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

## Multiple Choice Questions

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

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

**3. Which of the following demonstrates the successive squared denominator series?**
**(a)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . . **(b)** 1 + 1/4 + 1/9 + 1/16 . . . **(c)** 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . . **(d)** 1 + 1/2 + 3/4 + 4/5 . . .

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

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

## Short Answer Questions

**1.** What did Euler's sum surprisingly connect?

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

**3.** Which of the following was one of Gauss' early discoveries?

**4.** Where was Euler born?

**5.** What is true about the successive squared denominator series proposed by the Bernoullis?

## Short Essay Questions

**1.** What was Gauss's major unpublished achievement in geometry?

**2.** Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

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

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

**5.** Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

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

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

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

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

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

This section contains 800 words(approx. 3 pages at 300 words per page) |