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. What did Dunham describe as lacking from calculus previous to the mid-19th century?

2. When was Euler born?

3. What was most noticeable about Euler at a young age?

4. What sum did Euler find for the series?

5. Which phrase best describes Newton as a student at Cambridge?

Short Essay Questions

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

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

3. What great theorems and work of Newton did Dunham highlight?

4. Describe the controversy that Newton was caught in with his publication of his calculus methods.

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

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

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

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

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

10. Describe what the Bernoullis discovered about series, and give an example.

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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 2

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.

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