View a FREE sample

This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. Where was George Cantor born?

2. What hindered Euler's work as he grew older?

3. Who were Johann and Jakob Bernoulli?

4. Which of the following was a major part of Gauss' work in mathematics?

5. When was Euler born?

Short Essay Questions

1. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

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

3. Describe who were Jakob and Johann Bernoulli.

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

5. Describe Cantor's difficult personal life.

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

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

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

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

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

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 765 words (approx. 3 pages at 300 words per page) View a FREE sample