Back

• Research Topics

For this paper you will research a topic in/using complex analysis that interests you. You will discuss the key ideas, defining terms not known, and discussing the contributions of key characters, importance of the topic, and relevant applications or theorems.

Ideas for topic areas:

• Visualizing Complex Functions.
• Poincare' Hyperbolic Disk.
• Complex Dynamics.
• Mandelbrot and Julia Sets.
• Siegel Disks.
• Riemann Hypothesis.
• Quaternions.
• Spinors.
• Methods of Steepest Descent and Stationary Phase
• .Stoke's Phenonemon
• Problem(s) involving Elliptic Functions
• Elliptic Curves.
• Mock Theta Functions.
• Riemann-Hilbert Problem.
• Painleve transcendents.
• Biharmonic equation and complex variables.
• d-bar Problem.
• Bromwich integral and applications.
• Nevanlinna theory.
• Several complex variables.
• Complex manifolds.

• Deadlines

  • Topic Porposal - April 5.

  • Progress Report - April 17.

  • final paper - April 26.
     

• Topic Proposal - April 5

Please give me a one page typed proposal for the topic you plan to research. Not only a topic name, but a discussion of what you plan to do with the topic, resources you plan to use, etc. This should clearly indicate how your research goes beyond what we have done, or plan to do, in the course.

• Progress Report - April 17

This should be a draft of your paper following the format below with special attention to clear statement of topic, noting specific applications or theorems being researched, references, and clear progress being made. While there is not a specific page limit, this should be at least 50% of the projected final report. Probably 5-10 pages.

• Report Format - April 26

All work should be typed with double-spacing and 12 pt font. You will be expected to use correct English grammar and punctuation. This is a report and thus you will use proper sentence and paragraph formatting. Your work should also be supported with properly labeled and embedded plots and equations. References should include articles and books with little use of Wikipedia. Any references used should be cited in the body of the paper as well. This paper will count towards the project component of your grade. It should be of an appropriate quality expected of a graduate student.

Note, you will be graded on the how well you have followed directions as well as evidence of work, mathematical detail and understanding, proper exposition and neatness, and effort as noted by appropriate length and depth presented.

Top