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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

**2. What did mathematicians want to perfect in the mid-19th century?**
**(a)** The method of finding the volume of spheres. **(b)** The method of finding the area under a curve. **(c)** The definition of infinite. **(d)** The definition of pi.

**3. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?**
**(a)** It's a convergent series of triangular numbers. **(b)** It's a divergent series with a sum of 2. **(c)** It's a divergent series squared numbers. **(d)** It's a convergent series of cubic numbers.

**4. Which of the following is not denumerable, proven by Cantor's theorem?**
**(a)** A set of a geometric series. **(b)** A set of rational numbers. **(c)** A set of transcendental numbers. **(d)** A set of imaginary numbers.

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

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

**7. What was Dunham central theorem for this chapter?**
**(a)** That the area of a circle is fundamentally related to the square of its area. **(b)** That the sum of an infintire series is always infinite. **(c)** That the sum of a set of real numbers is finite. **(d)** That there are other transfinite cardinals greater than c.

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

**9. Who encourages Newton during his studies at Cambridge?**
**(a)** Isaac Barrow. **(b)** John Napier. **(c)** Henry Briggs. **(d)** Henry Stokes.

**10. Where did Newton go to school before he went to Cambridge?**
**(a)** The King's School. **(b)** Cambridge Prep. **(c)** Oxford Grammar School. **(d)** Charles II Grammar School.

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

**12. What did Cantor suspect about transfinite cardinals?**
**(a)** That the sum of the series is finite. **(b)** That there are transfinite cardinals much less than c. **(c)** That the sum of the series is infinite. **(d)** That there are transfinite cardinals even greater than c.

**13. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?**
**(a)** They are both fascinated on artificial images, such as photography. **(b)** They are both becoming less abstract. **(c)** They are both focused on realism. **(d)** They are both less concern with reality.

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

**15. Which name does NOT belong?**
**(a)** Francois Viete **(b)** John Napier. **(c)** Renee Descartes. **(d)** Blaise Pascal.

## Short Answer Questions

**1.** What did Gauss construct?

**2.** Where did Euler study at the age of 20?

**3.** What series was Euler most famous for?

**4.** What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

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

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