Foundations of Mathematics
Math
281
DaveÕs Syllabus
Fall 2014
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:
How do you
establish mathematical certainty?
Important
Facts:
Professor:

Dave
Kung 


175
Schaefer Hall, x4433 (or 2408954433 from offcampus) 



TA:

Anna
Steinfeld 




Office
Hours: 



Where
to go for help: To learn the key concepts of FOM,
weÕll use a variety of classroom activities, homework, and writing assignments
(both online and on paper). WeÕll do lots of work on the whiteboard
tables in 161 – please avoid scratching the tables with threering
binders or sharp jewelry. 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, Anna Steinfeld. 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 three different types of assignments: the
problem of the week, your blog and other homework from the book, and written
proofs.
Every Tuesday 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. (The first one is up and will be due Tuesday, Sept. 9^{th}.
PoW solutions are graded largely on the quality of
your attempt – and your lowest grade will be dropped before averaging the
rest.
For the blog, I recommend using
Wordpress.com (which allows for some math symbols). See the separate ÒGuide to
Writing a FOM BlogÓ for more details. In addition to your blog, problems from
the book will be occasionally assigned. Some will be done on your blog, others
on paper.
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 
Thursday, October 30th 
20 
Blog & Homework 
all semester 
15 
Written Proofs 
all semester 
15 
POWs 
all semester 
15 
Class Participation 
all semester 
10 
Takehome Final 
Due Dec. 15^{th}, 7pm 
25 
Total 

100 



The midterm will be in
class – though you may stay late if you need. The final will be a takehome
exam that must be done without consulting other people or other books.
Thanks for reading this far  on Thursday, September 4^{th}, please
come to the Math Wing of Schaefer Hall before class (not the regular room) –
but donÕt tell anyone else.
By the end of the semester,
you will understand the amazing role proofs play in mathematics, as well as how
and why to write them.
Fine Print
Rules for academic
misconduct are contained in your student handbook. Anyone violating those rules
will be dealt with quickly and effectively, to preserve the academic integrity
of your fellow students and SMCM.
If you have a documented
learning disability, please see me in the first week of classes to discuss your
accommodations.