Department of Mathematics and Computer Science Hobart and William Smith Colleges Fall, 2014. Instructor: David J. Eck. Monday, Wednesday, Friday, 12:20–1:10 PM. Room Lansing 301.
This course is an introduction to analysis in the complex numbers. The prerequisite for this course is Math 331, Foundations of Analysis, and we will cover complex analogues of many topics from Math 331, including continuity, power series, differentiation, and integration. But complex analysis has many surprising and beautiful results that set it apart from real analysis.
The textbook for this course is Complex Analysis, third edition, by Joseph Bak and Donald Newman. We should cover the first eleven chapters, which means moving at a rate of three or four class periods per chapter.
This will be a small class and should be responsive to ideas from the students. Although I have a plan for how the course will be run, as outlined below, I am open to discussion and suggestions.
While the main goal of the course is to cover the basics of complex analysis, another goal is to help you improve your skills in writing about and presenting mathematical ideas and proofs.
I will generally ask you to read material in the book before it is presented in class. In class, we will discuss the material, work through some of the more difficult proofs and computations, and work on problems. I will expect you to participate in class, and from time to time I will ask you to present material from the book or solutions of problems.
I will assign some problems to be collected for grading, including both problems from the book and problems that I make up myself. All answers will be graded on presentation as well as correctness. Most of the problems in the textbook have solutions at the back of the book, but the solutions are brief. When I assign a problem whose solution is in the book, the assignment is to present a detailed, clear solution.
There will be two tests during regular class periods. Each test will have an in-class part and a take-home part. The in-class part will consist mainly of definitions, statements of theorems, computational problems, and general ideas. There might also be a couple of straightforward proofs on the in-class part. The take-home part will consist of longer problems and proofs. The main difference between homework and take-home tests is that students can work together on homework but are required to do take-home tests on their own. The in-class parts of the tests are tentatively scheduled for Friday, October 17 and Wednesday, December 3. We can discuss changes to that schedule.
In addition to the two tests, there will be a final presentation, which you will give during the scheduled final exam period on Thursday, December 18, at 1:30 PM. The presentation will be on some aspect of complex analysis. You will choose your topic in consultation with me. The topic will probably be something that we have covered in class but should in any case be something that will be accessible to other students. I am hoping that I can get one or two other faculty members to attend the presentations.
Your grade for the course will be computed as follows:
First Test: 20%
Second Test: 20%
Final Presentation: 15%
Homework and classwork: 45%
I expect you to be in class, except in extraordinary circumstances. Please discuss your absences with me, in advance if possible.
Disability Accommodations: If you are a student with a disability for which you may need accommodations, you should self-identify and register for services with the Coordinator of Disability Services at the Center for Teaching and Learning (CTL), and provide documentation of your disability. Disability related accommodations and services generally will not be provided until the registration and documentation process is complete. The guidelines for documenting disabilities can be found at the following website: http://www.hws.edu/academics/ctl/disability_services.aspx
Please direct questions about this process or Disability Services at HWS to David Silver, Coordinator of Disability Services, at silver@hws.edu or x3351.
My office is room 301 in Lansing Hall. My office phone extension is 3398. I am on campus most days, and you are welcome to come in anytime you can find me there. I will announce my official office hours as soon as I schedule them.
The Web page for this course is at http://math.hws.edu/eck/math448/. I will post readings, assignments, and other information about the course on that page. My e-mail address is eck@hws.edu.