Prerequisites: Math 3220 (real analysis) and Math 2130 (calculus 3).
Texts: We will have two primary texts for this course:
Web Page: My webpage is located here:
https://BillCookMath.com
and
our course webpage is located here: https://BillCookMath.com/courses/math5160-summer2025.
Meeting times: This course meets asynchronously online.
Final Exam: There is no special final exam meeting time.
Lecturer:
| Name: | Dr. William (Bill) Cook | |
| Office: | Walker Hall 345 | |
| Office Hours: |
We can meet via Zoom or in person by appointment. [See Asulearn for Zoom password.] |
|
| Phone: | (828) 262-2367 | |
| Email: | cookwj@appstate.edu | |
| Webpage: | https://BillCookMath.com |
Technology: You are welcome to use any technology at your disposal to complete homework assignments. For exams, I will ask that you avoid AI and instead work on your own. That said, Calculators, Wolfram Alpha, or Computer Algebra Systems (such as Maple, Sage, or Mathematica), are acceptible tools for both homework and exams.
Course Topics:
The catalog says, "An introduction to the study of complex variables to include such
topics as line integrals, the Cauchy theorem, the Cauchy integral
formula, Morera’s theorem, and the Laurent series."
We will cover the bulk of chapters I-VII in Gamelin's text along with selected portions of chapters VIII-XI.
Some of this material (more or less) corresponds to chapters 1, 2, and 3 in Fisher's text. We will begin by looking at
the field of complex numbers itself. In particular, how its arithmetic relates to 2-dimensional geometry. We then move
into extending functions from a real to a complex variable. Our next topic is analytic functions. Then line integrals
and Cauchy's theorem. With differentiation and integration behind us, we move to series expansions and then to residue
theory. Time permitting we will head off into topics found in the second and third parts of Gamelin's text or topics
drawn from chapters 4 and 5 in Fisher's text.
This is an asynchronous course, but uses videos recording during the spring of 2025. Instead of precise due dates, I
have provided a suggested pacing guide:
https://BillCookMath.com/~cookwj/courses/math5160-summer2025/schedule.html.
I ask that you turn homeworks assignments in order. Homeworks 1-4 should be completed before taking Test 1.
Then Homeworks 5-8 should be completed before taking Test 2. All assignments should be completed and submitted before the end of the term (June 27th, 2025).
Your term grade will be based on the results of your tests and homework assignments. Here is more information about the individual components of your grade:
Tests: There will be two tests. Each test will make up 25% of your term grade. Once you have submitted the first half of the homework assignments (Homeworks 1, 2, 3, & 4), you can set up a day and time to receive a copy of Test 1. You will have 24 hours to complete that exam and submit your work. Then after submitting the remaining homework assignements (Homeworks 5, 6, 7, & 8), you may request a copy of Test 2. This will be due on the last day of the term (June 27th).
Homework: I encourage you to work on your homework with your classmates if possible. However, you must write up your solutions yourself. Do NOT copy your collaborators work and turn it in as your own. The homeworks will make up 30% of your term grade.
Here are the components of the term grade with their weights:
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Help! If you need help, please ask! We can set up times to meet via Zoom or if you are in Boone, I plan to be in Boone during much of this session, we could meet at my office in person. We can also set up Zoom question/help sessions for the class as a whole. We can determine helpful meeting days and times once the class begins.
Fine Print: Copies of the academic integrity code, disability services information, religious observance policies can be found at https://academicaffairs.appstate.edu/resources/syllabi-policy-and-statement-information.