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

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

3. What series was Euler most famous for?

4. What was most noticeable about Euler at a young age?

5. Where did George Cantor live in the 1860s and 1870s?

Short Essay Questions

1. Describe the connection between Fermat and Euler's work.

2. Describe Newton's days in Cambridge and what he eventually came to discover.

3. Describe Cantor's difficult personal life.

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

5. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

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

7. Explain any methods used by Cantor that were unsuccessful.

8. Describe some of Gauss's work.

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

10. Who was Georg Cantor, and what was significant about his work in mathematics?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.

Part 1) Describe what we know about geometry before Thales.

Part 2) In what ways were mathematics and geometry used before Thales?

Part 3) Explain what we know about Thales' work. How did it advance mathematics?

Essay Topic 2

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?

Essay Topic 3

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?

(see the answer keys)

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