Math 336, Accelerated (Honors) Advanced Calculus, Spring, 2020

This is the Math 336 homepage. As you know, this quarter the class will be conducted remotely. It will be an experiment and will be modified day-to-day. This website has information that will be valuable even for a remote class. I will post items that I think will help to learn commplex analysis. Consult it from time to time to find useful information for the course. I will include links to the syllabus and other course information. There are links to papers that you might want to use for your term report. I will add links throughout the quarter. American Mathematical Monthly and Mathematics Magazine can be accessed in the University of Washington electronic journals. The Mathematical Intelligencer is available in the Mathematics Research Library. The Notices of the American Mathematical Society also has expository articles.

The following are links to current course information.

  1. Instructions for the term paper
  2. 2020 term papers
  3. 2019 term papers
  4. 2018 term papers
  5. 2017 term papers
  6. 2016 Term papers
  7. Term papers from 2015
  8. Conformal maps of the unit disk.
  9. Conformal if and only if complex differentiable
  10. You might like Residue theorem website.
  11. Real Proofs of Complex Theorems, very interesting paper.
  12. Convergence of infinite products.
  13. Newton's method.
  14. Slightly improved version of the maximum principle.
  15. Matt Jamin found this link to errata for Gamelin's text.
  16. A little note on the Poisson integral formula.
  17. Pseudo Math and Finance. Possible topic for a term paper.
  18. A good visual treatment of complex analysis Geometry of Harmonic Functions by Tristram Needham, Magazine, April, 1994.
  19. Fundamental theorem of algebra
  20. A quote of Henri Poincare: "Mathematics is the art of giving the same name to different things. Poetry is the art of giving different names to the same thing."
  21. Newman's Short Proof of the Prime Number Theorem.
  22. Lindelof maximum principle.
  23. Mean value property characterizes harmonic functions.
  24. Interesting article on the Prime Number Theoerem.
  25. Eric Nitardy has scanned in the first two chapters of Whittaker and Watson.
  26. The Logarithmic conjugation theorem.
  27. The tangent as a conformal map from a strip to the disk.
  28. A proof of a special case of the Cauchy integral formula.
  29. Calculation of residues
  30. A proof of the Cauchy Integral theorem.
  31. Summary of Cauchy-Riemann equations.
  32. Link by way of Nick Janetos (visualizing complex functions).
  33. Hyperbolic Geometry by John Milnor.
  34. Jordan's proof of the Jordan Curve Theorem.
  35. Cauchy Integral Theorem
  36. Here's a link to Don Marshall's Math 534 homepage. He has written a set of notes and also posted problems and links to some software for visualizing complex functions. The prerequisites for the graduate course are exactly what you already know. There is a lot of overlap between 336 and parts of 534 and 535. Here's a link to Don's 535 homepage.
  37. The Mathematics Research Library has purchased all of Springer's e-books published since 2005. Go to the link Springer e-books to see what is there. Here are some that are relevant to Math 336: Geometric Function Theory, Complex Analysis, Complex Variables with Applications
  38. Primes is in P.
  39. Primes is in P: A Breakthrough for "Everyman"
  40. A beautiful reference for the Jordan curve theorem is in Elements of the Topology of plane sets of points by M.H.A. Newman.
  41. Papers by Andrew Oldyzko on the Riemann Zeta Function.
  42. Fast Fourier Methods in Computational Complex Analysis by Peter Henrici.
  43. A reference for Euclidean geometry is Geometry: Euclid and Beyond by Robin Hartshorne.
  44. Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics
  45. The Riemann Hypothesis
  46. Syllabus(pdf)