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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 Cantor finally prove his theory?

2. In what area was Gauss especially interested?

3. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?

4. What did Cantor struggle with later in his life?

5. Where was Euler born?

Short Essay Questions

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

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

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

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

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

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

7. Describe some of Gauss's work.

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

Essay Topic 2

Summarize the parts of Euclid's Elements. Use the following questions to guide your writing. What were the basic components to Elements? What were the most important theorems and proofs in Elements? How did Elements change the future of mathematics. Name a few mathematicians after Euclid who used Elements in their own work.

Essay Topic 3

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?

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