View a FREE sample

This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. What did Cantor develop?

2. Who were Johann and Jakob Bernoulli?

3. In what area was Gauss especially interested?

4. What series was Euler most famous for?

5. What did Cantor's beliefs lead him to think?

Short Essay Questions

1. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

2. Explain why Eulers sum of π²/6 was in some ways surprising.

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

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

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

6. Describe some of Gauss's work.

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write a a three part essay to explain how Cantor's work in mathematics also fit into the cultural movements of the time.

Part 1) Describe the artistic movements of the 1860s and 1870s. In general, how could they be related to mathematical philosophy at the time?

Part 2) What was Cantor's work in mathematics in the 1860s and 1870s?

Part 3) Explain how Cantor's philosophy and mathematical theorems fit with the new artistic and philosophic ideas of the time.

Essay Topic 2

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

Essay Topic 3

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

(see the answer keys)

This section contains 954 words (approx. 4 pages at 300 words per page) View a FREE sample