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

2. When was Euler born?

3. Who were Johann and Jakob Bernoulli?

4. What did Cantor define as the continuum?

5. What did Cantor's work do to mathematics?

Short Essay Questions

1. Describe Cantor's difficult personal life.

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

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

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 What was Gauss's major unpublished achievement in geometry?

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

6. Describe who were Jakob and Johann Bernoulli.

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

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

9. Describe some of Gauss's work.

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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 2

Explain the accuracy of Archimedes determination of pi. How did he determine the number value of pi? How accurate is Archimedes's measurement of pi? What other mathematician was able to determine a number value, though more accurate, for pi?

Essay Topic 3

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.

(see the answer keys)

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