Math 336, (Honors) Advanced Calculus

Lecture:  MTWTh 10:30, SMI 107
Instructor:  Jim Morrow
Phone:  543-1161

    E-mail:  morrow@math.washington.edu
    Web address: http://www.math.washington.edu/~morrow/336 13/336.html

Office Hours: MW 9:30-10:20, C439 Padelford
Quiz Section: F10:30, SMI 107
TA:  Jerry Li
Office Hours: TBA; C115 Padelford

    E-mail:  jerryzli@u.washington.edu

Text:  Complex Variables (required)
Author:  Joe Taylor

Math 336 is an introduction to complex analysis. I plan to cover the basics: complex numbers, complex functions, analytic and harmonic functions, sequences, series, elementary functions, complex integration, Taylor and Laurent series, residue calculus, harmonic functions, infinite products, gamma function, and zeta function. I hope to give a complete proof of the prime number theorem as the highlight of the course. This proof is a beautiful version of what was once an extremely complicated argument.

We will be using a new textbook and I will probably make several in-course adjustments to the syllabus. As part of the course, I will ask you to write an expository paper on a mathematical topic of your

choosing. This paper should read somewhat like a book review. The source material should come from a mathematical journal. During the quarter, I will post links on the 336 website to papers that I think are suitable. I have posted some links on the 334 and 335 website that are also recommended. I will also suggest journals that have articles that can be read by students at your level. If none of the suggestions I make appeal to you, I am open to your own suggestions. The topics need not be related to the material of 334/5/6 (for example combinatorics or number theory might appeal to you). In any case, I want you to discuss your choice with me before proceeding. I’d like you to make this choice before Monday, May 6 and submit a draft paper on Thursday, May 16. The final paper will be due on Thursday, May 30. This paper will count 10% of your course grade.

Homework will be collected at regular intervals and will count 20% of the course grade. You might find the homework this quarter to be harder than previous quarters. We are starting to function at the senior, early graduate, level now. We will rely on our knowledge of basic results in real analysis. Don’t be discouraged if you find them difficult.

There will be two 50-minute midterm tests which will each count 20% of the course grade. The midterm tests will be closed book but you will be allowed to bring notes on one side of a notebook size sheet of paper. There will be a two hour closed book final exam which will count 30% of the course grade. For the final you will be allowed to bring notes on both sides of a notebook size sheet of paper. No calculators will be allowed on tests.

I would like you to read chapters 1,2,3,sections 4.3 ,4.4, 4.5, 5.1, 5.2, 6.1, 6.2, 6.3, 6.5, 6.6, 7.1, 8.1, and chapter 9.

Here are the homework assignments (they will probably be modified) :

DATE ASSIGNMENT (from Taylor)
Apr. 5 1.1: 18; 1.3: 6; 1.4: 15
Apr. 12 2.2: 8, 12; 2.3: 7; 2.4: 2, 8, 9
Apr. 19 2.5: 4, 7, 14, 15; 2.6: 12; 2.7: 3
Apr. 26 3.1: 16; 3.2: 11, 12, 13, 14, 15, 16; 3.3: 4, 5, 8
Apr. 29 MIDTERM
May 3 3.4: 8, 9, 10; 3.5: 4, 5, 8, 10
May 10 4.3: 9, 11, 12; 4.4: 8, 11; 4.5: 1, 3, 5, 10, 11
May 17 5.1: 8, 13; 5.2: 2, 7; 6.1: 2, 3
May 20 MIDTERM
May 24 6.3: 3, 4; 6.5: 2, 10, 11, 12; 6.6: 6
May 31 7.1: 6, 7, 8; 8.1: 1, 2, 3, 7, 8, 9; 9.1: 5, 6, 8, 9, 10
June 7 9.2: 2, 3, 4, 5; 9.3: 1, 2, 3, 8; 9.4: 1, 6
June 10 FINAL EXAM (8:30-10:20 a.m.)

Monday, May 27 is a holiday. These assignments are due at the beginning of class on the due date.