*BookRags*. (c)2016 BookRags, Inc. All rights reserved.

Name: _________________________ | Period: ___________________ |

This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

## Multiple Choice Questions

**1. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?**
**(a)** Nobody has determined the sum. **(b)** 2. **(c)** Infinity. **(d)** 0.

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

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

**4. What did Cantor struggle with later in his life?**
**(a)** Blindness. **(b)** Mental illness. **(c)** Leukemia. **(d)** Seizures.

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

## Short Answer Questions

**1.** What was Dunham central theorem for this chapter?

**2.** What were the main technique(s) that Euler used to find the sum of the series?

**3.** What did Cantor's work do to mathematics?

**4.** Which of the following is not denumerable, proven by Cantor's theorem?

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

## Short Essay Questions

**1.** Describe what the Bernoullis discovered about series, and give an example.

**2.** Why did Euler start working on the sum of series?

**3.** Describe who were Jakob and Johann Bernoulli.

**4.** Who was Georg Cantor, and what was significant about his work in mathematics?

**5.** Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.

**6.** Describe the connection between Fermat and Euler's work.

**7.** Describe Newton's days in Cambridge and what he eventually came to discover.

**8.** What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

**9.** What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

**10.** Describe some of Gauss's work.

This section contains 817 words(approx. 3 pages at 300 words per page) |