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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 the same about the series proposed by Leibniz and the series proposed by Bernoulli?

2. Which word best describes Newton's childhood?

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

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

5. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?

Short Essay Questions

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

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

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

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

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

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

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

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

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

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 What was Gauss's major unpublished achievement in geometry?

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

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.

Essay Topic 3

Write a three part essay on the lives and work of both Euler and Gauss.

Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?

Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?

Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?

(see the answer keys)

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