
Syllabus
for Math 461
Fall Semester
2006
Background and goals: This
course is designed primarily for undergraduates intending to go
to
graduate school in mathematics, statistics, or engineering. Some
beginning graduate students in
these areas may also take this
course. Although students will need some background in writing
proofs,
one of the principal goals of the course is to improve
proofwriting
skills.
Textbook:
Elementary
Topology, by Michael Gemignani. We will cover most of
Chapters
24 and 79 of the
book.
Prerequisites: MTH 320 or MTH
428H. Recommended: MTH
310.
Grading
Scheme
The main components of the final grade
are homework, exams, and an inclass presentation.
(The test
dates are tentative for now.)
Component  Date 
Worth 
Homework  Wednesdays  30% 
Midterm
Exam  October
13  25% 
Presentation  Various  15% 
Final
Exam  December
12  30% 
Policy
on missed work. The only valid reasons for missing
an exam
are: (1) illness, or (2) a conflicting
University activity that
cannot be rescheduled. Claims involving
such contingencies must
be supported by verifiable documentation
signed by: (1) your
physician in case of illness, or (2) your
faculty supervisor in
case of a nonrescheduleable University
activity. Each case will
be handled on an individual basis.
No late homework will be
accepted. However, I will drop your lowest homework
score.
Homework Policy
Homework assignments will
be posted on the course
webpage, and
will typically be due on
Wednesdays.
No late homework will be accepted.
I encourage you
start early and work in groups. There
are only a couple of caveats to group
work:
 You should try to do all of the
problems on your own
before getting together
with others. It does not benefit you
(on exams and in
the real world when you need to use math) to
simply
get solutions from your classmates! In fact,
there is research
suggesting that group work is much
more productive when everyone has
thought about the
problems before getting together.
 Everyone must
turn in their own solutions. In other words,
you
should write up your final solutions in the
privacy of your own room
(or your own library, cafe,
bar, roof, etc.).
Here are a few
guidelines for how to write up the
proofs:
 Write up the problems in
order,
using only one side of the page
and leaving lots
of space for me to write
comments. Please staple your
sheets together.
 Begin each problem with a statement
of that problem.
 Proofs
should be written in complete sentences, with
appropriate
use made of mathematical notation (your
textbook will serve as
a guide to how to do
this). Proofread what you've done to be
sure that
it's complete and makes sense. Remember that
proofwriting
is above all an act of communication,
and that the ultimage goal is
clarity.
 If you leave a small gap in a proof
that you're not able
to fill in, note this down. I'll
try to indicate how to fill
it in my comments.
 Start early! This way, if you are
stuck, you can still discuss
the problem with other
students or with me.
Presentations
Toward the end of the semester, every student will have to give a 20minute inclass presentation
on a selfcontained topic in topology. The purpose of this is twofold. First of all, this field of
math has many interesting examples and special topics that don't fit neatly into a linear exposition.
These presentations are a way for all of us to be exposed to these ideas. Second of all, these
presentations are intended to help you practice the art of explaining difficult concepts. The ideas
of mathematics and the related quantitative sciences are hard enough that it becomes very important
to communicate them clearly. In fact, I've found that having to explain something makes me understand
it on a much deeper level.
We will start scheduling student presentations in late October or early November. You should definitely
discuss the topic with me before presenting it. I would also be more than happy to suggest topics for
presentations.
Academic Integrity
Students are reminded that the University's policy concerning academic integrity is
covered in the Spartan Life booklet, General Student Regulations. According to the
handbook, "no student shall claim or submit the work of another as one's own".
Important Dates
9/1/06 
Open add period by computer enrollment ends. 
9/21/06 
Last day to drop with no record of course on transcript; end of tuition refund period. 
10/17/06 
Last day to drop a course or withdraw from all courses with no grade reported. 
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Last modified: Wed Aug 23 14:31:53 PDT 2006
