Instructor: Farshid Hajir
Office: LGRT 1118
Phone: 545-6015 (office)
email: hajir@math.umass.edu
This page contains philosophical remarks. For more practical course
information, go to the main page.
I. Get some understanding and perspective on the general philosophy of mathematics from a mathematician's point of view.
II. Learn techniques of proof and the logic behind them.
III. Learn basic material for more advanced classes.
IV. Get some practice in speaking mathematics and in giving proofs in front of class and learn to work together in groups.
Some Words To the 300 Club
Is Mathematics an Art or a Science? It is neither and it is
both. When was the last time you made your own mathematical
discovery? You probably did more of this on your own as a kid than
you have in years. (Think of the first time you convinced yourself
"There is no 'biggest' number..."). In this course, you will have
what is likely to be your closest contact so far with mathematics in
the raw: Not the pre-packaged mathematics of typical high school Math
and Calculus classes, but the mathematics which is the Science/Art of
discovering and comprehending hidden patterns and structures. In a
sense, this is a language class: the language of rigourous reasoning.
The structure of the course, as engineered by Professor Extraordinaire
Bill Meeks, is what I like to think of as Challenging/Supportive. The
intensity will be somewhat similar to that of a language class:
methods, technical tools, and new ideas will be flying fast and
furious during the large lectures and no detail will be too gory for
inclusion. On the other hand, you will meet in a
very small group for an hour a week with extremely talented
and friendly undergraduate TAs who were in your shoes not so long ago
and who are very eager to help you to understand and appreciate the
material. The TAs and I will also be available on a fairly flexible
timetable so there will be people you can talk to one-on-one about the
material on an informal basis. Excellent course notes by Professor
Meeks, complete with sample homework problems, solutions, quizzes,
exams etc. are handed out free on the first day of class, so if you
can't find me or Laura or Garret, or Aaron, or Anna, or one of the
other 50 some odd members of the 300 Club with whom to discuss the
material, trusty Bill Meeks will always be there to discuss the
material with you.
To use another analogy, think of this as
a beginning class on flying an airplane. If doing mathematics is like
flying an airplane, then in typical Calculus classes, you learn how to
enter the cockpit, enter the coordinates for your destination in the
computer and engage the Automatic Pilot, who then takes over and does
everything while you sip your Diet soda. My main goal for this course
is to take you through enough manual take-offs and landings that by
the end, you have some kind of permit of basic skills competency for
flying on your own. This permit will hopefully also serve as your
ticket for success in future Mathematics classes such as Math 411,
461, and 523. At times, you might become so engrossed in the details
of how to fly a plane that you will forget to look at the beautiful
view. My secondary job will be to remind you to take your eyes off
the instruments and look out the window once in a while. For me, and
hopefully for you, too, mastering the techniques, which is not always
easy, is well worth the fantastic vistas we will have from on high.
Some Maxims We Will Encounter
It's good to be confused.
It's easy to make bad mistakes. It's very hard to make good mistakes.
To learn to fly a plane, it's important to crash it a few times.
When we figure this out, we're gonna feel pretty stupid.
If you build the right definitions, theorems will come. Pay homage to the Theorems, but Worship the Definitions.
Sometimes when a question is too hard, you need to ask a harder one to see what to do.
As the course goes on, hopefully you'll contribute some of your own maxims.
When working on any type of problem, it's good to keep in mind Polya's
Method: