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

2. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a composite number.
(b) The statement was a perfect number.
(c) The statement was not a prime number.
(d) The statement was a prime number.

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

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

5. Who eventually solved the sum of the successive squared denominator series?
(a) Johann Bernoulli.
(b) Jakob Bernoulli.
(c) Leonhard Euler.
(d) John Napier.

Short Answer Questions

1. Which of the following did Dunham concentrate on as one of Newton's great advances?

2. What did British scholars accuse Leibniz of?

3. What did Euler prove about 2²ⁿ + 1?

4. What did Gauss construct?

5. What did George Cantor discover?

Short Essay Questions

1. Explain any methods used by Cantor that were unsuccessful.

2. What was the great theorem of this chapter? Describe it briefly.

3. Describe who were Jakob and Johann Bernoulli.

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

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

6. What great theorems and work of Newton did Dunham highlight?

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

8. Describe the connection between Fermat and Euler's work.

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

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

(see the answer keys)

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