Math 425 — Complex Variables — Spring 2010

Here is a shortcut to the course schedule/homework page.

**Lectures:** MWF 10-10:50pm in PM 115
**Office Hours:** MWF 11am-12pm and TΘ12-1pm in PM 248

**Instructor:** Jonathan
Poritz
**Office:** PM 248
**E-mail:**
jonathan.poritz@gmail.com

**Phone:** 549-2044 (office — any time); 357-MATH
(personal; please use sparingly)

**Text:** *Complex Variables and Applications, 8 ^{th}
Edition*, by James Ward Brown and Ruel V. Churchill. Please bring
it to class every day.

**Prerequisite:** Math 325.

**Content:** We will cover most of *Chapters 1-7* of the textbook,
along with various other additional topics as time and interest allow (it
would be particularly fun to spend some time with *Chapters 9&10*). The
theme of all of this work is * doing calculus with complex-valued functions
of a complex variable*. The amazing thing is how perfectly it all fits
together, compared to calculus over the real numbers. If real analysis (the
grown-up term for "calculus over the real numbers") sometimes feels like

Guernica | |

by | |

Pablo Picasso |

well, then complex analysis is more like

Waterfall | |

by | |

M.C. Escher |

**Academic integrity:** Mathematics is more effectively and easily
learned — and more fun — when you work in groups.
However, all work you turn in must be your own, and any form of cheating
is grounds for an immediate F in the course for all involved parties.

**Students with disabilities:** The University abides by the Americans
with Disabilities Act and Section 504 of the Rehabilitation Act of 1973, which
stipulate that no student shall be denied the benefits of education "solely by
reason of a handicap." If you have a documented disability that may impact your
work in this class for which you may require accommodations, please see the
Disability Resource Coordinator as soon as possible to arrange accommodations.
In order to receive this assistance, you must be registered with and provide
documentation of your disability to the Disability Resource Office, which is
located in the Psychology Building, Suite 232.

**Your activity:** This is a typical 400-level class, in which the
primary goal is for you to understand and be able to work with *ideas*,
not numbers and formulæ (or even algorithms). It is expected that you
will take several (further) steps into the subculture of academic mathematics,
which has its own characteristic ways of speaking, listening, reading, writing,
and discourse, some of which are more than two thousand years old, while most
of the rest are at least several decades or centuries old... and yet they are
tremendously powerful and efficient. In fact, an argument could be made that
they underlie in a fundamental way the scientific method and the whole project
of modernism itself. It is for this reason that we will spend a fair bit of
time discussing and practicing these metamathematical processes both in class
and in work you do at home. In particular:

- Reading serious mathematics
*must*be a very active process, you should read with pen(cil) and paper in hand, to do calculations verifying an author's claims, to try out general statements on particular simple examples (you should always try to have a least one simple example with which you are quite comfortable and to which any general statement you are reading applies), to make note of connections to other ideas, to fiddle with related statements to those you are reading which have more hypotheses (and so are perhaps easier to prove) or fewer (and so are perhaps incorrect -- in which case you can note a counterexample) and stronger or weaker conclusions.

- All of the above applies equally well to learning from lectures or discussions in class (or in any other class or mathematics seminar). I would like all students to try to stay this focused and mentally active in class, and I will expect all students to participate (either by asking questions or volunteering questions or explanations or by being called upon to do so). This classroom participation will count as part of your course grade.
- There will be fairly significant weekly problem sets due eacy Monday. Feel free to work with your classmates (although you must hand in your own paper). We may also spend time in class discussing the problems before and after they are due. They will be graded and returned as quickly as I am able -- the HW points are a major part of your class grade, please give them your best effort. Sometimes you will be asked (or given the option) to rewrite a (or several) homework problem.
- We will have two midterms and a final, all with a possible in-class and
take-home part. Details and dates will be announced as we get nearer
to those dates, but certainly at least a week in advance. Our in-class
final will be
**on Thursday, April 29th, from 8:00-10:20 in our usual classroom**.

**Grades:** Your total homework points will be scaled to be out of
200. Both midterms will be graded out of 100, while the final will be out
of 150. Group activities, classroom participation an other impromtu activities
will together count for 50 more points. This means that the maximum possible
course points are 600. Letter grades will then be calculated in a way no more
strict than the old "90-100% is an A, 80-90% a B, *etc.*" system, based
on your total points. (Note that by Math Department policy, there will be no
+'s or -'s on final course grades.) On test days, attendance is required --
if you miss a test, you will get a **zero** as score; you will be able to
replace that zero only if you are regularly attending class and have informed
me, **in advance**, of your valid reason for missing that day.

**Contact outside class:** Don't hesitate to talk to me at my office,
PM 248, during official office hours -- or any other time/place you can find
me on campus. And if you cannot find me, e-mail at
jonathan.poritz@gmail.com is
the best alternative (except for emergencies, in which cases try my phone).