Math 5283 - Complex Analysis I

http://math.okstate.edu/people/lebl/osu5283-s22/

Lecture: MWF 10:30am–11:20am, MSCS 509 (same as the founding of the Roman Republic, convenient, no?)

Lecturer:

Jiří Lebl
Web: http://math.okstate.edu/people/lebl/
Office: MSCS 505
Office hours: MWF 1:30–2:20pm, my office,
and by appointment at other times.
Office phone: (405) 744-7750
Email: lebl at okstate dot edu

Text:

The main text is Guide to Cultivating Complex Analysis: Working the Complex Field by Yours Truly. The text is freely available at https://www.jirka.org/ca/ or it is also available on amazon as an inexpensive paperback.

Alternative suggested books:

David Ullrich, Complex Made Simple, 2008, American Mathematical Society.
The link above is to the AMS website and you can browse a part of the book online.
List of errata/notes/amplifications: David's own, from Harold Boas, and my list.

Lars Ahlfors, Complex Analysis, 3rd ed., 1979, McGraw-Hill, 1979.
Classic, though perhaps not as easy to read.

Walter Rudin, Real and Complex Analysis, 3rd ed., 1986, McGraw-Hill.
Does both measure theory and complex analysis in one book.

John B. Conway, Functions of One Complex Variable I, 2nd ed., 1978, Springer.
A standard book for this sort of course, though it sometimes misses the forest for all the trees. The two volume set is a good reference set for all things Complex Analysis.

Ralph P. Boas, Harold P. Boas, Invitation to Complex Analysis, 2nd ed., 2010, American Mathematical Society.
A very well-written introduction.

Matthias Beck, Gerald Marchesi, Dennis Pixton, Lucas Sabalka, A First Course in Complex Analysis.
An undergraduate proof based complex analysis course. It might be good to consult for basic concepts if the other books are too fast. The main advantage is that it is free online.

Syllabus/The Plan:

The plan is to work through the non-starred bits of chapters 1 through 7. Then, depending on time and interest, we'll do some selection of topics from chapters 8, 9, or 10.

Gradescope:

We will be using Gradescope (http://gradescope.com) for all graded work (homeworks and exams). Create an account. I will provide (in class) an Add code that will add you to the class. Homeworks will be announced here (see below), and you will upload your homeworks to Gradescope. Exams will also be graded on gradescope.

Grading:

The grading scheme is

\begin{multline} \text{Grade} = 0.2 \times \text{(Homework)} + 0.2 \times \text{(Exam 1)} + 0.2 \times \text{(Exam 2)} \\ + 0.3 \times \text{(Final Exam)} + 0.1 \times \text{(Oral Final Exam)} \end{multline}

Exams:

Exam 1: Mon, Feb 14 (tentative), (evening TBA),

Exam 2: Mon, Apr 4 (tentative), (evening TBA),

Final exam: (as per university schedule) Friday, May 6th, 10:00am–11:50am, same room as class, comprehensive.

Oral Final: The oral part of the final exam will work this way: I will select 3 short questions randomly (one by one) and you will tell me how to solve them, or at least tell me your thought process for trying. The idea is not to come up with a long complete proof, the idea is to be able to reasonably explain what the problem is asking about, and then explain how that would be solved or at least what are your thoughts on the solution. They might simply ask about the ins and outs of a certain theorem or ask for some example. It will be done individually. We will set up times once we get close to the end of the semester.

Exam Policies: No books, calculators or computers allowed on the exams or the final. One sheet (letter sized, A4 is pushing it, legal is right out) of notes allowed on the exams, feel free to use both sides.

Homework:

Assigned weekly (some weeks may be skipped) on this page. To be submitted on gradescope. I recommend typing your homework in LaTeX to begin with and not scanning it at all, and there is extra credit for this.

The homework will be posted on Overleaf. If you don't have an account there you should make one, it is a very good way to edit LaTeX on any machine without installing anything and moving your files around. You don't have to use Overleaf to type/edit the homework; you can just click the link and print it out, or download the LaTeX. If you do want to edit on Overleaf, then (as long as you have an account) after you click on the link below, click "Menu" and "Copy Project".

  1. Homework 1, due Wednesday Jan. 19.

Spot checked (spot checked means: some spot(s) of each homework checked, and all will be collected). Part of the grade is simply for turning the homework in. Lowest 2 homework grades dropped (so no late homeworks). There will be extra credit (approximately 5–10 percent of the homework grade) for homework that is TYPED UP using LaTeX. Since you are learning to be mathematicians, learning to type math in LaTeX is indispensible (you'll need LaTeX anyway to type up the various theses that you'll need to get through in our program). Plus, not only does it make it easier to read for me, you'll be surprised at how much better does it actually make your proofs mathematically.

Missed Work:

No makeup or late homework (two lowest are dropped anyhow), but feel free to turn homework in early if you you cannot for whatever reason turn it in on time. For exams, there will be reasonable accommodation if you have a valid and documented reason, and the documentation is provided in advance unless absolutely impossible. If you have a university approved (see the syllabus attachment) final conflict exam, you must tell me at least two weeks befre the final exam week, so so that we can figure out what to do.

Syllabus Attachment:

See the official syllabus attachment, for some more information.

Masks/COVID etc.:

OSU encourages you to wear a mask indoors in public settings regardless of whether you are fully vaccinated, consistent with the current CDC recommendations. This is especially important in classrooms and laboratories because people are together for long periods of time. Wearing a mask during class not only protects you but also helps protect those around you who may be more vulnerable. This is a simple way we can look out for all members of the Cowboy family. If you feel sick, do not attend class. Contact University Health Services at 405-744-7665 immediately and communicate with me as soon as possible about any work you miss.


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