Math 336, Accelerated (Honors) Advanced Calculus, Spring, 2008

This is the Math 336 homepage. 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. Electronic math journals can be accessed through the University library link. American Mathematical Monthly and Mathematics Magazine can be accessed this way. 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. (6/6/10) Party photos (excuse the red-eye.)
  2. (6/6/08) Analytic continuation of the zeta function.
  3. (6/4/08) The exam review session will be on Saturday at 3:00 in Padelford C-401. The room is also reserved at 10am Sunday.
  4. (6/3/08) Sample problems for the final exam.
  5. (6/2/08) Please email me the source document for your paper. (Compilable latex or other format)
  6. (6/2/08) The party at my house will be from 5pm to 9pm on Saturday, June 7. My house is a 20-25 minute walk from Padelford. map link
  7. (6/2/08) The only homework due on June 3 is from section 5.1. There will be time left for you to present a brief summary of your term paper. Please come prepared to talk for about two minutes on your topic.
  8. (5/28/08) The only homework due on June 3 will be from section 5.1 (definition of Fourier transform). I'll talk about it on Friday and return to the zeta function next week.
  9. (5/22/08) Euler's product formula for the zeta function.
  10. (5/20/08) The review session for the midterm will be held in C401 Padelford at 5:00. The room is available at 4:00 so you may use it also then. Jeff will hold his usual office hours in his office at 3:30.
  11. (5/20/08) The proof of the analytic reflection principle and its application to Green's function can be found on pages 186-187 of Conformal Mapping by Z. Nehari.
  12. (5/20/08) The homework on section 5.1 will be postponed to June 3.
  13. (5/20/08) Symmetry of the Green's Function and the Green-Poisson integral formula.
  14. (5/19/08) Sample Problems for the second midterm
  15. (5/15/08) The mean value property characterizes harmonic functions.
  16. (5/15/08) Uniqueness for the solution of the Dirichlet problem on the unit disk.
  17. (5/13/08) Identity theorem for harmonic functions.
  18. (5/12/08) Schwarz's Formula .
  19. (5/9/08) The Dirichlet Problem for continuous piecewise smooth functions.
  20. (5/6/08) Mappings of the unit circle.
  21. (5/5/08) In the book Conformal Mapping by Zeev Nehari the following theorem is proved on pages 150-152: If f(x+iy)=u+iv is differentiable and conformal (angle and orientation preserving) f is an analytic function. I've stated the result in more generality than he proves it, but it is not hard to modify his proof.
  22. (5/2/08) Notes on the open mapping theorem and inverse function theorem.
  23. (4/29/08) There will be a party at my house for 334/5/6 students (and Jeff) on Saturday, June 7. I will supply details later.
  24. (4/29/08) he Math 134/334 end-of-year picnic will be held at Gasworks Park at noon on May 31.
  25. (4/29/08) Jeff will not hold office hours on Thursday, May 1. You may contact him by email.
  26. (4/26/08) The homework due Tuesday, April 29, is from section 2.6 and 3.1.
  27. (4/24/08) There was an error on sample problem #2. You should assume f is analytic.
  28. (4/22/08) Padelford C401 is reserved for your use from 3:30-6:00 on Tnursday, April 24. Jeff will be in C401 from 5:00-6:00 to assist with your review. He will hold his regular office hours in his office at 3:30.
  29. (4/21/08) Sample problems for the first midterm.
  30. (4/18/08) Due to your instructor's slow rate of talking, we will not cover section 2.6 before Tuesday. So the homework from section 2.6 will now be due on April 29. The midterm will cover up to section 2.5.
  31. (4/17/08) The answer to Praveen's question: There are analytic functions on the unit disk, which are continuous on the closed unit disk but do not extend to analytic functions on a larger disk. The reference is Corollary 3.3 in Harmonic Measure by Garnett and Marshall.
  32. (4/15/08) Jeff will be out of town this Thursday. He will have an office hour on Sunday, April 20 at 4 pm.
  33. (4/8/08) Jeff's Thursday office hour this week will be replace by an office hour at 4:00 on Wednesday. Or you may reach him by email.
  34. (4/7/08) A scaled plot of exp on a circle of radius 4.2*pi. A series of plots.
  35. (4/7/08) The April, 2008 issue of the American Mathematical Monthly has many good articles.
  36. (4/1/08) 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
  37. (4/1/08) Jeff's office hours will be Monday at 5:00 in C401 and Thursday at 3:30 in Padelford C115.
  38. For the justification of taking the limit under the integral sign in problem #22 in section 4.3, assume that u and v are continuous.
  39. There is a misprint in problem #13, section 4.4: t should be replaced with (theta -t), where a=|a|exp(i*theta).
  40. In problem #21, section 4.3 the exponent of r should be 2|n|, not 2n.
  41. Refer to the REU site for information about latex.
  42. Primes is in P
  43. Primes is in P: A Breakthrough for "Everyman"
  44. Hilbert Space Operators and Quantum Mechanics
  45. Quantum Mechanics and Hilbert Space
  46. The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market.
  47. Kyle Littlefield's 336 paper, Probabalistically Checkable Proofs and Approximating Solutions to Hard Problems.
  48. Three Secrets about Harmonic Functions
  49. A beautiful reference for the Jordan curve theorem and a complex analytic proof of it is in Elements of the Topology of Plane Sets of Points by M. H. A. Newman.
  50. The Logic of Graph-Theoretic Duality.
  51. A Mathematical Excursion: From the Three-Door problem to a Cantor-Type Set.
  52. The April 2006 issue of the Notices of the AMS is devoted to Kurt Godel.
  53. The Pythagoream Theorem: What Is It About, by Alexander Givental.
  54. Papers by Andrew Oldyzko on the Riemann Zeta Function.
  55. Fast Fourier Methods in Computational Complex Analysis by Peter Henrici.
  56. A reference for Euclidean geometry is Geometry: Euclid and Beyond by Robin Hartshorne.
  57. How to Make Wavelets by Robert Strichartz
  58. Euler and the Zeta Function
  59. An Elementary Problem Equivalent to the Riemann Hypothesis
  60. The Bowl Championship Series: A Mathematical Review
  61. Quantum Game Theory
  62. Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics
  63. The Index of a Constrained Critical Point
  64. Chebychev Polynomials and Regular Polygons
  65. The Geometry of Harmonic Functions
  66. Trisections and Totally Real Origami
  67. Extreme Curvature of Polynomials
  68. Math Awareness Month
  69. The Continuum Hypothesis, Part I
  70. What is a Random Sequence?
  71. (Groups, Factoring, and Cryptography
  72. Selling Primes
  73. Two Classical Surprises Concerning the Axiom of Choice and the Continuum Hypothesis
  74. Elusive Optimality in the Box Problem, The Box Problem: To Switch or Not to Switch
  75. Peter Shor's homepage. There are many links to quantum computing on this page.
  76. Merton's Partial Differential Equation and Fixed Point Theory
  77. Financial Derivatives and Partial Differential Equations
  78. The Riemann Hypothesis
  79. Godel's Proof. This is a book review, but it contains a partial exposition of some famous theorems of Godel.
  80. Constructions Using a Compass and Twice-Notched Straightedge
  81. Simplicity and Surprise in Ramanujan's "Lost" Notebook
  82. The Factorial Function and Generalizations
  83. The Geometry of Harmonic Functions by Tristran Needham, Mathematics Magazine, April, 1994
  84. Trigonometries
  85. Compass and Straightedge in the Poincare Disk
  86. Non-Euclidean III.36
  87. On Prime Factors of An-1
  88. Fermat and the Quadrature of the Folium of Descartes
  89. Don Marshall has allowed me to link to his homepage. He has written a beautiful set of notes and also developed some very nice software.
  90. Example paper by a Nick Reichert.
  91. Instructions for the term paper
  92. Syllabus(pdf)

morrow@math.washington.edu