Foundations of Mathematics
Math
281
DaveÕs Syllabus
Fall 2010
ThereÕs some irony to the name of this course. YouÕve probably taken math
classes for 13 straight years and now
you get to the Foundations!?! WhatÕs 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 will hopefully get
to 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, weÕll work our
way through the following topics, all of which will be vital in future math
courses (and, actually, in life):
The thread that connects all of these
topics, and the main point of this course, is to answer this question:
What does it
take to establish mathematical certainty?
Important
Facts:
Professor:

Dave
Kung 


175
Schaefer Hall, x4433 (or 2408954433 from offcampus) 



TA:

Christiana
Sabett 



Office
Hours: 



Text: Foundations of Higher Mathematics: Exploration and Proof,
by Dan Fendel and Diane Resek.
Where
to go for help: To learn the key concepts of FOM,
weÕll use a variety of classroom activities, homework, and writing
assignments. Also, youÕll be expected to spend a significant amount of
time reading the textbook. When you get stuck, youÕll have three main
resources to draw on. 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
your able teaching assistant, Lydia Garcia, fresh back from a mathpacked
semester in Budapest. Your third resource is me  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).
Assignments:
There will be four different types of assignments: the
problem of the week, your journal, written proofs, and problem solutions.
Every Monday I will post a Problem of
the Week on the math wing. Please stop by and read the problem. Solutions are
due one week later. (Twice during the semester this will happen on Wednesday,
since Monday classes are cancelled on Labor Day and Fall Break. PoW solutions are graded largely on the quality of your attempt
– and your lowest grade will be dropped before averaging the rest.
For the journal, you may choose any
type of notebook/binder/daily diary. See the separate ÒGuide to Writing a
FOM JournalÓ 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.
Grading:
Assessment
Date
Percent
Midterm 
Wednesday, October 27^{th} 
15 
Journal 
all semester 
15 
Written Proofs 
all semester 
15 
Problem Solutions 
all semester 
10 
Class Participation 
all semester 
10 
Takehome Final 
Due Dec. 13^{th}, 10am 
20 
Final Project 
Due Dec. 6^{th} , in class 
15 
Total 

100 
The midterm will be in
class – though you may start as early as 8am if youÕd like. Anyone
who has an 8am class will be given an opportunity to have a similar amount of
time. The final will be a takehome exam which
must be done without consulting other people or other books. The final
project is your chance to be creative. Past projects include short films,
skits, board games, mathematical sculptures, short stories, musicals, and a
South Park takeoff called Math Park.