Re: Do you want to review my extremely elementary introduction to Lie groups?
- From: Angus Rodgers <angus_prune@xxxxxxxxxxx>
- Date: Sat, 16 Apr 2005 20:31:57 +0100
On 16 Apr 2005 12:06:27 -0700, "Jeffrey Emanuel"
<jeffrey.emanuel@xxxxxxxxx> wrote:
>I have actually been corresponging with Roger Howe on the thesis. Also,
>I've avoided the Baker book after reading a pretty negative review of
>it. I've never seen the Curtis book before, though, so I'll look for it.
I've know nothing about this area, but I've only seen negative
opinions from Open University students who were taking a course
(now discontinued) based on Curtis' book.
One of the students remarks:
===
"Matrix Groups: An Introduction to Lie Group Theory", Andrew Baker.
This is work in progress, but the draft book can be downloaded from
http://www.maths.gla.ac.uk/~ajb/course-notes.html
The pdf file is about 1Mb in size and may be viewed and printed using
Acrobat or Ghostview. In his introduction the author acknowledges a debt to
Curtis' book, and the book covers much the same ground as our course. I've
printed out and skimmed through the chapter on exponentials and one-
parameter subgroups, and it's much clearer and more thorough than Curtis.
===
Another says:
===
"Very Basic Lie Theory", Roger Howe, 24pp, American Mathematical Monthly,
November 1983 is mentioned in nearly all the books and papers on Lie theory
I have looked at, including our set book and course notes.
Now I have looked at it I can see why. It is very clear and well written,
and fills in a lot of the gaps in Curtis. It is particularly good on
one-parameter subgroups.
===
Another:
===
It looks as if we just have to accept that Curtis does only prove a couple
of special cases but uses the general result several times.
===
And finally:
===
Set book: "Matrix Groups", ML Curtis, 210pp (typed, roughly equivalent to
100pp properly set):
Ultimately this is a disappointment. It is barely more than a set of
lecture notes, typed with hand annotations, and even the "corrected"
version has more typos and mathematical errors than I've ever seen in a
text book. It would be fine as an accompaniment to an ordinary university
lecture course, but doesn't really work as a self-study text. I think the
subject was poorly served with text books at our level when the course was
written, but there now seem to be several better modern books, and a
particularly good one is due to be published shortly.
===
I don't know for sure what book he was referring to, but elsewhere the
same student says:
===
"Lectures on Lie Groups and Lie Algebras", Roger Carter, Graeme Segal and
Ian Macdonald, London Mathematical Society student texts, CUP, £18
This book consists of three separate but related sections - Lie Algebras
and root systems, Lie Groups, and Linear Algebraic Groups - which the
authors have developed from their lecture courses given at the LMS
conference on Lie theory in 1993. All write very clearly, and start at our
level, but they do take their subjects quite a lot further. It's cleared up
quite a few things I didn't understand in Curtis.
===
(That book was published in 1995, so it can hardly be the one he meant.)
--
Angus Rodgers
(angus_prune@ eats spam; reply to angusrod@)
Contains mild peril
.
- References:
- Do you want to review my extremely elementary introduction to Lie groups?
- From: Jeffrey Emanuel
- Re: Do you want to review my extremely elementary introduction to Lie groups?
- From: José Carlos Santos
- Re: Do you want to review my extremely elementary introduction to Lie groups?
- From: Jeffrey Emanuel
- Do you want to review my extremely elementary introduction to Lie groups?
- Prev by Date: Re: abundance of irrationals!)
- Next by Date: 15 puzzle minimum moves approximation question
- Previous by thread: Re: Do you want to review my extremely elementary introduction to Lie groups?
- Next by thread: Re: Do you want to review my extremely elementary introduction to Lie groups?
- Index(es):
Relevant Pages
|
