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This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. Who else, besides Newton, independently discovered a calculus method?**
**(a)** John Napier. **(b)** Pierre de Fermat. **(c)** Gottfried Leibniz. **(d)** Isaac Barrow.

**2. Which of the following was a major part of Gauss' work in mathematics?**
**(a)** Proofs to show that Archimedes' number theory was wrong. **(b)** Elemental proofs related to the foundations of algebra. **(c)** Proofs on the area of a square. **(d)** Simple proofs to demonstrate Bernoulli's series.

**3. What did Cantor's beliefs lead him to think?**
**(a)** That he was seeing God when he worked on equations. **(b)** That he was learning about the origins of God. **(c)** That he was God. **(d)** That he was tapping into the nature of God by delving into the infinite.

**4. What did Cantor develop?**
**(a)** A method to factor very large composite numbers. **(b)** A method to find the sum of a geometric series. **(c)** A system to identify prime numbers of very large size. **(d)** A system to compare relative sizes of cardinal numbers.

**5. What did Cantor's cardinal numbers represent?**
**(a)** Infinite sets. **(b)** Series of prime numbers. **(c)** Sets of all imaginary numbers. **(d)** Finite series.

**6. Who was Euler's teacher?**
**(a)** Isaac Newton. **(b)** Johann Bernoulli. **(c)** Jakob Bernoulli. **(d)** Gottfried Leibniz.

**7. What did Newton's calculus involve?**
**(a)** Proving the cubic equation. **(b)** Determining the area under a curve. **(c)** Proving the existance of pi. **(d)** Determining the volume of a sphere.

**8. What is one proof that Euler was able to prove?**
**(a)** Bernoulli's principle of lift. **(b)** "little Fermat theorem." **(c)** Newton's method of calculus. **(d)** Descartes' number theory.

**9. What didn't Euler attempt?**
**(a)** A series starting with the number 1. **(b)** A series where exponents are odd. **(c)** A series of sequencially smaller terms. **(d)** A series where exponents are even.

**10. When was Euler born?**
**(a)** 1658. **(b)** 1707. **(c)** 1796. **(d)** 1903.

**11. Who, in modern day, is given credit for the calculus method?**
**(a)** Newton, **(b)** Both Newton and Leibniz. **(c)** Leibniz. **(d)** Johann Bernoulli.

**12. Which of the following was one of Gauss' early discoveries?**
**(a)** A method to simplify Newton's calulus. **(b)** A proof that the Pythagorean Theorem was correct. **(c)** A way to construct a regular 17-sided polygon. **(d)** A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .

**13. What was aleph naught?**
**(a)** A symbol to represent the number of items in a set. **(b)** A method to determine the sum of a series. **(c)** A method to numerate terms. **(d)** A symbol to state the sum of a series.

**14. How did Cantor finally prove his theory?**
**(a)** By extension of the Pythagorean Theorem. **(b)** By refining and expanding set theory. **(c)** By using basic algebra. **(d)** By extension of the infinite series.

**15. Where was Euler born?**
**(a)** Germany. **(b)** Denmark. **(c)** Finland. **(d)** Switzerland.

## Short Answer Questions

**1.** What did George Cantor determine to be true of a set of rational numbers?

**2.** What did Gauss construct?

**3.** What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

**4.** Which of the following demonstrates the successive squared denominator series?

**5.** Where does the center of mathematical thinking shift to after Italy?

This section contains 545 words(approx. 2 pages at 300 words per page) |