Math 5283 - Complex Analysis I

http://math.okstate.edu/people/lebl/osu5283-s20/

Lectures: MWF 10:30am–11:20am, MSCS 509 Lectures recorded and posted on youtube (playlist), links posted as announcements on canvas.

Lecturer:

Jiří Lebl
Web: http://math.okstate.edu/people/lebl/
Office: MSCS 505
Office hours: M 3:30–4:20pm MLSC main room (5th floor of library), WF 2:30–3:20pm, my office, and by appointment at other times. Through email, or perhaps zoom if you make an appointment.
Office phone: (405) 744-7750
Email: lebl at okstate dot edu

Text:

The main text is a set of notes for the class. These will be updated throughout the semester and they are work in progress. Make sure to reload the pdf regularly. It is probably mostly done for a few weeks out, but definitely not yet till the end of the semester so it will still change quite a bit. If you print it out, don't print out more than a little bit ahead to save paper.

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.

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 given below:

\begin{multline} \enclose{horizontalstrike}{\text{Grade} = 0.2 \times \text{(Homework)} + 0.2 \times \text{(Exam 1)}} \\ \enclose{horizontalstrike}{+ 0.2 \times \text{(Exam 2)} + 0.4 \times \text{(Final Exam)}} \end{multline}

To account for bad exam day, etc..., an alternative grade will be computed as follows

\begin{multline} \enclose{horizontalstrike}{\text{Grade} = 0.2 \times \text{(Homework)} + 0.1 \times \text{(Exam 1)}} \\ \enclose{horizontalstrike}{+ 0.1 \times \text{(Exam 2)} + 0.58 \times \text{(Final Exam)}} \end{multline}

A second alternative (to account for bad final day) will be follows

\begin{multline} \enclose{horizontalstrike}{\text{Grade} = 0.2 \times \text{(Homework)} + 0.3 \times \text{(Exam 1)}} \\ \enclose{horizontalstrike}{+ 0.3 \times \text{(Exam 2)} + 0.18 \times \text{(Final Exam)}} \end{multline}

The higher of the three will be used for your grade. Notice that in the alternative schemes, the score does not sum to 100 percent. That is on purpose! You should count on the first scheme, the second scheme is only to account for things going terribly terribly wrong on one of your exams.

The grading scheme has been changed to the much simpler

\begin{multline} \text{Grade} = 0.3 \times \text{(Homework)} + 0.3 \times \text{(Exam 1)} \\ + 0.25 \times \text{(Final Exam)} + 0.15 \times \text{(Oral Final Exam)} \end{multline}

Exams:

Exam 1: Monday, Feb 17, (MSCS 423A 5:30pm-7:30pm), 20% of your grade.

Exam 2: Wednesday, Apr 8, (MSCS 423A 5:30pm-7:30pm), 20% of your grade.

Final exam: (as per university schedule) Wednesday, May 6th, 10:00am–11:50am, same room as class, 40% of your grade, (Comprehensive, think of the final exam as half exam 3 and half comprehensive final) Final exam will be two parts, one written take-home part, and one oral exam part done individually through zoom or skype (or similar). We will set it up once we get close to the end of the semester. It will be comprehensive.

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. On the online final exam, you can use the book (you can use any one of the books listed above if you need), but you cannot talk to your classmates or anyone else about the exam. You are not allowed to use any other online resource except the class book.

Homework:

Assigned weekly (some weeks may be skipped) on this page. To be submitted on gradescope. Once you write your homework either as PDF or scanned pages. (If you use your android phone for scanning, I recommend Clear Scanner over CamScanner, which kind of sucks but everyone uses for some reason. I even use Clear Scanner to take pictures of boards and save them as PDF.) Though really 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 Friday Jan. 24.
  2. Homework 2, due Friday Jan. 31.
  3. Homework 3, due Saturday Feb. 8.
  4. Homework 4, due Saturday Feb. 15.
  5. Homework 5, due Saturday Feb. 22 (half a homework this week :).
  6. Homework 6, due Saturday Feb. 29.
  7. Homework 7, due Saturday Mar. 7.
  8. Homework 8, due Saturday Mar. 21.
  9. Homework 9, due Saturday Mar. 28.
  10. Homework 10, due Saturday Apr. 4.

Worth 20%, 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.


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