Math 421 — Advanced Calculus I — Fall 2009

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

**Lectures:** MTWF 11-11:50pm in PM 116
**Office Hours:** MWF 9-10am in PM 248

**Study group:** T 9-10am and &Theta 11-12am, outside PM 248.
This is an informal get-together of students who are interested in talking
about the class and current assignments, in which I will participate.

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

**Phone:** 549-2044 (office — any time); 337-1210 (cell)
and 473-8928 (home) (both for emergencies only, please)

**Text:** *Understanding Analysis*, by Stephen Abbott. Please bring
it to class every day.

**Prerequisites:** Math 307 and three additional upper division math
courses.

**Content:** We will cover most of *Chapters 1-7* of the textbook,
along with various other additional topics as time and interest allow. At one
level, the theme of all of this work is to work carfully with the concept of
*taking a limit*, in the context of numbers, sequences, series, functions,
*etc.* At another, the point of course might be explained as to revisit
many of the ideas, definitions and techniques of the standard Calc I and II
class and to do them all very carefully and solidly. There could be very much
a "so you *thought* you understood that a while ago, but what about
*this*?", really with an idea of tearing down the house in order to
expose its lack of foundations, then to build those foundations and rebuild
the house (or start rebuilding). For example, we will start the term with
the question "Are you sure you know what the real numbers are?"

**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 may be one of your first classes in which the
primary goal is for you to understand and create *proofs*, not
calculations or algorithms. It is expected that you will take several 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.

Please keep a notebook (or organized sheaf of papers) of your reading notes. These will be collected periodically and graded (on a very coarse scale along the lines of 0 (missing) - 1 (far too skimpy) - 2 (quite thorough and clear) - 3 (worthy of publication in its own right). - 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, graded on a similarly coarse scale to that described above, 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 to rewrite a proof or other 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 Friday, December 11th, from 10:30-12:50 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, worksheets, your notesbooks and classroom
participation will together count for 50 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.

**The MFAT:** Students are required to take the MFAT (Major Field
Achievement Test) to obtain a grade in Math 421. It will be given at a
date and time to be determined, near the end of the term.

**Contact outside class:** Over the years I have been teaching, I have
noticed that the students who come to see me outside class are very often the
ones who do well in my classes. Now correlation is not causation, but why not
put yourself in the right statistical group and drop in sometime? I am always
in my office, PM 248, during official office hours. If you want to talk to me
privately and/or cannot make those times, please mention it to me in class or
by e-mail, and we can find another time. Please feel free to contact me for
help also by e-mail at
jonathan.poritz@gmail.com, to
which I will try to respond quite quickly (usually within the day, often
much more quickly); be aware, however, that it is hard to do complex
mathematics by e-mail, so if the issue you raise in an e-mail is too hard
for me to answer in that form, it may well be better if we meet before the
next class, or even talk on the telephone (in which case, include in your
e-mail a number where I can reach you).

**A request about e-mail:** E-mail is a great way to keep in touch
with me, but since I tell all my students that, I get *a lot* of e-mail.
So to help me stay organized, please put your full name and the course name
or number in the subject line of all messages to me. Also, if you are writing
me for help on a particular problem, please do not assume I have my book, it
is often not available to me when I am answering e-mail; therefore, you should
give me enough information about the problem so that I can actually help you
solve it (*i.e.,* "How do you do problem number *n* on page *p*"
is often not a question I will be able to answer).