Math 334, Accelerated (Honors) Advanced Calculus, Fall, 2008

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.

(12/04/08) Padelford C401 is reserved Saturday and Sunday from 10:00-1:00 for review sessions. Nate will be there on Sunday.
(12/03/08) Area formula for a hypersurface in Rⁿ⁺¹ which is the graph of a function.
(12/01/08) Sample problems for the final exam.
(11/18/08) Review sessions for the midterm will be in Padelford C-401 from 10:00-1:00 Saturday and Sunday. Nate will be there Saturday 10:00-11:00 and Sunday 10:00-1:00.
(11/18/08) Here is the promised version of Fubini's theorem. I found this version in Hubbard and Hubbard Vector Calculus, Linear Algebra, and Differential Forms. The proof is mine, using upper and lower sums.
(11/17/08) Sample problems for the second midterm.
(11/14/08) Dylan has sent me a link to an article by (Sir) Michael Atiyah, "Advice to a Young Mathematician". Although the article is addressed to a graduate student in mathematics, it is good advice for anyone. Michael Atiyah is a Fields Medalist and also president of the Royal Society from 1990 to 1995.
(11/10/08) Nate's Monday office hours will be 3:45-4:45.
(11/10/08) Be sure to attend the lecture by Joe Felsenstein: Evolutionary trees, coalescents, and gene trees: can mathematicians find the woods? Link to MAC.
(11/6/08) Lecture on manifolds.
(10/31/08) Here's the promised note on positive definiteness. (not a Halloween joke)
(10/29/08) Some of you asked about appropriate conditions on F in problem #6 in section 2.5. The answer is no conditions are needed. Here is the explanation.
Join the Math Club. Math Club web site. Pizza/Lecture (Tues 10/28, PDL C036, 4pm-5pm) Speaker: Benjamin Hayes Title: Gauss's Lemma In the Heisenberg Group.
(10/21/08) Padelford C401 is reserved for review sessions Saturday and Sunday from 10:00-1:00. Nate will be there for most of the Saturday session. Nate will also be in his office Friday 2:30-5:00.
(10/20/08) Sample problems for the first midterm.
(10/14/08) Counterexamples to L'Hopital's Rule;Indeterminate Forms Revisited.
(10/14/08) On Being Mean to the Mean Value Theorem; On Avoiding the Mean Value Theorem; Rethinking Rigor in Calculus: The Role of the Mean Value Theorem .
(10/10/08) My remarks about checking uniform continuity were wrong unless they are made more precise. Here is an argument to cover the special case of the function x^1/2.
(10/03/08) The principle of induction.
(9/30/08) A geometric proof that (sin x)/x -> 1 as x->0.
(9/26/08) Nate's office hours will temporarily be Monday 3:30-4:30, Wednesday 5-6, and Thursday 1:30-2:30 in PDL C115.
(9/25/08) Cauchy-Schwartz notes
(9/25/08) 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.
(9/22/08) Basic Real Analysis by Tony Knapp is a good reference.
(9/16/08) Thomas Edison (attributed) "I have not failed. I've just found 10,000 ways that won't work."
(9/16/08) 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.
(9/16/08) 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.)
(9/16/08) Nate's mailbox is not in alphabetical order among the regular TA mailboxes. It is off in the upper right hand corner of the TA mailboxes. It is shared with Eric Nitardy.
(9/16/08) I will not talk about the Heine-Borel theorem and you will not be required to learn it.
(9/16/08) 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.
(9/16/08) SAGE website.
(9/16/08) For those of you who have either of the first two printings of the text the old errata link is appropriate.
(9/16/08) The Encyclopedia of Integer Sequences is a great resource.
(9/16/08) Mathworld link.
(9/16/08) History of Mathematics Archive
(9/16/08) 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
(9/16/08) 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.
(9/16/08) Syllabus(pdf)

morrow@math.washington.edu