Geometry and Topology of String Theory
2004 <http://math.northwestern.edu/~getzler/Strings/>

--
Herb

I gave the [WRONG] title for the better document:

"herbmartin52" wrote>
> 2) [WRONG] "An Introduction to Tensors for Students of Physics and
> Engineering"  ([WRONG]NASA TM-2002-211716 [WRONG]) by Joseph Kolecki.

> There are TWO tensor papers by Kolecki of NASA, the shorter one is
> about 30 pages and not nearly as good as this longer one (about 120)
> pages.  Both are worth reading independently, not nearly as much
> redundancy as I expected when I recently found the one listed here.

Even though I was aware how close these two document titles are, I
confused the NAMES of the two Kolecki "tensor" articles, and I must
apologize for the confusion but the longer and better article is NOT
the one above but rather:

The better article is NASA/TP—2005-213115:
"Foundations of Tensor Analysis for Students of Physics and Engineering
With an Introduction to the Theory of Relativity"
http://gltrs.grc.nasa.gov/cgi-bin/GLTRS/browse.pl?2005/TP-2005-213115.html
http://gltrs.grc.nasa.gov/reports/2005/TP-2005-213115.pdf

Key differences in title etc:
Date in 2005, longer title which mentions 'analysis' and also the
"theory of relativity".

Sorry about that (especially  if anyone wasted time downloading the
wrong article only -- they are however both GOOD).

--
Herb

--- In rtrfans@yahoogroups.com, "knarfian" <palazzol@...> wrote:
> I'll just jump in and add...

Excellent!

> ... the a Phase Space is a familiar concept to
> engineers, since it applies to all possible states of classical
> systems, like mechanical systems or electrical circuits.

That makes perfect sense with the definitions that I
found and finally came to understand.

> The notion of a Configuration Space, which spans "all possible
> systems" of some kind, that one I've only seen in Physics books -
> usually applied to quantum systems.

All possible positions (e.g., of particles) seems to be
what is generally meant by Configuration Space or Manifold.

> I haven't even gotten to the Physics part of Penrose yet, so I hope
> this comment isn't redundant with something in there :)

Penrose opens the discussion of the Configuration and Phase
Spaces in RTR Chapter 12 and returns to them in RTR Chapter 20
where he indicates that (paraphrasing but close to an actual
quote):

< The Langrangian is a (smooth) function on the Tangent Bundle of
the Configuration Space, while the Hamiltonian is a (smooth)
function on the Cotangent Bundle of the Phase Space. >

I struggled through these sections on first reading RTR, although I
did learn quite a bit about Langrangians and Hamiltonians
eventually (and I am also sure I missed many of the details.)

> -Frank

Thanks Frank.

Finally, I have found a really clear and memorable understanding of
the critical differences between covariant and contravariant vectors
and other tensors.

My new understanding and confidence is due to two free and online sources:

1) The General Relativity Section (esp. Chapters 23-24) of the
Blandford and Thorne book "Applications of Classical Physics" which I
mentioned in a recent post.

2) "An Introduction to Tensors for Students of Physics and
Engineering"  (NASA TM-2002-211716) by Joseph Kolecki.

There are TWO tensor papers by Kolecki of NASA, the shorter one is
about 30 pages and not nearly as good as this longer one (about 120)
pages.  Both are worth reading independently, not nearly as much
redundancy as I expected when I recently found the one listed here.

As I mentioned, I may be onto some simple yet fully technical
explanations of Lie Groups and Algebras as well.

(For instance, I now have a CLEAR picture of the relationship between
a Lie Group and the associated Algebra -- and why we would care about
the differences and distinctions.  The key point is that the Lie
Algebra allows us to LINEARIZE the Lie Group and may make dealing with
the math and implications easier once it is in linear form.)

But I am still puzzling through the rules and features and intend also
to revisit "Deep Down Things" where the Lie Groups are conceptually
related to the rules of the Gauge theory and the characteristics
(e.g., abelian etc.) are related to things such as the mass of the
force carrier or whether the force carrier has the force charge
itself.  (differences found in photons, gravitons, gluons or W/Z bosons)

--
Herb

I'll just jump in and add the a Phase Space is a familiar concept to
engineers, since it applies to all possible states of classical
systems, like mechanical systems or electrical circuits.

The notion of a Configuration Space, which spans "all possible
systems" of some kind, that one I've only seen in Physics books -
usually applied to quantum systems.

I haven't even gotten to the Physics part of Penrose yet, so I hope
this comment isn't redundant with something in there :)

-Frank

Today, I finally got clear on the basic difference and
relationship between Configuration Space and Phase Space.

Configuration Space is the space of all possible physical
positions of the objects being considered, and therefore
a portion of the typical Phase Space which is....

Phase Space is the space of all measurable quantities,
obverables, or degrees of freedom of a system, typically
including both position AND momentum but possible including
other observables such as tempature, pressure, physical
composition, etc. as separate axis in the space or manifold.

--
Herb

PS>  I may finally have found some Lie Groups & Algebra sources
which include close contact with physical systems and practical
interpretaions.  More later if anyone is interested....

Textbook, lectures, animations, Mathematica notebooks:
http://www.courses.fas.harvard.edu/~phys16/Textbook/

Videos link is present but this seems to be restricted to Harvard
student only access. (Drat!)

I found the above through a link on E. F. Taylor's
site supplementing his (and Wheeler's) book on General
Relativity and Black Holes.

The linking page was: "Principle of Least Action"
http://www.eftaylor.com/leastaction.html

There is much there on Least Actiona and Lagrangian
Mechanics.

--
Herb

Einstein's Equation and Twistor Theory: Recent Developments
Dr. Roger Penrose, ITP & Oxford University
http://online.kitp.ucsb.edu/online/gravity99/penrose/

Audio plus (about 20) slides.

--
Herb Martin

> Caltech's Physics 237-2002
> Gravitational Waves
> PART A:  GRAVITATIONAL-WAVE THEORY AND SOURCES
> Course Outline
> http://elmer.tapir.caltech.edu/ph237/CourseOutlineA.html
> (with links to each week, and link to the second half of the course.)

In the assignments for this course, Kip Thorne offers a link to his
graduate level course "APPLICATIONS OF CLASSICAL PHYSICS" which
includes introductions to both Special and General Relativity.  I
highly recommend it for filling in many of the details left vague in
RTR, while not being as long or tedious as most Differential Geometry
and Tensor texts: http://www.pma.caltech.edu/Courses/ph136/yr2004/
(He revises it each year, so get the 2004, or later, version if it
appears -- answers to the exercises are also posted.)

Read Chapters 1 and 23-25 (optionally add 26), plus anything else that
strikes your fancy.  Stated goal of the course: "...to teach the
fundamental concepts, which are not so extensive that they should
overwhelm, and to illustrate those concepts."  Section and even
chapters were designed to be largely self-contained with cross
references for those parts that aren't clear without the whole.


Why did you read "The Road to Reality"?

For me, it was largely about being able to understand the math and
actual science of modern physics, as opposed to mere analogy and
popularization.

Penrose made an implicit and explicit promise to the reader:  Just
keep going.  Skip what you don't understand.  I [Penrose] will get you
through this, if you [the reader] will just pay attention and never
allow yourself to remain stuck.  You may not understand everything
immediately, but as your guide we can get you to as deep an
understanding as you wish, given the amount of work you are willing to
perform.  We will do this (together as reader and guide) much faster,
and with less pain than through other methods such as obtaining a
formal graduate degree in physics.


Obviously, the above is in my words, but Penrose did make such
promises in the Introduction to RTR.

He delivered.

Without being modest about my own diligence (doing the work), or lack
of formal math and physics (having never done the work before), I can
honestly say that the results of Penrose's guidance are surprising and
amazing.

While watching the second half of the fifth Kip Thorne lecture, for
the main purpose of LEARNING the math and physics better, it occurred
to me that not only was Thorne teaching the real physics I had always
wanted to learn, but that I was understanding almost everything and
before reading RTR even the vocabular, much less the math, would have
been almost completely foreign to me.  (E.g., I wasn't even sure of
the distinctions between Div, Grad, Curl, when I started and I
certainly didn't understand Differential Equations or Differential
Geometry.)

So, here I was, trying to use Thorne's lecture to 'learn the math',
and yet this very lecture is one of the things that previously I would
have been delighted to merely be able to follow.

The coolest thing about Thorne's course is that they are DOING
RELATIVITY, using Einstein's equations to develop both the theory of
Gravitional Waves and then to understand both the design and of the
detectors and the methods of analyzing the data that will be [is now
being] collected.

Prior to watching the first couple of videos, Gravitational Waves
seemed pretty mundane, but if the LIGO and LISA programs meet
expectations this may be as big a jump in astronomy and cosmology
(mabye even particle physics) as the introduction of radio astronomy
to supplement visual light observations.  Potentially, it will let us
'see' black holes, neutron stars, the Big Bang (back into the 100,000
opaque era), and maybe even string theory 'brane' effects.

Now, as soon as I just read another 20,000 pages or so, the rest
should get easier.  <grin>

In all seriousness, I am a speed reader, and so IF (and WHEN) my
understanding of the vocabulary and math improves to a critical level,
speed reading will become possible even in these subjects.  This goal
is also in sight*, if not yet in hand.

[*I have flashes where it works for short passages, and I did use the
techniques in SOME of RTR.]

Contrary to popular misconception you CAN use speed reading with
technical material, even math, but ANY speed reading is predicated
upon a strong understanding of the vocabulary.

For example, you can't speed read a foreign language until you know
the language well, and you can't speed read Arabic until the
characters no longer appear as separate entities but rather words, and
even sentences, appear and are understandable as larger units without
decoding each character.

I really wish someone else would post something....

My toughest areas are probably Lie Groups now.  Not the basics, but
understanding how to really apply the formal knowledge.

If you enjoy these posts of mine, or if they irritate you, please let
me know.

--
Herb

--- In rtrfans@yahoogroups.com, "herbmartin52" <herbmartin@...> wrote:
> > FWIW - I really enjoyed Kip Thorne's "Black Holes & Time Warps"
> > book when I read it a few years back.

Currently, I am on the fourth class (second week) and enjoying this
immensely.

The first 2 1/2 classes will cover the basics of LIGO, and perhaps
whet your appetite for more.

The class was pitched as graduate level, but Kip (he insists on this
appellation) accepted students without a background in General
Relativity.  The 2nd half of the 3rd class and the entire 4th class
were devoted to GR and Tensor analysis so that everyone could keep up.

Most of you know that I have been self-studying GR and Differential
Geometry for a couple of months and there was nothing in 1-3 that was
beyond my capabilities, but after those Kip felt that some in the
class needed an entire session on the math, and thus devoted all of #4
to the math basics.

The 4th class is a great introduction to Differential Geometry and
Tensors for anyone having trouble on their own.

More and more I feel this is pitched just about the same as RTR.  Math
for those who can follow it; words for those who cannot but have an
interest anyway.

Caltech's Physics 237-2002
Gravitational Waves
PART A:  GRAVITATIONAL-WAVE THEORY AND SOURCES
Course Outline
http://elmer.tapir.caltech.edu/ph237/CourseOutlineA.html
(with links to each week, and link to the second half of the course.)

The first half of the course is theory; the second half is about
detectors and experiment.

--- In rtrfans@yahoogroups.com, "herbmartin52" <herbmartin@...> wrote:
> > FWIW - I really enjoyed Kip Thorne's "Black Holes & Time Warps"
> > book when I read it a few years back.

Currently, I am on the fourth class (second week) and enjoying this
immensely.

The first 2 1/2 classes will cover the basics of LIGO, and perhaps
whet your appetite for more.

The class was pitched as graduate level, but Kip (he insists on this
appellation) accepted students without a background in General
Relativity.  The 2nd half of the 3rd class and the entire 4th class
were devoted to GR and Tensor analysis so that everyone could keep up.

Most of you know that I have been self-studying GR and Differential
Geometry for a couple of months and there was nothing in 1-3 that was
beyond my capabilities, but after those Kip felt that some in the
class needed an entire session on the math, and thus devoted all of #4
to the math basics.

The 4th class is a great introduction to Differential Geometry and
Tensors for anyone having trouble on their own.

More and more I feel this is pitched just about the same as RTR.  Math
for those who can follow it; words for those who cannot but have an
interest anyway.

Caltech's Physics 237-2002
Gravitational Waves
PART A:  GRAVITATIONAL-WAVE THEORY AND SOURCES
Course Outline
http://elmer.tapir.caltech.edu/ph237/CourseOutlineA.html
(with links to each week, and link to the second half of the course.)

The first half of the course is theory; the second half is about
detectors and experiment.

--- In rtrfans@yahoogroups.com, "Frank Palazzolo" <palazzol@...> wrote:
>
>
> FWIW - I really enjoyed Kip Thorne's "Black Holes & Time Warps" book
when I
> read it a few years back.
>
> I realize I've been neglecting this list lately.  This summer has
been full
> of surprises.  I have a plan to get back into Penrose though, in a
big way,
> starting next week.  Herb, thanks for all your contributions in the mean
> time.  I really hope I wont leave you hanging much longer! :)
>
> -Frank

I like Kip Thorne too (who looks vaguely like pictures and Hollywood
portrayals of Gen. Custer).

He seems to be a genuinely nice guy with very few pretentions.

All you have to do is egg me on just a little bit to keep me
posting.... <grin>

More Kip:

Kip Thorne: Einstein's General Relativity, from 1905 to 2005 11/16/2005
[56k modem] [broadband] [cable/DSL] 73 minutes
In an Einstein lecture, Kip Thorne, Feyman Professor of Theoretical
Physics at Caltech, discussed the theory of general relativity, which
Einstein announced 90 years ago in November 1915. Since then,
physicists have struggled to understand and test its predictions. This
struggle has led to theories about black holes, gravitational waves,
and the acceleration of the universe; and at Caltech/JPL, to powerful
tools for probing warped spacetime.
<http://today.caltech.edu/theater/item?story_id=11126>

--
Herb

-----Original Message-----
From: rtrfans@yahoogroups.com [mailto:rtrfans@yahoogroups.com] On Behalf Of herbmartin52
Sent: Friday, July 07, 2006 3:30 PM
To: rtrfans@yahoogroups.com
Subject: [rtrfans] Re: Caltech's Physics 237-2002 Gravitational Waves -- Kip Thorne

--- In rtrfans@yahoogroups.com, "herbmartin52" <herbmartin@...> wrote:
>
> Caltech's Physics 237-2002 Gravitational Waves
> Kip Thorne Course Materials (Real media link works)
> (Other lecturers will appear also.)
> Does NOT assume a course in GR, but rather gives
> a (quick) coverage of GR needed for course.
> 19 Lectures (10 on theory of GW / 9 on detection of GW)
> <http://elmer.tapir.caltech.edu/ph237/CourseMaterials.html>

Warning: I am having trouble finding ALL of the PDF-slide documents
-- they may not exist for later subjects, and I do not yet know if
later videos have readable boardwork or if there is going to be a
serious issue.

Kip Thorne is a member of cajagwr, a CalTech-JPL Gravity Wave
association, and in the first lecture slide set is a reference to the
cajagwr website which includes these presentations:

Gravitional Waves
<http://www.its.caltech.edu/~cajagwr/scripts/seminars.html>

06.27.06
"Searching for Gravitational Waves with Einstein@Home Project"
Teviet Creighton
video pdf
06.13.06
"The Evidence for Astrophysical Black Holes"
Jean-Pierre Lasota
video pdf
04.18.06
"Squeezed States in GW Interferometers"
Nergis Mavalvala
video
04.04.06
"Hunting Correlation Patterns in the CMB Anisotropy"
Tarun Souradeep
video
03.14.06
"Gravitational Wave Bursts from Cosmic Strings: Quantitative Analysis
and Constraints"
Xavier Siemens
video
03.07.06
"Tuning LIGO to Listen to Gravitational Waves"
Rana Adhikari
video
02.28.06
"BBO and the Neutron-Star-Binary Subtraction Problem"
Curt Cutler
video pdf
02.20.06
"Searching for Gravitational Waves from Black Hole Binaries in Data
From the LIGO Detectors: Challenges and Prospects"
Eirini Messaritaki
video pdf
01.03.06
"Compensating Thermal Lensing in Initial LIGO"
Stefan Ballmer
video
12.20.05
"Searches for Periodic Gravitational Waves"
Rejean Dupuis
video pdf
11.15.05
"Can We Detect the Inflationary Gravity Wave Background with CMB?"
Andrew Lange
video
10.11.05
"Experimental Design Tradeoffs for the LISA Mission"
Peter Bender
pdf
08.10.05
"Bayesian Methods Applied to LISA Source Identification"
Graham Woan
video pdf
05.17.05
"Source Modeling, Detection and Science of GW Emitted by Precessing
Compact Binaries"
Alessandra Buonanno
video pdf
05.13.05
"GW Detection Using Radio Pulsar Timing"
Frederick Jenet
video
03.08.05
"Quantum Nondemolition GW Detectors: The Future of LIGO"
Yanbei Chen
video pdf
02.22.05
"LISA Pathfinder and ST7"
William Folkner
video
01.25.05
"Status of VIRGO"
Paolo La Penna
video pdf
12.07.04
"Sensitivity Improvements in the LIGO Interferometers"
Rana Adhikari
video pdf
11.16.04
"LIGO-TAMA Joint Search for GW Bursts"
Patrick Sutton
video pdf
06.01.04
"A Synthetic LISA, with Science and Engineering Applications"
Michele Vallisneri
video pdf
05.18.04
"GW from Binaries with Spin-Orbit Precession"
Benjamin Owen
video pdf
04.13.04
1. Probing Extra Dimensions Using a Superconducting Gravity Gradiometer
2. GW Experiments on the Moon
Ho Jung Paik
video
03.26.04
"Adolescent Years of Experimental Physics"
Vladimir Braginsky
video pdf
03.09.04
"The Most Relativistic Double Pulsar: Implications for GW Detection
and Neutron Star Formation"
Vicky Kalogera
video pdf
03.02.04
"Multidimensional Supernova Simulations"
Adam Burrows
video pdf
01.29.04
"Interferometry for LISA: New Concepts and Experimental Progress"
Daniel Shaddock
video pdf
01.13.04
"LIGO's Continuing Search for GW"
Patrick Brady
video pdf
01.06.04
"The Stochastic GW Background: Prospects for Search and Detection"
Peter Fritschel
video
12.02.03
"Search for GW Signatures of Violent Cosmic Events"
Szabolcs Marka
video
11.18.03
"Data Analysis for LISA Capture Sources"
Curt Cutler
video
10.07.03
"Time-Delay Interferometry for LISA: The Next Generation"
Massimo Tinto
video pdf
06.10.03
"TAMA300: Current Status and Joint Observation with LIGO"
Koji Arai
video pdf [28 MB]
05.06.03
"Search for Stochastic GW Background with LIGO S1 Data"
Albert Lazzarini
video pdf
04.22.03
"Search for GW Bursts in LIGO S1 Data"
Alan Weinstein
video pdf
04.15.03
"First LIGO/GEO Upper Limits on Pulsar Gravitational Emissions"
Teviet Creighton
video pdf
03.11.03
"First LIGO Search for Binary Inspirals"
Peter Shawhan
pdf with embedded audio audio only video slideshow
03.04.03
"LIGO II and LIGO III: The View from Moscow"
Vladimir Braginsky
pdf video slideshow
02.11.03
"Direct Measurement of Mirror Thermal Noise"
Kenji Numata
pdf video
02.04.03
"Studying Galactic Compact Binaries with LISA"
Gijs Nelemans
pdf video slideshow
01.28.03
"Progress in Atomic Clocks and Tests of Fundamental Laws"
Lute Maleki
pdf video
01.14.03
"Tidal Excitation of White Dwarf Oscillations"
Roger Blandford
pdf video
12.03.02
"The Cassini Gravitational Experiment"
John Armstrong
video
11.05.02
"CMB Polarisation and Future Polarimeters"
James Bock
video
10.18.02
"Galileo Galilei: The Space Mission and the Prototype"
Anna Nobili
video
10.08.02
"Long-Term Evolution of Massive Black Hole Binaries"
Milos Milosavljevic
video
05.24.02
"The Late Inspiral of Binary Black Holes: The Epoch When
Post-Newtonian Expansion Becomes Suspect. How Do We Detect
Gravitational Waveforms?"
Alessandra Buonanno
05.17.02
"Quantum Noise in Advanced LIGO Interferometers"
Yanbei Chen
05.07.02
"The Status and Prospects for Resonant GW Detectors"
William Hamilton
video
04.19.02
"The Current Status of the TAMA300 Interferometric GW Detector"
Seiji Kawamura
video
04.05.O2
"Time-Delay Interferometry for LISA"
Massimo Tinto
video
03.15.02
"LIGO Data Analysis for the Recent E7 and Coming S1 Run: Status and
Plans"
Albert Lazzarini
video
03.08.02
"Gravitational Wave Research at Moscow University: Past, Present, and
Future"
Vladimir Braginsky, Farid Khalili
video
03.01.02
"TAMA's Gravitational Wave Search"
Nobuyuki Kanda
video
02.15.02
"Shannon's Theorem, Olbers' Paradox, and the Confusion Limit in
Gravitational Wave Astronomy"
Sterl Phinney
video
01.18.02
"Numerical Relativity: Promises, Status, Challenges, and Prospects"
Luis Lehner
animations
video
12.14.01
"Interferometers for LISA and Its Precursor"
Robert Spero
10.19.01
"Disturbance reduction system - A proposed space demonstration of
drag-free technology"
William Folkner, Robert Spero, Andreas Kuhnert
video
10.05.01
"Gravitational Radiation From the Electroweak Phase Transition"
Arthur Kosowsky
video
06.08.01
"The Capture of Compact Objects by Massive Black Holes, and Its
Implications for LISA"
Sterl Phinney
video
05.25.01
"The VIRGO Gravitational Wave Project: Status and Plans"
Benoit Mours
05.11.01
"Gravitational Waves from Stellar Core Collapse"
Chris Fryer
04.27.01
"The LIGO End-to-End Model and Its Application to LIGO I"
Hiro Yamamoto, Matt Evans
03.02.01
"Gravitational-wave searches via pulsar timing"
Donald C. Backer
02.16.01
"The LIGO-I gravitational wave detectors"
Stan Whitcomb
02.02.01
"Resonant-mass (bar) detectors for gravitational waves"
Eugenio Coccia
01.19.01
"Gravitational wave bursts from cosmic strings"
Alexander Vilenkin
01.05.01
"Noise in LIGO interferometers: Thermorefractive noise, laser
frequency fluctuations of nonlinear origin, electrostatic actuator
noise, and others"
Vladimir B. Braginsky, Valery P. Mitrofanov
12.01.00
"R-Mode oscillations in spinning neutron stars: Are their
gravitational waves detectable by LIGO?"
Lee Lindblom
11.17.00
"LISA: A space observatory for low-frequency gravitational waves"
E. Sterl Phinney, William M. Folkner
11.03.00
"Low-frequency gravitational wave searches using spacecraft Doppler
tracking"
John W. Armstrong
10.13.00
"Quantum noise and quantum nondemolition in gravitational-wave
interferometers"
Kip S. Thorne
09.29.00
"Searching for extremely low-frequency gravitational waves by their
influence on the cosmic microwave background"
Marc Kamionkowski, Andrew Lange
<http://www.its.caltech.edu/~cajagwr/scripts/seminars.html>

--- In rtrfans@yahoogroups.com, "herbmartin52" <herbmartin@...> wrote:
>
> Caltech's Physics 237-2002 Gravitational Waves
>   Kip Thorne Course Materials  (Real media link works)
>   (Other lecturers will appear also.)
>   Does NOT assume a course in GR, but rather gives
>   a (quick) coverage of GR needed for course.
>   19 Lectures (10 on theory of GW / 9 on detection of GW)
>   <http://elmer.tapir.caltech.edu/ph237/CourseMaterials.html>

Warning:  I am having trouble finding ALL of the PDF-slide documents
-- they may not exist for later subjects, and I do not yet know if
later videos have readable boardwork or if there is going to be a
serious issue.

Kip Thorne is a member of cajagwr, a CalTech-JPL Gravity Wave
association, and in the first lecture slide set is a reference to the
cajagwr website which includes these presentations:

Gravitional Waves
<http://www.its.caltech.edu/~cajagwr/scripts/seminars.html>

06.27.06
"Searching for Gravitational Waves with Einstein@Home Project"
Teviet Creighton
video      pdf
06.13.06
"The Evidence for Astrophysical Black Holes"
Jean-Pierre Lasota
video      pdf
04.18.06
"Squeezed States in GW Interferometers"
Nergis Mavalvala
video
04.04.06
"Hunting Correlation Patterns in the CMB Anisotropy"
Tarun Souradeep
video
03.14.06
"Gravitational Wave Bursts from Cosmic Strings: Quantitative Analysis
and Constraints"
Xavier Siemens
video
03.07.06
"Tuning LIGO to Listen to Gravitational Waves"
Rana Adhikari
video
02.28.06
"BBO and the Neutron-Star-Binary Subtraction Problem"
Curt Cutler
video      pdf
02.20.06
"Searching for Gravitational Waves from Black Hole Binaries in Data
From the LIGO Detectors: Challenges and Prospects"
Eirini Messaritaki
video      pdf
01.03.06
"Compensating Thermal Lensing in Initial LIGO"
Stefan Ballmer
video
12.20.05
"Searches for Periodic Gravitational Waves"
Rejean Dupuis
video      pdf
11.15.05
"Can We Detect the Inflationary Gravity Wave Background with CMB?"
Andrew Lange
video
10.11.05
"Experimental Design Tradeoffs for the LISA Mission"
Peter Bender
pdf
08.10.05
"Bayesian Methods Applied to LISA Source Identification"
Graham Woan
video      pdf
05.17.05
"Source Modeling, Detection and Science of GW Emitted by Precessing
Compact Binaries"
Alessandra Buonanno
video      pdf
05.13.05
"GW Detection Using Radio Pulsar Timing"
Frederick Jenet
video
03.08.05
"Quantum Nondemolition GW Detectors: The Future of LIGO"
Yanbei Chen
video      pdf
02.22.05
"LISA Pathfinder and ST7"
William Folkner
video
01.25.05
"Status of VIRGO"
Paolo La Penna
video      pdf
12.07.04
"Sensitivity Improvements in the LIGO Interferometers"
Rana Adhikari
video      pdf
11.16.04
"LIGO-TAMA Joint Search for GW Bursts"
Patrick Sutton
video      pdf
06.01.04
"A Synthetic LISA, with Science and Engineering Applications"
Michele Vallisneri
video      pdf
05.18.04
"GW from Binaries with Spin-Orbit Precession"
Benjamin Owen
video      pdf
04.13.04
1. Probing Extra Dimensions Using a Superconducting Gravity Gradiometer
2. GW Experiments on the Moon
Ho Jung Paik
video
03.26.04
"Adolescent Years of Experimental Physics"
Vladimir Braginsky
video      pdf
03.09.04
"The Most Relativistic Double Pulsar: Implications for GW Detection
and Neutron Star Formation"
Vicky Kalogera
video      pdf
03.02.04
"Multidimensional Supernova Simulations"
Adam Burrows
video      pdf
01.29.04
"Interferometry for LISA: New Concepts and Experimental Progress"
Daniel Shaddock
video      pdf
01.13.04
"LIGO's Continuing Search for GW"
Patrick Brady
video      pdf
01.06.04
"The Stochastic GW Background: Prospects for Search and Detection"
Peter Fritschel
video
12.02.03
"Search for GW Signatures of Violent Cosmic Events"
Szabolcs Marka
video
11.18.03
"Data Analysis for LISA Capture Sources"
Curt Cutler
video
10.07.03
"Time-Delay Interferometry for LISA: The Next Generation"
Massimo Tinto
video       pdf
06.10.03
"TAMA300: Current Status and Joint Observation with LIGO"
Koji Arai
video       pdf [28 MB]
05.06.03
"Search for Stochastic GW Background with LIGO S1 Data"
Albert Lazzarini
video       pdf
04.22.03
"Search for GW Bursts in LIGO S1 Data"
Alan Weinstein
video       pdf
04.15.03
"First LIGO/GEO Upper Limits on Pulsar Gravitational Emissions"
Teviet Creighton
video       pdf
03.11.03
"First LIGO Search for Binary Inspirals"
Peter Shawhan
pdf with embedded audio       audio only       video       slideshow
03.04.03
"LIGO II and LIGO III: The View from Moscow"
Vladimir Braginsky
pdf       video       slideshow
02.11.03
"Direct Measurement of Mirror Thermal Noise"
Kenji Numata
pdf       video
02.04.03
"Studying Galactic Compact Binaries with LISA"
Gijs Nelemans
pdf       video       slideshow
01.28.03
"Progress in Atomic Clocks and Tests of Fundamental Laws"
Lute Maleki
pdf       video
01.14.03
"Tidal Excitation of White Dwarf Oscillations"
Roger Blandford
pdf       video
12.03.02
"The Cassini Gravitational Experiment"
John Armstrong
video
11.05.02
"CMB Polarisation and Future Polarimeters"
James Bock
video
10.18.02
"Galileo Galilei: The Space Mission and the Prototype"
Anna Nobili
video
10.08.02
"Long-Term Evolution of Massive Black Hole Binaries"
Milos Milosavljevic
video
05.24.02
"The Late Inspiral of Binary Black Holes: The Epoch When
Post-Newtonian Expansion Becomes Suspect. How Do We Detect
Gravitational Waveforms?"
Alessandra Buonanno
05.17.02
"Quantum Noise in Advanced LIGO Interferometers"
Yanbei Chen
05.07.02
"The Status and Prospects for Resonant GW Detectors"
William Hamilton
video
04.19.02
"The Current Status of the TAMA300 Interferometric GW Detector"
Seiji Kawamura
video
04.05.O2
"Time-Delay Interferometry for LISA"
Massimo Tinto
video
03.15.02
"LIGO Data Analysis for the Recent E7 and Coming S1 Run: Status and
Plans"
Albert Lazzarini
video
03.08.02
"Gravitational Wave Research at Moscow University: Past, Present, and
Future"
Vladimir Braginsky, Farid Khalili
video
03.01.02
"TAMA's Gravitational Wave Search"
Nobuyuki Kanda
video
02.15.02
"Shannon's Theorem, Olbers' Paradox, and the Confusion Limit in
Gravitational Wave Astronomy"
Sterl Phinney
video
01.18.02
"Numerical Relativity: Promises, Status, Challenges, and Prospects"
Luis Lehner
animations
video
12.14.01
"Interferometers for LISA and Its Precursor"
Robert Spero
10.19.01
"Disturbance reduction system - A proposed space demonstration of
drag-free technology"
William Folkner, Robert Spero, Andreas Kuhnert
video
10.05.01
"Gravitational Radiation From the Electroweak Phase Transition"
Arthur Kosowsky
video
06.08.01
"The Capture of Compact Objects by Massive Black Holes, and Its
Implications for LISA"
Sterl Phinney
video
05.25.01
"The VIRGO Gravitational Wave Project: Status and Plans"
Benoit Mours
05.11.01
"Gravitational Waves from Stellar Core Collapse"
Chris Fryer
04.27.01
"The LIGO End-to-End Model and Its Application to LIGO I"
Hiro Yamamoto, Matt Evans
03.02.01
"Gravitational-wave searches via pulsar timing"
Donald C. Backer
02.16.01
"The LIGO-I gravitational wave detectors"
Stan Whitcomb
02.02.01
"Resonant-mass (bar) detectors for gravitational waves"
Eugenio Coccia
01.19.01
"Gravitational wave bursts from cosmic strings"
Alexander Vilenkin
01.05.01
"Noise in LIGO interferometers: Thermorefractive noise, laser
frequency fluctuations of nonlinear origin, electrostatic actuator
noise, and others"
Vladimir B. Braginsky, Valery P. Mitrofanov
12.01.00
"R-Mode oscillations in spinning neutron stars: Are their
gravitational waves detectable by LIGO?"
Lee Lindblom
11.17.00
"LISA: A space observatory for low-frequency gravitational waves"
E. Sterl Phinney, William M. Folkner
11.03.00
"Low-frequency gravitational wave searches using spacecraft Doppler
tracking"
John W. Armstrong
10.13.00
"Quantum noise and quantum nondemolition in gravitational-wave
interferometers"
Kip S. Thorne
09.29.00
"Searching for extremely low-frequency gravitational waves by their
influence on the cosmic microwave background"
Marc Kamionkowski, Andrew Lange
<http://www.its.caltech.edu/~cajagwr/scripts/seminars.html>

Caltech's Physics 237-2002 Gravitational Waves
   Kip Thorne Course Materials  (Real media link works)
   (Other lecturers will appear also.)
   Does NOT assume a course in GR, but rather gives
   a (quick) coverage of GR needed for course.
   19 Lectures (10 on theory of GW / 9 on detection of GW)
   <http://elmer.tapir.caltech.edu/ph237/CourseMaterials.html>

PDF 'slides' are available; Kip (he insists on this appelation) uses
the slide/page numbers and verbally 'points' to current topic on the
slides to help keep audience synchronized.

Approximately 1/2 of class participants had previously taken taken a
GR course.

From a partial viewing of the first episode this lecture series seems
that it might be at a very similar level as RTR.

Coverage of math and physics necessary to understand the course (by
those without the background) is promised, homework and exercises for
those with the skills and interest to receive credit for the course.


Please help me find any decent video on GR, Diff Geometry, Tensors,
Lie Groups, Particle physics, Cosmology, etc.

There is some video on QM and lesser math (that I have previously
posted); a bit on Lie Groups too, but more is still needed to really
cover these subjects.

--
Herb Martin


More (random) video items I have found in the past day or so:

Elementary College Physics (like MIT 8.01)
	 · Video Lectures (University of North Carolina Wilmington)
	 · Course homepage
<http://freescienceonline.blogspot.com/>

Duke University Multimedia Classroom Video Archives Main Index
<http://www.math.duke.edu/computing/broadcast.html>
String Theory Lectures
<http://www.math.duke.edu/computing/Broadcasts/StringTheory.html>

The Mechanical Universe  52 lectures on video
<http://www.learner.org/resources/series42.html>

· Tom Witelski Math 160  Complex Simultaneous Equ.
Newton's Method
<http://www.math.duke.edu/computing/Broadcasts/Classes.html>