Fall 2018

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?)