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 concept did Dunham end his book with?

2. What did Gauss construct?

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

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

5. Who was Euler's teacher?

Short Essay Questions

1. Describe who were Jakob and Johann Bernoulli.

2. What was Gauss's major unpublished achievement in geometry?

3. Describe what the Bernoullis discovered about series, and give an example.

4. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

5. What great theorems and work of Newton did Dunham highlight?

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

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

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

9. Why did Euler start working on the sum of series?

10. Describe the great theorem explained by Dunham in this chapter.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write a a three part essay to explain how Cantor's work in mathematics also fit into the cultural movements of the time.

Part 1) Describe the artistic movements of the 1860s and 1870s. In general, how could they be related to mathematical philosophy at the time?

Part 2) What was Cantor's work in mathematics in the 1860s and 1870s?

Part 3) Explain how Cantor's philosophy and mathematical theorems fit with the new artistic and philosophic ideas of the time.

Essay Topic 2

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 3

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.

(see the answer keys)

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