Format of the test:
Matching questions for mathematicians and facts about them.
Short answer (1-3 sentences) questions over history of mathematicians.
Some computations from applications shown or assigned in presentations.
Mathematical writing corrections

1. Entrance into and Emergence from The Dark Ages: The Decline and Revival of Mathematics
Why did the Christian Movement from the 4th century B.C. on lead to a decline in mathematical and scientific scholarship?
What role did the Eastern Byzantine Empire play in the preservation of Greek knowledge?
Mohammed bin Musa al-Khowarizmi -- approximately when and where  did he live.  One fact about his mathematical accomplishments.
Fibonacci's real name, where he was from, approximate dates --  What are the Fibonacci numbers.   What else is he known for.

2. Mathematical Writing
I'll have a few examples of "bad" mathematical writing and you will state what's wrong and/or fix.

3.  Student Presentations  :

Blaise Pascal
Birth and death dates, where he lived.
Historical facts of his  life and education.
Work in projective geometry: 

What is the Pascaline
Pascal's Triangle:  How is each line formed,  How can you use it to find coefficients of expansion of (x + y )ⁿ
How can you use it to find 11ⁿ for some value of n
Classic problem of DeMere that he worked on through letters with Fermat, establishing the beginnings of basic probability  theory.
 Cycloids

Sir Isaac Newton
Birth and death dates, where he lived.
His role along with Leibniz in forming foundations for integral and differential calculus
The three books of Principia
Describe Newton's three laws of motion
Newton and Kepler's contribution to laws of planetary motion
Newton's famous "Shoulder's of Giants" quote
Solve a projectile motion problem like the assigned homework.

G. F. Bernhard Riemann

Birth and death dates, where he lived. Where did his do his graduate work,  under whom did he do his dissertation.
What is the zeta function  (give its precise definition in formula form, defining all terms)?  
Precisely state the Riemann Hypothesis, and then give its relationship to the density of the prime numbers.
Give the definition of a Riemann Sum for a function f(x) over an interval [a,b].  Give the definition of a definite integral in terms of the limit of a Riemann Sum.   Compute a left or right Riemann Sum for a particular function on a particular interval.   Problem like the homework problems.

Carl Friedrich Gauss

Birth and death dates, where he lived and worked.
How did he develop the formula as a child for summing the integers 1 through n.
State the Fundamental Theorem of Algebra.
State the  Prime Number Theorem (In the form that he gave)
Given an integer n, use Gauss's result to estimate the number of primes less than or equal to n.
State the Fundamental Theorem of Arithmetic
What is a Fermat Prime?   How did Gauss relate these to regular polygon's.  What is a heptadecagon?
What is the method of least squares?  (precisely)  --  How did Gauss use the method of least squares (what types of applications). 
What is a triangular number.  Determine whether a given number is triangular.

Pierre-Simon Laplace
Birth and death dates, when and where he lived and worked. 
Give an example of his arrogance.
What was his most important work (book)  -- what kind of information did these volumes contain?
What is Laplace's version of Bayes Theorem -- apply to a specific example.
Outline the ideas behind the Buffon-Laplace Needle problem.  What was the problem?  How was multivariable calculus used to solve the problem?

Leonhard Euler
Birth and death dates, when and where he lived, studied, worked.
What mathematician was a childhood mentor to him.
What is the Euler Phi function?
What does Euler' Theorem state (in terms of this function)
Euler showed that the sum (1/n^2), n= 1...infinity converged to _____
Explain the Konigsberg bridge problem and how he solved it as a graph problem (what was a necessary sufficient condition for a path which is not a circuit, necessary and sufficient condition for a circuit).  Apply to a graph (or bridge).
What is Euler's relation and why is it considered particularly elegant.