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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. How did Gauss feel about his best work?

2. When was Euler born?

3. What was Dunham central theorem for this chapter?

4. In what area was Gauss especially interested?

5. Which of the following was one of Gauss' early discoveries?

Short Essay Questions

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

2. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

3. Describe some of Gauss's work.

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

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

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

7. Describe Cantor's difficult personal life.

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

9. Why did Euler start working on the sum of series?

10. Describe who were Jakob and Johann Bernoulli.

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

Summarize the discoveries on series made by the Bernoulli brothers and later, Euler. How did the Bernoullis advance mathematical understanding of an infinite series, and how did Euler even further advance this knowledge? Give examples. What principles about series and the sum of series are still being worked out in modern mathematics?

Essay Topic 3

In Dunham's book, there were many descriptions of mathematicians and their personal lives. Write an essay to describe the common elements or characteristics that seem to be shared among these historically famous mathematicians. Also, explain what personal characteristics made them all excellent mathematicians.

(see the answer keys)

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