Journey Through Genius: The Great Theorems of Mathematics Test | Mid-Book 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. Where was Archimedes born?

2. Which of the following is an example of a postulate that must be accepted in Elements?

3. Who was Heron?

4. What provided most of the content in the book Elements?

5. Which of the following best describes Cardano's character?

Short Essay Questions

1. Explain in two sentences Euclid's method to prove the Pythagorean Theorem.

2. Describe Euclid's postulates and notions in how they were important in constructing his proofs.

3. Explain what Neils Abel proved.

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

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

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 What was Gauss's major unpublished achievement in geometry?

7. Describe what work of Euclid's fascinated Plato and his theory on the shape of the Universe.

8. What was the great theorem of this chapter? Describe it briefly.

9. Describe the controversy that Newton was caught in with his publication of his calculus methods.

10. What did Dunham describe in the epilogue of the chapter?

Essay 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 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 3

Write a three part essay on the lives and work of both Euler and Gauss.

Part 1) What was similar about Euler and Gauss from an early age? What characteristics did they have in common?

Part 2) Give some examples of great theorems proposed by Euler and by Gauss. Do you think their work had anything in common mathematically?

Part 3) What could be considered Euler's greatest work? What could be considered Gauss's greatest work? How did both mathematicians advance the study of mathematics?

(see the answer keys)

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