Foundations of Mathematics
Math
281
DaveÕs Syllabus
Spring 2017
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 Ð 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:

Emily Stark (enstark@smcm.edu) 

Textbook: 
Book of Proof (free to download,
cheap at the bookstore) 

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 Ð 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 Ð 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, Emily Stark. 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 frequently, but not between 11pm and 7am).
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 (PoW)
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, Jan. 24^{th})
PoW solutions are graded largely on the quality of
your attempt Ð 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. They will be graded on
a credit/no credit basis, but you may revise and resubmit them as many times as
youÕd like Ð with two catches:
1. You
must turn something in on the duedate of each proof.
2. What
you turn in must be at least your
second draft. Demonstrate this by stapling them together (first drafts in
back).
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,
March 9th 
15 
Blog & Homework 
all semester 
15 
Written Proofs 
all semester 
30 
POWs 
all semester 
10 
Class Participation 
all semester 
10 
Takehome Final 
Due
Sat., May 6^{th}, 2pm 
20 
Total 

100 



The midterm will be in
class Ð 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.
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.
Learning Outcomes: At the
completion of this course, youÕll be able toÉ
á implement the rules
of mathematical logic as demonstrated by incorporating logic into valid
mathematical proofs.
á use the principles of
set theory as demonstrated by computing the results of set operations and
proving properties of sets and set operations.
á judge the validity of
a mathematical argument as demonstrated by analyzing attempts at mathematical
proofs and assessing whether or not these attempts constitute actual proofs.
á solve novel problems
in mathematics as demonstrated by successfully completing problems and proofs
that involve unfamiliar mathematical definitions.
á construct clear and
rigorous mathematical arguments as demonstrated by writing proofs that are
readable and mathematically correct.
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.