Math 199 - Syllabus
Q: What is this class for?
A: This class is known as a bridge class,
since the aim is to help you transition from "regular" math classes to
"proof based" math classes which are required of math majors. Our philosophy
is that proofs are best seen in their native habitat, among fun and sometimes
Q: How is the course structured?
We will take a "problems-first" approach. We break each topic into two-day
units. Before the first day, you will be given some problems to work on.
You will then hand your progress on these problems in the form of a
"working paper" at the beginning of the first day. Progress may range
from exploring some examples and breaking the problem down into smaller
questions to giving full solutions. Then on the first day of the unit we will
work on groups on these problems plus a few more, handing in further progress
when appropriate. The second day will be more of a lecture, based on the
material covered by the problems from the first day. We will formalize
problem-solving techniques and give proofs of facts which apply generally.
The proofs will be easier to follow, since we will have encountered
the main ideas on the first day.
The units will happen on M,Tu and W, F. On the following Monday there will be
a set of problems from these two units which are to be written up in
in your best, polished style. (This is in addition to the working paper
for the next unit).
Q: How will grading work?
The grading is explicitly described on the
Q: What are our texts?
The main text is "Mathematical thinking: problem solving and
proofs" by D'Angelo and West. We chose this text because
it has by far the best collection of problems. Parts of it
can be difficult to read. One challenge
of the class will be trying - often together - to understand
what the text is getting at. More friendly introductions to some
topics can be found in "The heart of mathematics" by Berger and
Starbird. I have purchased a six extra copies of this book
and have left them in Hilbert Space, the gathering lounge for
math majors and friends on the second floor of Deady Hall.
Q: What material will we be covering?
First part: getting started.
Problems at the beginning of the book
Chapter 1 - (very briefly) Numbers, sets and functions
Chapter 2 - Language and proofs
Chapter 3 - Induction
Second part: Number Theory
Chapter 4(a) - Representation of natural numbers
Chapter 7 - Modular arithmetic
possible suplemental material - error checking and cryptography
Third part: Combinatorics and Geometry
Chapter 4(b) - Bijections
Chapter 5 - Combinatorial reasoning
Chapter 11 - Graph theory.
possible supplemental material - Platonic solids