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

Short Answer Questions

1. Which of the following was a major part of Gauss' work in mathematics?

2. In what area was Gauss especially interested?

3. Who else, besides Newton, independently discovered a calculus method?

4. What concept did Dunham end his book with?

5. What did Cantor develop?

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

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

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

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

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

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

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

10. Describe Cantor's difficult personal life.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.

Essay Topic 2

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 3

What was Hippocrates's most famous work as presented by Dunham? What questions about Hippocrates's work were left incomplete until Ferdinand Lindeman's proof? Explain.

(see the answer keys)

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