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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. What is true about real numbers between 0 and 1?**
**(a)** They are denumerable, **(b)** They are not denumerable. **(c)** There is no set for these numbers. **(d)** No sum can be determined.

**2. How did Euler prove if the number 4,294,967,297 was prime or composite?**
**(a)** He used Newton's calulus methods. **(b)** He divided it by 2. **(c)** He used his own rule of squares. **(d)** He factored it.

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

**4. Where was George Cantor born?**
**(a)** Germany. **(b)** Russia. **(c)** Switzerland. **(d)** Britian.

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

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

**7. What did most of 19th century mathematics focus on, as highlighted by Dunham?**
**(a)** Algebra. **(b)** Geometry. **(c)** The theoretical. **(d)** The immediately practical.

**8. In his later life, what position did Isaac Newton hold?**
**(a)** Professor of philosophy in Paris. **(b)** Angelican father. **(c)** Principle science advisor to Charles II. **(d)** Warden of the Mint.

**9. What did Gauss construct?**
**(a)** A proof that demonstrated the circumference of Earth. **(b)** A system where the angles of a triangle add up to more than 180 degrees. **(c)** A system where the angles of a triangle add up to fewer than 180 degrees. **(d)** A proof that demonstrates Newtonian physics.

**10. Which phrase best describes Newton as a student at Cambridge?**
**(a)** A highly praised genius. **(b)** Quiet recluse of no intelligence. **(c)** Tolerant, mildly interested in science. **(d)** Unnoticed, but remarkable.

**11. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?**
**(a)** That the set is infinite. **(b)** That the set is still equal to c. **(c)** That the set is equal to 1. **(d)** That the series is infinite.

**12. Where did George Cantor live in the 1860s and 1870s?**
**(a)** Germany. **(b)** Scotland. **(c)** Russia. **(d)** Britian.

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

**14. What did George Cantor determine to be true of a set of rational numbers?**
**(a)** They are denumerable. **(b)** They are all prime numbers. **(c)** They are non-denumerable. **(d)** They are all composite numbers.

**15. Which word best describes Newton's childhood?**
**(a)** Cold. **(b)** Simple. **(c)** Troubled. **(d)** Hard.

## Short Answer Questions

**1.** What did Cantor struggle with later in his life?

**2.** Who were Johann and Jakob Bernoulli?

**3.** What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

**4.** What did Newton's calculus involve?

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

This section contains 499 words(approx. 2 pages at 300 words per page) |