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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) Cold.
(b) Troubled.
(c) Hard.
(d) Simple.

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

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

4. 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 way to construct a regular 17-sided polygon.
(c) A proof that the Pythagorean Theorem was correct.
(d) A method to simplify Newton's calulus.

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

Short Answer Questions

1. What concept did Dunham end his book with?

2. What did most of 19th century mathematics focus on, as highlighted by Dunham?

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

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

5. What is one proof that Euler was able to prove?

Short Essay Questions

1. Describe the controversy that Newton was caught in with his publication of his calculus methods.

2. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.

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

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 What was Gauss's major unpublished achievement in geometry?

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

6. Describe some of the characteristics of Leonhard Euler, and what made him successful.

7. Describe the great theorem explained by Dunham in this chapter.

8. Describe Cantor's difficult personal life.

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

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

(see the answer keys)

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