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

2. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

3. What did Gauss do with his best work?

4. Which of the following did Dunham concentrate on as one of Newton's great advances?

5. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?

Essay Topics

Essay Topic 1

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 2

Debate in essay format one of the following controversies:

a) Newton versus Leibniz.

b) Cardano versus Tartaglia.

Explain a defense for each side of the controversy, then propose your opinion with your final conclusions.

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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