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. Which of the following was a major part of Gauss' work in mathematics?

2. Which word best describes Newton's childhood?

3. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?

4. Which of the following is a quote from Bertrand Russell included by Dunham?

5. Which of the following demonstrates the successive squared denominator series?

Short Essay Questions

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

2. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

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

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

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

6. Describe Cantor's difficult personal life.

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

8. Describe who were Jakob and Johann Bernoulli.

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Summarize the puzzles that were presented as a result of Euclid's infinitude of primes. Name and describe some of these puzzles from a historical perspective, then explain what is known about each in modern mathematics. What puzzles remain unsolved today?

Essay Topic 2

Describe how Gerolamo Cardano became involved in the solution to cubic equations. Why was their a controversy over his publication of the solution to cubic equations? Explain.

Essay Topic 3

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.

(see the answer keys)

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