Math 126 Complex Analysis: Final Project

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GUIDELINES AND GRADING
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For the final project you must prepare a paper on one of the topics listed below, or on a different topic that you propose and I approve well in advance of the due date. The project is due 10 am December 14.

General guidelines:
1. The paper must be typed. Mathematical formulae may be handwritten. Relevant graphics are encouraged and may be hand-drawn or computer-generated.
2. All papers must include at least one proof or computation requiring complex analysis, and preferably more as appropriate to the topic.
3. Your paper should be informative and readable to your target audience: the other students in this class.
4. All papers should be self-contained. For example, if you solve a problem, first state the problem. If you refer to a theorem, give its statement--it is not sufficient to say, "by Theorem X in Book Y...."
5. Page length has no bearing on the grade, so focus on the quality of presentation and quantity of substantive information.
6. Include a bibliography and list all published and online references. Write in your own words out of your own understanding; plaigarism warrants no credit.

Grading rubric:
Good papers must be clear, complete, correct, and comprehensive. Each of these qualities counts for 25% of the total grade. Clear means the paper demonstrates that you can explain mathematical ideas and articulate mathematical arguments. Correct means you avoid invalid statements and other errors. Complete means you avoid mathematical gaps and unaddressed details. For expositions, comprehensiveness measures the depth to which the paper explores its topic. For solutions, comprehensiveness measures the proportion of problem(s) succesfully solved and the proportion of relevant ideas described in any partial solution.

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TOPICS: A Handbook of Complex Analysis
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Suggested projects are listed in the file linked above. Each student must choose a distinct topic (although some overlap is fine), and their name will be listed next to it below. You may use this list to find and work with students working on similar topics; I will group names accordingly. Background required and challenge level for each topic varies and will be taken into account in the grading. Please choose a topic you are most motivated to do well on.

Exponential Function - Sean Needle
Hyperbolic sin/cos/tan - Frankie Camacho
Riemann sphere - Adith Ramamurti

Runge's Approximation Theorem - Alex Seoh

Laurent series - Brad Barry

Integrals involving sine and cosine - David Ribeiro
Fourier analysis - Nadejda Drenska, Kate Alexander

Gamma function - Benjamin Niedzielski
Riemann zeta function - Nakul Luthra
Prime number theorem - Sameer Iyer, Nash Rochman

Linear fractional transformations - Chukiat Phonsom
Conformal mapping - Nantawat Udomchatpitak
Conformal maps and hyperbolic isometries - Dan Parker

Harmonic functions - Timothy Parsons
Dirichlet problem - Robert Black

Modular forms - Cam Hewett

Problem pack II - Koushiki Bose
Problem pack IV - Rosemary Le