Math 416, Fall 2017
John E. McCarthy
Class TuTh 11.30-1.00 in Eads 204
JM Office 105 Cupples I
JM Office Hours M 3.00-4.00, Tu 2.00-3.45, Th 10.00-11.30, and by appointment
Exams There will be two exams in the course:
1) Exam 1 In
class. Thursday October 19.
2) Exam 2 Final exam. Monday December 18, 1.00-3.00.
There will be weekly homework sets during the semester, assigned on Tuesday and due the following Tuesday.
Homework 1, due September 5.
Homework 2, due September 12.
Homework 3, due September 19.
Homework 4, due September 28.
Homework 5, due October 3.
Homework 6, due October 10.
Homework 7, due October 24.
Homework 8, due November 7.
Homework 9, due November 14.
Homework 10, due November 21.
Homework 11, due December 7.
Math 318, or permission of instructor.
Complex Analysis is an essential tool in (almost) all areas of modern
mathematics. It started with
Tartaglia's solution of the cubic - in order to find the real roots of a real cubic polynomial, the formula
requires complex numbers. The fundamental theorem of algebra says that every complex polynomial
can be factored into linear factors. This means that every matrix has complex eigenvalues, though not necessarily real ones.
Analytic functions of complex variables - functions that can locally be written as power series - are the heart of the subject.
They are both flexible and rigid, in ways we will discuss, and make the subject very attractive.
Basis for Grading
Attendance and class participation will be 5% of your grade, homework
will be 30%, the midterm will be 30%, and the final will be 40%.
Homework is an extremely important part of the course. Whilst talking
to other people about it is not dis-allowed, too often this degenerates
into one person solving the problem, and other people copying them
(often justified to themselves by saying "I provide the ideas, X does
the details" - but the details are the key. If you can't translate the
idea into a real proof, you don't understand the material well enough).
So I shall introduce the following rules:
(a) You can only talk to some-one else about a problem if you have made a genuine effort to solve it yourself.
(b) You must write up the solutions on your own. Suspiciously similar write-ups will receive 0 points.
I expect you to come to class every day, and to participate in
I also expect you to stay abreast of the material we are covering, and may call on you at any time to answer a question.
Class etiquette: don't be disruptive or discourteous. No beeping, ringing, crunching, rustling, leaving early or arriving late. No texting, sleeping, checking your phone.
Texts Complex Function Theory by Donald Sarason (AMS, 2007)
Any book on complex analysis in Olin library will contain all the
material we cover.
Find one whose style you like and check it out.