Foundations of Mathematics

Math 281                                Dave’s Syllabus                                      Fall 2006

There’s some irony to the name of this course.  You’ve probably taken math classes for 13 straight years and now you get to the Foundations!?!  What’s all of your math knowledge built on anyway, sand?  Nothing?

Actually your path through mathematics mirrors the historical development of those same ideas.  Limits and derivatives were being used for 170 years before good definitions were developed.  Various cultures talked about a concept of infinity for centuries before Georg Cantor provided the foundations for the mathematical study of infinity.  (He proved a stunning fact that we might learn in this course – not only are there different sizes of infinity, but there are actually an infinite number of sizes of infinity!)

In this semester of FOM, we’ll work our way through the following topics, all of which will be vital in future math courses (and, actually, in life):

• What it means to prove something & why we prove things.
• Set theory - sets, power sets, combinations of sets.
• Logical statements - the real language underlying mathematics.
• Quantifiers – mathematically precise uses of “for all” and “there exists”.
• Induction – proving an infinite number of cases – all at once!
• Problem solving skills – systematic ways to get unstuck when you’re stuck on a problem.

To learn these key concepts in mathematics we’ll use a variety of classroom activities, homework, and writing assignments.  Also, you’ll be expected to spend a significant amount of time reading the textbook.

Important Facts:

Professor:

Dave Kung

175 Schaefer Hall, x4433

(or 240-895-4433 from off-campus)

dtkung@smcm.edu

TA:

Mary Koran

mekoran@smcm.edu

Office Hours:

 Mon 2:40-3:40 and by appointment. Thu 1:30-2:30 Fri 10:40-11:40

Where to go for help: You have three main resources to draw on when you need help in this class. The first and most important is your fellow classmates. This course will be hard – at times very hard.  It will go much smoother for all of us if you start getting to know your classmates and start studying with them outside of class early in the semester.  The second is me – my contact info and office hours appear above.  I will also be around at other times - feel free to drop by and say hi.  If you can't find me, email or call and we'll schedule an appointment that works for both of us.  If an emergency comes up and you are forced to miss class, you should drop me an email (I check it very frequently).

Your third resource will be your TA, Mary, who excelled in this course last year.

Assignments: There will be three different types of assignments: your journal, written proofs, and problem solutions.

For the journal, you may choose any type of notebook/binder/daily diary.  See the separate “Guide to Writing a FOM Journal” for more details.

Written Proofs will be assigned about once a week and collected in class.  You will be graded on how complete and understandable your proofs are.  For your first two proofs, you will be encouraged to revise and resubmit them.  This will give you some time to adjust to our expectations.  We encourage you to work with others to develop your proofs but the writing must be entirely your own.

For several years we have posted a Problems of the Week on the MathCS wing.  We will continue to do this and part of your grade will be based on your work on these problems.  Although you may not be able to solve each one, you must turn in your work for each one – showing the progress you made toward understanding and solving the problem.  Your lowest grade will be dropped before averaging the rest.