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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. In his later life, what position did Isaac Newton hold?

2. What did mathematicians want to perfect in the mid-19th century?

3. Where did George Cantor live in the 1860s and 1870s?

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

5. In what area was Gauss especially interested?

Short Essay Questions

1. Describe Cantor's difficult personal life.

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

3. Describe some of Gauss's work.

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

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

6. What great theorems and work of Newton did Dunham highlight?

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

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

9. Describe Newton's days in Cambridge and what he eventually came to discover.

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

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

Write a three part essay to describe third century Alexandra.

Part 1) Describe the geographic location of Alexandria. Why did its location affect its scholars?

Part 2) Name and describe the work of a few scholars in third century Alexandria.

Part 3) Who was Heron? How did his achievements improve mathematics?

Essay Topic 3

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?

(see the answer keys)

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