COURSE
OUTLINE FOR MATH 3CI: FALL 2009
MWF 11-12:15, Building 940, 1010
Professor: John Douglas Moore, SH6714, TuTh 1-2:30 or by appointment
Email: moore@math.ucsb.edu
TA: Robert Ream, SH 6432D,
Web page: http://math.ucsb.edu/~moore/3CI2009.htm
Outline
of course:
This is an honors version of Mathematics 3C and
covers mostly the same material that is covered in the usual version of
Mathematics 3C, the beginnings of the theory of differential equations and elementary
vectors and matrices.
This course is partially supported by a grant from
the Educational Advancement Foundation.
This foundation was set up by mathematicians who believe that the best
way to prepare future mathematicians and scientists is to have them discover
the key ideas through mathematical inquiry instead of listening to lectures in
a hall with hundreds of other students.
The idea is to have students grapple with the key ideas on their own so
that they can develop a deeper understanding of the subject.
The way the course operates is that the instructor
will pose questions or projects for you to work on. The idea is that you not consult textbooks for solutions
because that would interfere with the inquiry process. On the other hand, you can talk with
your classmates, the instructor or the TA whenever you like. If you have seen how to solve a problem
before, work with your classmates without telling them how to do it. You may find that by carefully thinking
through the problem again you may learn the ideas behind it more thoroughly.
It is important that you use ideas developed or
agreed to in this course, not results obtained from other sources. There may also be times when the
instructor will give a short lecture or an excerpt from a book or article to
work from.
Although as students you will develop many of the
key ideas on your own, we will try to ensure that you also acquire the skills
you need for success in subsequent courses.
We will expect you to be very careful about
notation. Do not write down
something down if you do not know what it means. We will work carefully to make sure the mathematical
reasoning that you use is complete and precise. This takes hard work, so be prepared to rewrite and reconsider
your ideas repeatedly.
From time to time (perhaps twice during the
quarter) you should present your solutions to problems to the class as a
whole. This will give you a chance
to improve your communication skills as well as solidify your understanding of
the material.
Notebook
for the class:
You should get a large spiral notebook from the
bookstore and use it record all the ideas and calculations for the course. You should write the entries in ink and
indicate the date each time you start a session. Do not worry about errors. If you realize that something is wrong, cross it out and
start over. Sometimes you will
find that earlier mistakes had some correct ideas, ideas that you can use on
other problems. Your notebook will
contain good ideas and bad ideas, false starts, rewrites of things you have
fixed up, as well as notes from class.
If you write up something on a computer, just staple it into your
notebook.
The notebook will be collected twice a quarter as
evidence of your class work.
Course
evaluation:
Your
grade in the class will be based on your class participation (20%), the
mathematics in your notebook combined with homework scores (30%), two midterms
(15% each) and a final (20%).
During
class, we will discuss how the exams are structured. They will be a combination of in-class and take-home exams.
You
will have homework after each class.
Sometimes the homework will consist of exercises for practice, or one or
two problems to be studied in depth.
Often it will simply consist of an assignment to think about, and work
on, and what ideas you might try to solve it.
Your
homework should be written down in your notebook, and if we discuss it in
class, you should write down corrections next to it. If you should miss a class, phone a classmate to find out
what happened or email the instructor or TA.