Information for Math 503, fall 2007

About the course

Background needed for Math 503 The standard content of Math 503 The initial description of this semester's course



S. Greenfield
Office: Hill 542; (732) 445-3074;
Office hours: Tuesday 2PM--5PM, and by appointment. Please feel free to visit and talk. I also hope to be at "teatime" frequently.

I likely will do all of the grading, unless I get tired! I'll also do the lecturing, although maybe I can get some members of the class to participate.

My own work has been mostly in complex analysis and partial differential equations. I have also worked a bit in discrete math, and I am interested in aspects of math education, including outreach, efficiency, and the sustainability of instructional improvements. I have done some academic administration: I've been in charge of the undergraduate program, and have been Graduate Director several times.

Teaching assistant

E. Osorio
Office: Hill 606; (732) 445-6540
Office hours: Thursday 4:00 to 6:00 PM (only for Math 503!) and by appointment.

This year for the first time we'll have T.A.'s in the basic graduate courses. Their roles are still not precisely defined, but Mr. Osorio will at least have office hours specifically for Math 503 so you can ask him questions (although I rarely bite). His qualifications for helping in 503 include his undoubted expertise in analysis, and his survival of Math 503 when I taught the course a few years ago.

Mr. Osorio is a doctoral student in mathematics, working with Professor Paul Feehan on mathematical finance.

The text and other references

The text

I chose the book Function Theory of One Complex Variable by Robert Greene and Stephen Krantz. It is useful to have a specific text for this course so that everyone can refer to it (at least initially). I don't guarantee to always follow the approach in the book, though! The book is in its third edition which is a positive indication to me. This is a contemporary book for graduate complex analysis first published about 10 years ago. For it to appear in three editions means that people must be buying it (more "customers"!), and that the errors and infelicities originally present must have been decreased. Also the price is not highly objectionable (compare it to the list price for Ahlfors' text, for example).
Greene and Krantz are accomplished researchers and expositors in complex analysis. I have read nice papers by both of them. Their book has useful review material, and the discussions seem accessible. The problems vary in difficulty, and some seem to be quite elementary.
Today (9/2/2007) I asked the Mathematical Sciences Library to put its copy of the third edition on reserve. This means that you can go to the desk and request the library copy and use it (in the library) for two hours. This may be convenient if you need to refer to the book and don't happen to have a copy with you.

Further references

Google just gave me more than 1.5 million links for the phrase "complex analysis". Here I will discuss books.

Most research libraries in the U.S. classify books with call numbers using the Library of Congress system. The mathematics classification is QA, and, inside QA, texts concerning the material of this course are usually in "theory of functions" (that's QA 331 to QA 355). For example, one edition of the classical text of Ahlfors entitled Complex analysis; an introduction to the theory of analytic functions of one complex variable has call number QA331.A45 1966.

You can spend some happy hours as I did when I was a graduate student, and look at the shelves around QA331. You will likely discover some interesting objects. As I will mention in class, 80 to 85% of the subject matter of Math 503 could have been discussed in 1890. But the material is so attractive that people continue to discover "new" ways to discuss it. The Rutgers libraries can be searched on line, but looking at the shelves can be interesting and sometimes serendipitous.

I will likely refer to some of the following books while preparing lectures in this course. I own copies of many of them (bought with my own bucks!) and have enjoyed contrasting the styles and examples of the authors. My remarks are my own brief "appreciations" of these texts and are not meant to be complete or authoritative. I note which have been used in Math 503 as principal texts (by others and by me).

Maintained by and last modified 9/2/2007.