### Review Sheet for WebCT Test 1 on Paper 1

**One 8.5 by 11 sheet with writing on both sides allowed.
**

One Calculator
mandatory.

To review, skim through the
paper 1 links for each person,
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:**
### Muhammad ibn Muhammad

Know the definition of magic square, and the formulas to compute
the magic constant and the center square number given n as the number of
rows (or columns). Know the elements of the dihedral group,
and how to compose elements geometrically.
You do not need the definition of a group - this will be given to you
if it is needed. Know how to apply elements of the dihedral group
to a magic square centered at (0,0) in the x-y plane, and how to
check and see whether the result is still a magic square.
### Thomas Fuller

Know and understand Fuller's calculation mentioned in the presentation
and paper. Skim through and understand the ideas in

The digital century: Computing through the ages,

the history of computer speed

Java Applet 1885 Felt &Tarrant "Comptometer" adding machine.
"The interactive Adding Machine, one you can use!!"
### Maria Agnesi

Know how to geometrically construct the witch of Agnesi,
and equations of the curve.
### Benjamin Banneker

Know the mothods of single false position and double false position
and be able to work with them to solve problems
(I will give you the formula for double false
position so you do not need to put it on your sheet).
Know examples where each method works, where each method
fails, and understand what substitution you need to make
to see that
double false position is the secant line approximation method
in disguise.
### Sophie Germain

Know the statement of Fermat's Last Theorem,
examples of why the statement in Fermat's Last Theorem
doesn't hold for n=2, or if we drop the condition that we must have
non-zero whole numbers. Know the definition of "mod", and
be able to calculate with it.
Understand why Germain needed
non-consecutive whole numbers in her proof (see paper or notes on
presentation),
and how this relates to Sophie Germain primes.
Understand how Sophie Germain primes are used in coding theory.
### Sonia Kovalevsky

Know and understand the model that Kovalevsky worked on, and the ideas of
center of mass and rotation axis.
Know what a differential equation and partial differential equation is,
what solutions are, and some examples. Review taking derivatives
and partial derivatives
using the product rule, chain rule and power rule, and be able to
work with these to test and see whether a function satisfies a de or
pde.
### Dudley Woodard

Know the definition and examples of simple, closed curves.
Know the Jordan-Curve Thorem statement, and understand why it is
hard to prove. Know how this relates to Woodard's mathematics.
### Emmy Noether

Given the definition of
a ring, ideal or Noetherian ring (ie you do not have to put these
on your sheet -
I will give them to you), be able to work with examples and the axioms.
Know examples of rings, non-rings,
ideals in Z and F={continuous functions mapping [0,1] to R},
subsets of Z and F that are not ideals,
a Noetherian ring, and
a ring which is not a Noetherian ring, and know why.
### Elbert Cox

Know what a difference equation is, what solutions are, and
some examples. Know and understand the Fibonnaci sequence,
and the traffice flow solution from the presentation.
Know what kind of difference equations that Cox worked on.
Understand how a difference equation is different than a de or pde.