### 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:

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.