### Review Sheet for WebCT Test 3 on Paper 3

To review, skim through the
links below
and skim through the student papers.
In addition, carefully go over class notes and the worksheets.
**I am happy to help with anything you don't understand in
office hours and/or the WebCT bulletin board.**
In addition to what I wrote below,
be sure that you know importance of these ideas within the context
of mathematics, and applications to real-life.
**Some other guidelines
for the mathematics:**
Understand how Newton's method of approximation is really the
tangent line approximation used to find a root.

Given two functions in two unknowns, understand how to find the
Jacobian matrix and the Wronskian (the determinant), and plug points into
them to find values.

Understand how to use Newton's method to find a root (where something
is 0).

Understand that Tapia was working with complicated des. He
wanted to know about them and find their max/mins. This is equivalent to
finding a root of the derivative (ie where the derivative is 0),
so a version of the Newton method called the weak Newton method is
used.
Understand the definition of distance in taxicab geometry as
|x2-x1| + |y2-y1|, and understand how to use it.

Understand that taxicab geometry is useful for taxicab drivers
in a city set on a grid and also for ecological distance between species.

Know why SAS does not hold in taxicab geometry

Understand that Schattschneider was looking at transformations that
preserve the taxicab distance between points
and proved that there were only 8 of them.
She worked in soap bubble geometry - the geometry of minimal surfaces.
These have applications in chemistry, biology and packaging.

One of the things that
she proved was that three surfaces meet along a smooth curve at
120 degree angles.

Understand the definition of mean curvature and how to apply it
to different surfaces.

Understand that soap films have constant mean curvature.

Understand that a spherical
bubble has the least amount of surface area for a
given volume.
Understand that a Buckyball is a molecule comprised of
60 carbon atoms arranged in a form similar to a soccer ball,
and that mathematical properties have applications to chemisty
and physics.

Understand Euler's formula and when it applies

Understand the Icosahedron

Understand how to form a Buckyball from an Icosahedron.
Understand the question "Can you hear the shape of a drum?"
and her solution to the problem.

Understand the definition of a mathematical drum.

Understand that sound-alike drums must have the same area
and perimeter, and know how to apply this.
Know that an F-test is used for testing numerical data, not the percentage
or proportions of a sample for a particular category.

Know that a better test for analyzing proportional data
is a chi-squared test.

Know how to find the expected value of
elements in a table and what this means.

Understand that it seems that Hrabowski has matured statistically
from his 1977 article "Graduate School Success of Black
Students from White Colleges and Black Colleges" to his
1995 article "Enhancing the Success of African-American Students in the
in the Sciences: Freshmen Year Outcomes".

Know some basics of statistics from Dr. Richie's comments
Understand that he works in the field of graph theory, which
has many applications to real life, such as organizing a schedule of
teams playing each other during a season.

Know the definitions of a path and a cycle.

In one of Dean's papers, a lemma that he proves discusses
the number of paths it takes in order to decompose a graph made up
of 1 , 2 or 3 cycles, and know why decomposition is important.

Know that his proof of the lemma is by contradiction.
Know the definition of characteristic p, review the definition
of a mod b, and be able to work with it.

Understand how characteristic p helps when working on solutions to
an equation.
Know the definition of a lattice and examples and counterexamples.