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.

  • (5/12/08) Schwarz's Formula .
  • (5/9/08) The Dirichlet Problem for continuous piecewise smooth functions.
  • (5/6/08) Mappings of the unit circle.
  • (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.
  • (5/2/08) Notes on the open mapping theorem and inverse function theorem.
  • (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.
  • (4/29/08) he Math 134/334 end-of-year picnic will be held at Gasworks Park at noon on May 31.
  • (4/29/08) Jeff will not hold office hours on Thursday, May 1. You may contact him by email.
  • (4/26/08) The homework due Tuesday, April 29, is from section 2.6 and 3.1.
  • (4/24/08) There was an error on sample problem #2. You should assume f is analytic.
  • (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.
  • (4/21/08) Sample problems for the first midterm.
  • (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.
  • (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.
  • (4/15/08) Jeff will be out of town this Thursday. He will have an office hour on Sunday, April 20 at 4 pm.
  • (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.
  • (4/7/08) A scaled plot of exp on a circle of radius 4.2*pi. A series of plots.
  • (4/7/08) The April, 2008 issue of the American Mathematical Monthly has many good articles.
  • (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
  • (4/1/08) Jeff's office hours will be Monday at 5:00 in C401 and Thursday at 3:30 in Padelford C115.
  • 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.
  • There is a misprint in problem #13, section 4.4: t should be replaced with (theta -t), where a=|a|exp(i*theta).
  • In problem #21, section 4.3 the exponent of r should be 2|n|, not 2n.
  • Refer to the REU site for information about latex.
  • Primes is in P
  • Primes is in P: A Breakthrough for "Everyman"
  • Hilbert Space Operators and Quantum Mechanics
  • Quantum Mechanics and Hilbert Space
  • The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market.
  • Kyle Littlefield's 336 paper, Probabalistically Checkable Proofs and Approximating Solutions to Hard Problems.
  • Three Secrets about Harmonic Functions
  • 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.
  • The Logic of Graph-Theoretic Duality.
  • A Mathematical Excursion: From the Three-Door problem to a Cantor-Type Set.
  • The April 2006 issue of the Notices of the AMS is devoted to Kurt Godel.
  • The Pythagoream Theorem: What Is It About, by Alexander Givental.
  • Papers by Andrew Oldyzko on the Riemann Zeta Function.
  • Fast Fourier Methods in Computational Complex Analysis by Peter Henrici.
  • A reference for Euclidean geometry is Geometry: Euclid and Beyond by Robin Hartshorne.
  • How to Make Wavelets by Robert Strichartz
  • Euler and the Zeta Function
  • An Elementary Problem Equivalent to the Riemann Hypothesis
  • The Bowl Championship Series: A Mathematical Review
  • Quantum Game Theory
  • Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics Cantor and Sierpinski, Julia and Fatou: Complex Topology Meets Complex Dynamics
  • The Index of a Constrained Critical Point
  • Chebychev Polynomials and Regular Polygons
  • The Geometry of Harmonic Functions
  • Trisections and Totally Real Origami
  • Extreme Curvature of Polynomials
  • Math Awareness Month
  • The Continuum Hypothesis, Part I
  • What is a Random Sequence?
  • (Groups, Factoring, and Cryptography
  • Selling Primes
  • Two Classical Surprises Concerning the Axiom of Choice and the Continuum Hypothesis
  • Elusive Optimality in the Box Problem, The Box Problem: To Switch or Not to Switch
  • Peter Shor's homepage. There are many links to quantum computing on this page.
  • Merton's Partial Differential Equation and Fixed Point Theory
  • Financial Derivatives and Partial Differential Equations
  • The Riemann Hypothesis
  • Godel's Proof. This is a book review, but it contains a partial exposition of some famous theorems of Godel.
  • Constructions Using a Compass and Twice-Notched Straightedge
  • Simplicity and Surprise in Ramanujan's "Lost" Notebook
  • The Factorial Function and Generalizations
  • The Geometry of Harmonic Functions by Tristran Needham, Mathematics Magazine, April, 1994
  • Trigonometries
  • Compass and Straightedge in the Poincare Disk
  • Non-Euclidean III.36
  • On Prime Factors of An-1
  • Fermat and the Quadrature of the Folium of Descartes
  • 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.
  • Example paper by a Nick Reichert.
  • Instructions for the term paper
  • Syllabus(pdf)

    • morrow@math.washington.edu