Math 334, Accelerated (Honors) Advanced Calculus, Fall, 2012
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.
- (12/5/12) Integrability of sup(f,g) and
inf(f,g).
- (12/4/12) Sample problems for the final exam.
- (11/16/12) Dave Duncan's thesis with a
Fubini counterexample
- (11/15/12) Joe Taylor's analysis book Foundations of Analysis,
J. L. Taylor, AMS Pure and Applied Undergraduate Texts vol. 18, 2012 is a good
reference for the change of variables formula.
- (11/14/12) Sample problems for the second
midterm.
- (11/14/12) Properties of the Cantor set.
- (11/13/12 A characterization of limsup.
- (10/14/12) Sample problems for the first
midterm. This is quite a long list. Work as many as you can. Latex file for sample1.pdf.
- (10/11/12) Topologist's sine curve
- (9/13/12) A proof of Lebesgue's theorem on Riemann integration.
- (9/13/12) A discussion of norms.
- (9/13/12) The class email address is math334a_au12@uw.edu.
- (9/13/12) Hyperbolic functions.
- (9/13/12) The Cauchy-Binet formula and areas
of submanifolds.
- (9/13/12) Areas of hypersurfaces and
parallelotopes.
- (9/13/12) Federer's exposition of Geometric Measure Theory. His very dense book is 676 pages long.
- (9/13/12) Volume of the n-ball.
- (9/13/12) Fubini's theorem
- (9/13/12) A set is Jordan-measurable if and only if the outer area of its boundary is 0.
- (9/13/12) A geometric proof that (sin x)/x ->
1 as x->0.
- (9/13/12) Differentiability
- (9/13/12) Thomae's function.
- (9/13/12) Best book ever written on inequalities: Inequalities by Hardy, Littlewood, and Polya.
- (9/13/12) Jensen's Integral Inequality.
- (9/13/12) Hadamard's Inequality
for determinants of matrices and its application to measures.
- (9/13/12) Jensen's inequality.
- (9/13/12) The Arithmetic mean - geometric mean inequality and consequences.
- (9/13/12)
Derivation of
least squares.
- (9/13/12) Scanned first exercises from Folland)
- (9/13/12) Cauchy's inequality
- (9/13/12) 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.
- (9/13/12) Basic Real Analysis by Tony Knapp is a good reference.
- (9/13/12) 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.
- (9/13/12) 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.)
- (9/13/12) If you are trying to access journal links from
off campus via MYUW, Comcast, Qwest, etc., you must remember to
authenticate yourself as UW affiliated.
- (9/13/12) SAGE website.
- (9/13/12) For those of you who have either of the first two
printings of the text the old errata link is appropriate.
- (9/13/12) The Encyclopedia of Integer Sequences is a great resource.
- (9/13/12) Mathworld
link.
- (9/13/12) History of Mathematics Archive
- (9/13/12) 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
- (9/13/12) 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.
- (9/13/12) Syllabus(pdf)
morrow@math.washington.edu