Journey Through Genius: The Great Theorems of Mathematics Test | Final Test - Hard

William Dunham (mathematician)
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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 aleph naught?

2. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

3. To how many decimal places did Newton determine the number for pi?

4. Which name does NOT belong?

5. What did Cantor define as the continuum?

Short Essay Questions

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

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

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

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

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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 2

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

Essay Topic 3

Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.

(see the answer keys)

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