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:

Richard A. Tapia

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.

Doris Schattschneider

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.

Jean Taylor

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.

Fan Chung Graham

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.

Carolyn Gordon

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.

Freeman A. Hrabowski, III

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

Nathaniel Dean

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.

Karen Smith

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.

Jonathan Farley

Know the definition of a lattice and examples and counterexamples.