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. On who's work did Euler base his number theory?

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

3. What is true about real numbers between 0 and 1?

4. What did Cantor struggle with later in his life?

5. Which name does NOT belong?

Short Essay Questions

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

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

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

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

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

6. What was Gauss's major unpublished achievement in geometry?

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Write a three part essay to explain Archimedes determination of circular area.

Part 1) According to Archimedes what was pi, and why is this value needed to determine circular area?

Part 2) Explain how Archimedes used a right triangle to determine the area of a circle.

Part 3) Why was the determination of circular area useful at the time of Archimedes, and how did it advance the future of mathematics?

Essay Topic 2

Write a three part essay to describe third century Alexandra.

Part 1) Describe the geographic location of Alexandria. Why did its location affect its scholars?

Part 2) Name and describe the work of a few scholars in third century Alexandria.

Part 3) Who was Heron? How did his achievements improve mathematics?

Essay Topic 3

Summarize the discoveries on series made by the Bernoulli brothers and later, Euler. How did the Bernoullis advance mathematical understanding of an infinite series, and how did Euler even further advance this knowledge? Give examples. What principles about series and the sum of series are still being worked out in modern mathematics?

(see the answer keys)

This section contains 818 words (approx. 3 pages at 300 words per page) View a FREE sample