# Mathematics 185: Complex Analysis, Spring 2018

Lectures: MW 5:10-6:30, 3107 Etcheverry
Class Number: 42636
Instructor: Constantin Teleman, 905 Evans.
Office Hours: Mo 2–4, and by appointment.
GSI: Bryan Gillespie, bgillespie at you know where
Office Hours: W 12–2 and 3–5, 939 Evans; Th 2–5, 959 Evans; F 2–5, 939 Evans.

Prerequisites: Math 104.
Syllabus: Introduction to the theory of analytic functions of one complex variable. Main topics:

• Analysis: Contour integration, Cauchy's Theorem, power series and Laurent series expansions of analytic
functions, isolated singularities and the residue theorem, with application to evaluation of definite integrals.
• Geometry: Winding numbers, the argument principle and conformal mappings, Moebius transformations.

Required Texts: Sarason, Notes on complex function theory; Schaum Outlines, Complex Variables
Recommended Reading: Needham, Visual Complex Analysis.

Using the texts:
Sarason's notes are an excellent but brief account of the material, with elegant proofs and no wasted words.
Schaum's outlines have a wealth of exercises and many solved examples. (They also contain complete proofs,
but I have spotted some typos and small mistakes). This can be a good counterweight to Sarason's `pure' approach.
Needham's book offers beautiful geometric reasonings.

Grading: Weekly homework, 25%. Two in-class exams, 25% each. Final, 50%.
You will receive letter grades for each of these, and the lowest 25% of this 125% will be discarded — this means
either the lowest of the midterm of homework grades, or else, if the final is the lowest grade, it will only count for 25%.

Exams: In class, Wednesday 2/21 and Wednesday, 4/4. Final, Friday 5/11, 3–6, Cory 237

Make-up exams: Not normally offered; small variations in exam time may be permitted with good cause.
Sometimes, having a subsequent exam count twice may be the only solution. This must be agreed in advance.

Homework: Assigned weekly, on the web, due on Wednesdays at the start of class.
Only a selection of problems will be marked; please write your answers clearly to ensure you get proper credit.
Mind that the assignment is not firmly set until right after lecture on the prior Wednesday, even if it is posted early,
so do check the assignment page before completing. Please staple your sheets together. Late homework is not accepted:
the reader's time is constrained and timely homework must take priority. If you must miss a lecture, have friend submit it
for you, or leave it under my door before the lecture.

Collaboration: You are welcome to study in groups, and even discuss homework questions a bit, but any solutions
submitted must be your own. See, for example, the Academic Senate's guidelines spelling out the Honor Code.

General guidelines: For homework questions, basic exercises and review, your GSI is a good first port of call;
you may also meet your colleagues from other sections there. Questions related to lecture or reading assignments,
class policy, exam preparation and the like are best addressed to me. Mind that different sections of Math 185
are not synchronised and use different texts. Please make an effort to think about the questions ahead of time
and come with an agenda, to benefit most from interaction during office hours.

Queries and suggestions: Always welcome. I may not return your email if no immediate action is needed but I will