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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 was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?

2. Which of the following was NOT a field in which Isaac Newton made enormous advances?

3. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

4. How did Cantor finally prove his theory?

5. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

Short Essay Questions

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

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

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

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

5. Describe who were Jakob and Johann Bernoulli.

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

7. Describe some of Gauss's work.

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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.

Essay Topic 2

Debate in essay format one of the following controversies:

a) Newton versus Leibniz.

b) Cardano versus Tartaglia.

Explain a defense for each side of the controversy, then propose your opinion with your final conclusions.

Essay Topic 3

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.

(see the answer keys)

This section contains 950 words (approx. 4 pages at 300 words per page) View a FREE sample