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. Which phrase best describes Newton as a student at Cambridge?

3. What was Dunham central theorem for this chapter?

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

5. What did Cantor struggle with later in his life?

Essay Topics

Write an essay for ONE of the following 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

In Dunham's book, there were many descriptions of mathematicians and their personal lives. Write an essay to describe the common elements or characteristics that seem to be shared among these historically famous mathematicians. Also, explain what personal characteristics made them all excellent mathematicians.

Essay Topic 3

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.

(see the answer keys)

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