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 didn't Euler attempt?

2. What is one proof that Euler was able to prove?

3. What was similar about both Euler and Gauss as children?

4. What was Dunham central theorem for this chapter?

5. Which of the following did Dunham concentrate on as one of Newton's great advances?

Short Essay Questions

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 What was Gauss's major unpublished achievement in geometry?

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

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

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

5. Describe who were Jakob and Johann Bernoulli.

6. Describe some of Gauss's work.

7. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

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

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

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

Summarize the parts of Euclid's Elements. Use the following questions to guide your writing. What were the basic components to Elements? What were the most important theorems and proofs in Elements? How did Elements change the future of mathematics. Name a few mathematicians after Euclid who used Elements in their own work.

Essay Topic 2

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.

Essay Topic 3

What was Hippocrates's most famous work as presented by Dunham? What questions about Hippocrates's work were left incomplete until Ferdinand Lindeman's proof? Explain.

(see the answer keys)

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