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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. What did Dunham describe as lacking from calculus previous to the mid-19th century?
(a) Description of the word "area."
(b) Definitions of infinately large and small quantities.
(c) Foundations that link it to the principles of geometry.
(d) An explanation of non-Eulidean mathematics.

2. To how many decimal places did Newton determine the number for pi?
(a) Three places.
(b) Nine places.
(c) Twelve places.
(d) Eight places.

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

4. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were composed of successively smaller terms.
(b) Both series were composed of successively larger terms.
(c) Both series were divergent.
(d) Both series were convergent.

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

Short Answer Questions

1. What series was Euler most famous for?

2. Who was Euler's teacher?

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

4. On who's work did Euler base his number theory?

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

Short Essay Questions

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

2. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

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

4. Explain how Gottfried Leibniz was able to publish his method of calculus.

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

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

8. Give an example of a series who's sum is still unknown.

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

10. Describe some of Gauss's work.

(see the answer keys)

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