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 is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

2. What did Cantor's beliefs lead him to think?

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

4. Where does the center of mathematical thinking shift to after Italy?

5. What concept did Dunham end his book with?

Essay Topics

Essay Topic 1

Summarize the discoveries on series made by the Bernoulli brothers and later, Euler. How did the Bernoullis advance mathematical understanding of an infinite series, and how did Euler even further advance this knowledge? Give examples. What principles about series and the sum of series are still being worked out in modern mathematics?

Essay Topic 2

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

Essay Topic 3

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?

(see the answer keys)

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