Math 334, Accelerated (Honors) Advanced Calculus, Fall, 2013

This is the Math 334 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.

The following are links to current course information.

(12/6/13) The review sessions will be in Padelford c36, 10am-1pm Saturday/Sunday. John will be there on Sunday.
(12/2/13) George Green
(12/2/13) Definition of cosine.
(12/2/13) A Surface area counterexample.
(11/30/13) Sample problems for the final.
(11/22/13) A counterexample to my statement of Tonelli's theorem.
(11/20/13) Dave Duncan's thesis and a discussion of Fubini's theorem.
(11/12/13> There will be review sessions from 10:30-1:30, both Saturday and Sunday in C36, and John will be there on Sunday.
(11/12/13) Quote from Jacobi. Dirichlet alone, not I, nor Cauchy, nor Gauss knows what a completely rigorous mathematical proof is. Rather we learn it first from him. When Gauss says that he has proved something, it is very clear; when Cauchy says it, one can wager as much pro as con; when Dirichlet says it, it is certain ... Quoted in G Schubring, Zur Modernisierung des Studiums der Mathematik in Berlin, 1820-1840.--
(11/12/13) Integrability of sup and inf
(11/11/13) Sample problems for the second midterm.
(11/9/13) Fundamental theorem of algebra
(11/5/13) Links to 336_13 papers, 336_12 papers, and 336_11 papers.
(11/3/13) A discussion of Tiknonov regularization and least squares.
(10/17/13) First midterm review sessions Saturday and Sunday October 19 and 20. Padelford C36, 10:30-1:30. John will be there on Sunday.
(10/14/13) Sample problems for the first midterm.
(10/10/13) Dirichlet-(Heine?)-Lebesgue proof of the uniform continuity of a continuous function on a compact set.
(10/9/13) The connected sets of \( \mathbb{R} \) are intervals.
(10/7/13) More on norms.
(10/7/13) A proof of the Heine-Borel Theorem. (a distillation of various proofs)
(10/2/13) More details on sequential continuity.
(10/2/13) History of Heine-Borel Theorem
(9/26/13) Exercises from 1.1 and 1.2
(9/18/13) Topologist's sine curve
(9/13/13) A proof of Lebesgue's theorem on Riemann integration.
(9/13/13) A discussion of norms.
(9/13/13) The class email address is math334a_au13@uw.edu.
(9/13/13) Hyperbolic functions.
(9/13/13) The Cauchy-Binet formula and areas of submanifolds.
(9/13/13) Areas of hypersurfaces and parallelotopes.
(9/13/13) Federer's exposition of Geometric Measure Theory. His very dense book is 676 pages long.
(9/13/13) Volume of the n-ball.
(9/13/13) Fubini's theorem
(9/13/13) A set is Jordan-measurable if and only if the outer area of its boundary is 0.
(9/13/13) A geometric proof that (sin x)/x -> 1 as x->0.
(9/13/13) Differentiability
(9/13/13) Thomae's function.
(9/13/13) Best book ever written on inequalities: Inequalities by Hardy, Littlewood, and Polya.
(9/13/13) Jensen's Integral Inequality.
(9/13/13) Hadamard's Inequality for determinants of matrices and its application to measures.
(9/13/13) Jensen's inequality.
(9/13/13) The Arithmetic mean - geometric mean inequality and consequences.
(9/13/13) Derivation of least squares.
(9/13/12) Scanned first exercises from Folland)
(9/13/13) Cauchy's inequality
(9/13/13) The book Principles of Mathematical Analysis by Walter Rudin has a construction of the real numbers (as Dedekind cuts) from the rational numbers. It is on reserve in the math library. The reals can also be constructed from the rationals using Cauchy sequences by a general process known as completion that applies to any metric space.
(9/13/13) Basic Real Analysis by Tony Knapp is a good reference.
(9/13/13) A quote from Felix Klein (famous German mathematician) Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.
(9/13/13) Some printings of Folland have an error on problem 6b, page 125. It should read grad F₃(a)=0. (There should be a subscript 3 on F.)
(9/13/13) SAGE website.
(9/13/13) For those of you who have either of the first two printings of the text the old errata link is appropriate.
(9/13/13) The Encyclopedia of Integer Sequences is a great resource.
(9/13/13) Mathworld link.
(9/13/13) History of Mathematics Archive
(9/13/13) Errata for Folland's text. It is updated regularly. You should send email to folland@math.washington.edu if you spot any errors not already listed
(9/13/13) In problem number 7, section 1.3, consider f(x) to be defined only for x>0. Also assume the integers p and q are positive.
(11/26/13) Syllabus

morrow@math.washington.edu