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

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

3. Who else, besides Newton, independently discovered a calculus method?
(a) Gottfried Leibniz.
(b) Pierre de Fermat.
(c) John Napier.
(d) Isaac Barrow.

4. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to infinity.
(b) The sum converges to a finite term.
(c) The sum diverges to infinity.
(d) The sum grows ever smaller.

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

Short Answer Questions

1. What did Cantor's cardinal numbers represent?

2. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?

3. How did Euler prove if the number 4,294,967,297 was prime or composite?

4. What was Dunham central theorem for this chapter?

5. What was most noticeable about Euler at a young age?

Short Essay Questions

1. Describe Cantor's difficult personal life.

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

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

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

5. Describe some of Gauss's work.

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

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

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

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

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 What was Gauss's major unpublished achievement in geometry?

(see the answer keys)

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