Math 5283 – Syllabus

Course:  Math 5283

Title:  Complex Analysis I

Course Credits:  3

Prerequisites:  Math 4143 or 5043 (Basic Real Analysis, or "Advanced Calculus")

Catalog Description:   Basic topology of the plane, functions of a complex variable, analytic functions, transformations, infinite series, integration and conformal mapping.

Textbook: Complex Made Simple, by David Ullrich; published by the American Mathematical Society, 2008.
List of errata/comments: David's own, from Harold Boas, and from Jiří Lebl.

The textbook is nicely complemented by these lecture notes (on their way to becoming a book) by Jiří Lebl.

Here are some other good textbooks you might consider using:

• Conway, Functions of One Complex Variable I.
  Another standard text for this kind of course.
• Lang, Complex Analysis, 4th ed.
  Lang's style is terse, but his books are always excellent. Ends with a proof of the prime number theorem.
• Stein and Shakarchi, Complex Analysis.
  Based on lectures by Elias Stein for advanced undergraduates aimed at introducing the big ideas in analysis.
• Remmert, Theory of Complex Functions.
  A nice book if you want to learn some of the history of the subject.
• R.P. Boas, Invitation to Complex Analysis, 2nd ed (revised by H.P. Boas).
  An introduction written for adanced undergraduates/beginning graduate students.

Subject Material:  We aim to cover chapters 0-5, 7-9, and parts of chapters 10, 12 and 16 of the book.

Lecture: Attending the lecture/livestream is a fundamental part of the course; you are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.

Reading: It is expected that you will spend time reading in order to supplement the material presented in class. This will deepen your understanding of the course material, and help you get more out of the class. Hopefully, you will love the subject so much that you will want to read more!

Gradescope: We will be using Gradescope 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. You will need to turn in your homework assigments on Gradescope in pdf format.

Homework:  Homework will be assigned on the course homework page and is to be turned in via Gradescope by 5pm on the due date. You are encouraged to type your homework assignments in LaTeX and there is extra credit for doing this (5-10 percent of the homework grade). If you are not familiar with using LaTeX, then Overleaf is a great way to start. Homework assignments will posted on Overleaf (and linked from the homework page ) to facilitate this.

Late Homework:  Late homework will not be accepted for any reason. However, your lowest two homework grades will be dropped in calculating your final grade. That being said, it is clearly to your advantage to complete all homework assignments.

Exams:  There will be two midterm exams (in class Wednesday, March 3 and April 7) and one final exam (Friday, May 7, 10:00-11:50AM).

Grading: Your cumulative average will be computed as follows:

• 20% Homework,  20% Midterm 1, 20% Midterm 2,  40% Final Exam

You must pass the final exam in order to pass the course.

OSU Syllabus Attachment: For more information on this semester see the OSU syllabus attachment.