The math camp students get two three-hour lecture
sessions everyday. Each week, the morning and afternoon sessions each have
their separate “themes”. Here’s the lineup:

Basic Mathematical Background-Professor O’Nan

Our first lesson at math camp (and 4 more later that week) involved those
things you don’t always learn in school, but are basic to any geeks toolkit
anyway. Professor O’Nan introduced the logical topics of truth tables,
contrapositive and negation of statements. Later lectures involved quantifiers
and mathematical induction. On the last day, we had the first part of the Stage
D’Euler, a competition among the groups in which puzzles had to be solved as
fast as possible.

Graph Theory-Professor Bergstrand

The afternoon sessions were on graph theory. No that's not properties of the
x-intercept when the equation is such and such. It's about nice figures (called
"graphs", surprisingly enough :) ) with very big vertices and edges
or lines between them. They have all sorts of interesting properties, and a
whole new world opened up for us. Professor Bergstrand saw to it that we were
all very happy. Sorry, that's an inside joke. We learned about the different
classifications of graphs, about Ramsey numbers (how many people do you need at
a party to have at least x strangers or y mutually acquainted people) used in
complete graphs (where every vertex is connected to all others). If you want to
know all the other little things we learned, go to math camp at Rutgers this
summer!

Algorithms in Graph Theory-Professor Wantland

Professor Evan Wantland was there to wake us up when we filed in after
breakfast everyday during the second week, teaching us about such things as
Kruskle's and Prim's algorithms (some solutions to the traveling salesman
problem, or that of finding the spanning tree in a graph with the least total
weight on it. Don't ask.) Other topics included Hall's Theorem (finding the
perfect matching in a bipartite graph. See Kruskle's theorem if you have any
questions.). Max flow and min cut were topics helping the potential engineers
among us, and on the last day we got to learn how calculators work nice and
efficiently with postflux, and how screwed up the human brain really is when
doing arithmetic. Fun stuff.

Combinatorics -Professor McNulty

All of Monday morning, the group had been teased by comments about how Prof.
Wantland would kick our a...butts in soccer together with Prof. McNulty. Off
course, we couldn't think of anything else during lunch! :D. We sat through the
oh-so-wonderful introduction on Montana, and then we got to learn more math!.
Combinatorics is basically a nice word for counting. So we started out with
addition, but our great intelligence helped us to quickly understand that topic
and advance to permutations and combinations. Other topics included Bell's and
Sterling numbers, binomial coefficients, about five hundred (all right maybe,
8) variations on the how can I put/arrange n balls in x boxes problem, and
lastly ever-present Catalan, Fibonnacci, and other interesting types of numbers.
We were supposed to have another competition at the end of the work, but it
turned into a who-can-build-the-nicest-thing-with-blocks type of thing for
about half of us.

Number Theory-Professor McNulty

During the third next week, the oh-so-exciting topic of number theory lay before
us. Number theory, we learned on Monday, is very old. It seems to mainly talk
about primality, but we also took a look at Fermat's and perfect numbers.
Modular arithmetic is another topic in number theory. But again, the main topic
of the week was prime numbers. How does one determine if a number is prime in
the most efficient way? Can we find a formula for finding prime numbers? What
are Mersenne primes? But most importantly, there is Goldbach's conjecture. This
unsolved problem in mathematics states that any even number greater than two
can be stated as the sum of two primes. Other weird questions that bothered us
during the week included that of the magical witches, and the coding process
Prof. McNulty must have had for them. Prof. Wantland also strolled in magically
at exactly the right moment to perform some weird card trick with Prof.
McNulty. How do you guess what card someone has if you only get to see four
seemingly unrelated cards?

Robotics-Professor Coffey

The afternoon sessions of week three were more exciting than some of the other
sessions, just because they were so different. Rather than staring at overhead
projectors all day, every group got Lego kits. Yes, Lego! A program called
Robolab helped us program our self-designed robots, which we were supposed to
disguise as animals. On Friday, there was a competition, when Professor
Rosenstein and others judged each robot, demonstrated at work in its
environment by its builders, to determine who won what. For the 6 groups, there
were 4 prizes: Most creative, Best engineered, Best overall, and everyone's
favorite: The little engine that could!

Mathematical Applications – Professor O’Nan

By the fourth week, we have learned many different aspects of math. Right now,
we are learning and solving many puzzles and games. It's a fun week considering
we are solving puzzles and working as a group to finish the homework. This week
requires a bunch of information that we learned in the previous weeks, such as
various theorems and topics. An example of a puzzle would be slicing a square
into various shapes to make a rectangle of a certain measurement.

Fractals - Professor Perciante

The afternoon of the fourth week consists of many visual math. The last week's
afternoon classes are about fractals (and a bit of chaos theories). Fractals
are visual images such that every part of them contains a complete down-scaled
picture of the whole thing. They are often very pretty :). The professor is
funny, for example calling fractals "totally now"; so our routine of
8 hours of math a day for four weeks ends on a good note.