Professor: Jeff Johannes
Section 1 MWF
11:30a-12:20p Sturges 105
Office: South
326A
Telephone: 245-5403
Office Hours: Monday 2:30 - 3:20p, Tuesday 10:30 - 11:20a, 8:00
- 9:00p, Wednesday 12:30 - 1:20p, Thursday 8:00 - 9:00p, and by appointment
or visit, and by appointment or visit
Email Address: Johannes@Geneseo.edu
Web-page: http://www.geneseo.edu/~johannes
Textbook
An
Introduction to Complex Analysis and Geometry by John P.
D'Angelo
Purposes
Extending almost all mathematics to complex numbers.
High school algebra and geometry (including trigonometry, logarithsm
and exponentials), calculus, linear algebra, differential equations,
abstract algebra, topology, …
Overview
Because of the fact that we will be extending so many
areas, this is a perfect opportunity to solidify everything that you have
done before, or to get little tastes of things you haven't seen before.
We'll start with some basics of real numbers, then learn the
basics of what and why complex numbers are. After that we will see
interplay with geometry, linear algebra, and then head toward topics from
calculus: series, differentiation and end with the richest area of all
- integration.
Learning Outcomes
Math 371 - Upon successful completion of Math 371 -
Complex Analysis, a student will be able to:
- Represent complex numbers algebraically and geometrically,
- Define and analyze limits and continuity for complex functions as well
as consequences of continuity,
- Apply the concept and consequences of analyticity and the
Cauchy-Riemann equations and of results on harmonic and entire functions
including the fundamental theorem of algebra,
- Analyze sequences and series of analytic functions and types of
convergence,
- Evaluate complex contour integrals directly and by the fundamental
theorem, apply the Cauchy integral theorem in its various versions, and
the Cauchy integral formula, and
- Represent functions as Taylor, power and Laurent series, classify
singularities and poles, find residues and evaluate complex integrals
using the residue theorem.
Grading
Half of your grade will come from problem sets.
Another tenth will come from a final project and each of two midterm
exams. The final fifth will come from the final exam.
Problem Sets
After we finish each chapter problem sets will be
collected. They will be returned with a letter grade based on the
following factors: number of exercises correctly completed (with
potential but unlikely modifications based on difficulty of exercises
correctly completed), number of exercises completed by classmates, and some
subjective determination on my part as to what seems appropriate. Each
problem set will be scaled using a linear function of the number of
exercises completed (problems correctly completed by only one student will
earn two points). Submitting no problem set by the day it is due will
earn a score of zero. I strongly recommend consulting with me as you
work on these problem sets. I also recommend working together on them,
however I want to carefully emphasise that each must write up their own
well-written solutions. A good rule for this is it is encouraged to
speak to each other about the problem, but you should not read each other's
solutions. A violation of this policy will result in a zero for the
entire assignment and reporting to the Dean of Students for a violation of
academic integrity.
Solutions and Plagiarism
There are plenty of places that one can find all kinds of
solutions to problems in this class. Reading them and not referencing
them in your work is plagiarism, and will be reported as an academic
integrity violation. Reading them and referencing them is not quite
plagiarism, but does undermine the intent of the problems. Therefore,
if you reference solutions you will receive 0 points, but you will *not* be
reported for an academic integrity. Simply - please do not read any
solutions for problems in this class.
Presentations
When discussing the new material for each section, each
day will begin with an opportunity for student presentation. Potential
problems will be offered in class and maintained here.
Students will earn one extra point for the corresponding problem set by
presenting well and correctly. I will have a priority list at all
times for presentations. Students may present more than once per
problem set, but representations have lowest priority. Students may
earn no more than one point per problem set in this fashion.
Opening Meeting
Students will earn one extra point on the first problem
set by visiting office hours during the first two weeks of classes, i.e. no
later than 10 September.
Final Project
Your final project will constitute writing up a detailed
explanation (filling in the gaps) of a topic in the text that we will omit
(or another topic selected by you and approved by me), and a completion of a
problem set (graded as above) from the exercises in that section.
Exams
The exams will consist of a few straightforward problems
designed to emphasise a personal understanding of the basics.
Feedback
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for how the
course is running. Remember, the sooner you tell me your concerns, the
more I can do about them. I have also created a web-site
which
accepts anonymous comments. If we have not yet discussed this in
class, please encourage me to create a class code. This site may also
be accessed via our course page on a link
entitled anonymous
feedback. Of course, you are always welcome to approach me
outside of class to discuss these issues as well.
Academic Dishonesty
While working on homework with one another is encouraged,
all write-ups of solutions must be
your own. You are expected to be able to explain any solution you
give me if asked. The Student Academic Dishonesty Policy and Procedures will
be followed should incidents of academic dishonesty occur.
Disability Accommodations
SUNY Geneseo will make reasonable accommodations for
persons with documented physical, emotional or learning disabilities.
Students should consult with the Director in the Office of Disability
Services (Tabitha Buggie-Hunt, 105D Erwin, tbuggieh@geneseo.edu) and their
individual faculty regarding any needed accommodations as early as possible
in the semester.
Religious Holidays
It is my policy to give students who miss class because
of observance of religious holidays the opportunity to make up missed
work. You are responsible for notifying me by September 10 of plans to
observe a holiday.
Schedule (loose and subject to variations)
August 27 Introduction
29
1-3.0 Chapter 1 (1-2, 3, 4, 5)
31
3.2, 3.1
September 5 3.3
7
4
10 5
12 Chapter
2 (1, 2, 6, 7, 8) 1
14 PS1 due
17 2
19 6
21 7
24 8
26 PS2 due
28 Review for
exam
October 1 exam (Chapter 1-2)
3 1 Chapter 3 (1, 2,
4, 5)
5 2
10 4
12 5
15 2.3
Chapter 4 (2.3, 2.4, 2.5, 1, 2)
17 2.4
19 PS3 due
22 2.5
24 1
26 2
29 5.1
31 Chapter 5 (1,
2, 3, 4, half of 5) PS4 due
November 2 review
5 exam (Chapter
3-4)
7 2
9 3
12 4
14 5 (up to exercise
5.34)
16 Chapter 6 (1, 2, 4,
5) 1
19 PS5 due
26 2
28 4
30 5
3 Chapter 7 (1, 2) 1
5 2
7
10
Review, PS6-7 due, Final Project due
Friday, December 14 8-11a Final Exam (half 5-7, half 1-4) (maybe
8:30-11a? 8-10:30a? 8:30-11:30a?)