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 did George Cantor discover?

2. Where did Newton go to school before he went to Cambridge?

3. What did most of 19th century mathematics focus on, as highlighted by Dunham?

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

5. Which word best describes Newton's childhood?

Short Essay Questions

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

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

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

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

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

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

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

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 What was Gauss's major unpublished achievement in geometry?

9. Describe who were Jakob and Johann Bernoulli.

10. Describe Cantor's difficult personal life.

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

What was Hippocrates's most famous work as presented by Dunham? What questions about Hippocrates's work were left incomplete until Ferdinand Lindeman's proof? Explain.

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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