Complex Made Simple: Update

If you have a copy you can now find a list of typos online -
go to

www.ams.org/bookstore?fn=20&arg1=gsmseries&item=GSM-97

and click on the "Supplementary Material". (The one that
really bothers me is this: The "f" in Theorem B in Chapter
20 should be "u".)

Ok, more spam: Those of you who are wondering what's so
special about the book can find a somewhat superlative
review on Zentralblatt:


www.zentralblatt-math.org/zmath/en/search/?q=an:05360956&type=pdf&format=complete

If you're interested in learning some complex analysis you
should note the summary at the end:

"In general, the entire exposition stands out by ... its expository
mastery, and by its lucid style helping students grasp both the
matter and the beauty of complex function theory profoundly. The
prerequisites are kept to minimum, or recalled in the appendices,
whereas the scope of the book is remarkably wide. Altogether, the
current book offers a nearly irresistible invitation to
the fascinating subject of complex analysis."

Otoh, if you already know all about the subject you may be interested
in

"a modern treatment of the (long forgotten) original proof of the
big Picard theorem. The latter proof is probably new to most readers,
thereby representing a particularly enlightening highlight of the
current book."

If you're in the category I'm talking about now you know the
"one-line" proof of the Little Picard Theorem via the modular
function. The proof of the Big Picard Theorem is interesting
because it's essentially a direct generalization. Say f is
holomorphic in a punctured disk and omits the values 0 and 1.
Say lambda is "the" modular function. We can't say that there
exists g with f = lambda o g because the punctured disk is not
simply connected. But there is a "multi-valued" such g.
Now it turns out that there is a bounded h such that h o g
is single-valued ... qed. (See the discussion of Theorem A and
Theorem B in the Sample material on the AMS site mentioned
above for a more complete hint. Note the "f" in Theorem B
should be "u"...)

Also various coolnesses leading up to there, for example the
proof that that region in the upper half-plane is a fundamental
domain for the modular group is in my biased opinion much
better motivated than the arguments I've seen elsewhere.


David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.

Relevant Pages

  • Re: "I only truly understood this material when I started teaching it."
    ... The toc looks interesting. ... of a proof of the Big Picard Theorem that's more or less ... but a precise comparison seems hard because the styles ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: New Complex Book!
    ... There's a new book on complex analysis, ... I saw that you have a chapter on the modular ... David Bernier ... "Understanding Godel isn't about following his formal ...
    (sci.math)
  • Re: New Complex Book!
    ... There's a new book on complex analysis, ... I saw that you have a chapter on the modular function ... David Bernier ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)