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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's work do to mathematics?

**2.** Who, in modern day, is given credit for the calculus method?

**3.** Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

**4.** How did Gauss feel about his best work?

**5.** What did Cantor's beliefs lead him to think?

## Short Essay Questions

**1.** Describe some of Gauss's work.

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

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

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

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

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

**7.** Describe who were Jakob and Johann Bernoulli.

**8.** Explain any methods used by Cantor that were unsuccessful.

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

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

## Essay Topics

Write an essay for ONE of the following topics:

### Essay Topic 1

In all of the great theorems presented in Dunham's book, which theorem do you think made the most impact on the history of mathematics? Write an essay to defend your opinion with reference to Dunham's descriptions and conclusions.

### 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

Compare Pythagoras's proof of the Pythagorean Theorem and how Heron's formula for triangular area can be used as an alternative proof of the Pythagorean theorem. What are the common assumptions in both proofs? What components of each proof are different?

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