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

always think about it. Please come by in the first or second week
to introduce yourself and tell me about your background.