Math
416, Spring 2021
Complex
Analysis
Instructor
John E. McCarthy
Class
TuTh
11.30-12.45
Office Hours M: 4-5 Tu: 2.30-3.15 Th: 1.00-1.45 Zoom Office Hours
Phone
935-6753
Exams There will be two exams in the course:
1) Exam 1 Midterm - Friday March 19.
2) Exam 2 Final exam. Tuesday May 11,
1.00-3.00.
Homework
There will be weekly homework sets during the semester, assigned on Tuesday and due the following Tuesday.
Study/Wellness Days
The following dates are either Study days in the Mathematics and Statistics Department, or Wellness Days in Arts and Sciences:
Tuesday Feb 9
Tuesday Mar 2
Wednesday Mar 3
Monday Mar 22
Monday April 12
On these days, there are no office hours or classes. Any assignment due that day is extended 24 hours
(so the one assigned Feb 2 is due Feb 10, and the one assigned Feb 23 is due Mar 4).
Prerequisites
Math 318, or permission of instructor.
Description
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.
Content
Basis for Grading
Attendance and class participation will be 30% of your grade, homework
will be 30%, the midterm will be 15%, and the final will be 25%.
Homework
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.
(c) You may not get solutions from the internet.
Academic Integrity
Academic Integrity is especially important when we are struggling to allow remote learning.
During exams, you may not get help from anyone else, or seek solutions online.
I will ask you to write and sign the following Honor Statement on each exam:
“I affirm that I have not given or received any unauthorized help on this assignment, and that this work is my own.”
I expect you to attend class every day, and to participate in class discussions.
It is important to stay abreast of the material. At the beginning of class I will call on people to give definitions or state theorems; this will be part of your grade. I may call on you at any time to answer a question.
Class etiquette (in person): don't be disruptive or discourteous. No beeping, ringing, crunching, rustling, leaving early or arriving late. No texting, sleeping, checking your phone.
Class etiquette (online): please stay fully engaged - no multitasking. Except for compelling reasons, please keep your video on.
Texts Complex Function Theory by Donald Sarason (AMS, 2007)
Additional Reading
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 (some of them are ebooks).
Accommodations
based upon sexual assault:
The University is committed to offering reasonable academic accommodations
to students who are victims of sexual assault. Students are eligible for
accommodation regardless of whether they seek criminal or disciplinary
action. Depending on the specific nature of the allegation, such measures
may include but are not limited to: implementation of a no-contact order,
course/classroom assignment changes, and other academic support services and
accommodations. If you need to request such accommodations, please direct
your request to Kim Webb,
Director of the Relationship and
Sexual Violence Prevention Center, or Jen Durham Austin, Support
Services Counselor. Both Kim Webb and Jen Durham Austin are confidential
resources; however, requests for accommodations will be shared with the
appropriate University administration and faculty. The University will
maintain as confidential any accommodations or protective measures provided to
an individual student so long as it does not impair the ability to provide such
measures.
If a student comes to me to discuss or disclose an instance of sexual
assault, sex discrimination, sexual harassment, dating violence, domestic
violence or stalking, or if I otherwise observe or become aware of such an
allegation, I will keep the information as private as I can, but as a faculty
member of Washington University, I am required to immediately report it to my
Department Chair or Dean or directly to Ms. Jessica Kennedy, the University's
Title IX Director. If you would like to speak with directly Ms. Kennedy
directly, she can be reached at (314) 935-3118, jwkennedy@wustl.edu, or by visiting the Title IX office in
Umrath Hall. Additionally, you can report incidents or complaints to the
Office of Student Conduct and Community Standards or by contacting WUPD
at (314) 935-5555 or
your local law enforcement agency. See: Title IX
You can also speak confidentially and learn more about available resources
at the Relationship and Sexual Violence Prevention Center by calling (314)
935-3445 for an appointment or visiting the 4th floor of Seigle
Hall. See: RSVP Center
Bias
Reporting:
The University has a process through which students, faculty, staff and
community members who have experienced or witnessed incidents of bias,
prejudice or discrimination against a student can report their experiences to
the University's Bias Report and Support System (BRSS) team.
See: brss.wustl.edu.
Mental
Health:
Mental Health Services' professional staff members work with students to
resolve personal and interpersonal difficulties, many of which can affect the
academic experience. These include conflicts with or worry about friends or
family, concerns about eating or drinking patterns, and feelings of anxiety and
depression.
Center for
Diversity and Inclusion (CDI):
The Center of Diversity and Inclusion (CDI) supports and advocates
for undergraduate, graduate, and professional school students from
underrepresented and/or marginalized populations, creates collaborative
partnerships with campus and community partners, and promotes dialogue and social
change. One of the CDI's strategic priorities is to cultivate and
foster a supportive campus climate for students of all backgrounds, cultures
and identities.
See: diversityinclusion.wustl.edu/