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 and 1 (of 3) essay topics.

Short Answer Questions

1. What did Cantor suspect about transfinite cardinals?

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

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

4. What concept did Dunham end his book with?

5. What did Gauss do with his best work?

Essay Topics

Essay Topic 1

Write a three part essay to compare Archimedes's and Newton's determination of a number value for pi.

Part 1) Explain what general approach each mathematician used in the determination of pi.

Part 2) What prior knowledge of mathematics is required to use each method?

Part 3) Which number determination for pi was more accurate, Newton's or Archimedes? Explain.

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

Write an essay to explain what is meant by "infinitude of primes." Use the following questions to guide your writing. What was Euclid's definition of a prime number? How were prime and composite numbers related according to Euclid?

(see the answer keys)

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