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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 did Cantor struggle with later in his life?

2. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?

3. When was Euler born?

4. What is true about the successive squared denominator series proposed by the Bernoullis?

5. Which word best describes Newton's childhood?

Short Essay Questions

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

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

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

4. Explain why Eulers sum of π²/6 was in some ways surprising.

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

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

7. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

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

9. Describe some of the characteristics of Leonhard Euler, and what made him successful.

10. Describe some of Gauss's work.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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?

Essay Topic 2

Dunham presented a number of controversies over publication and intellectual property rights in the history of mathematics. Explain what seems to be the common issues historically in the publication of one's discoveries. Describe what conditions often lead to controversy over intellectual property rights.

Essay Topic 3

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?

(see the answer keys)

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