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 was aleph naught?

2. What did most of 19th century mathematics focus on, as highlighted by Dunham?

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

4. Who encourages Newton during his studies at Cambridge?

5. What did George Cantor determine to be true of a set of rational numbers?

Short Essay Questions

1. Describe who were Jakob and Johann Bernoulli.

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

3. Describe the great theorem explained by Dunham in this chapter.

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

5. Describe some of Gauss's work.

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

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

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.

Essay Topic 2

Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.

Essay Topic 3

Summarize the puzzles that were presented as a result of Euclid's infinitude of primes. Name and describe some of these puzzles from a historical perspective, then explain what is known about each in modern mathematics. What puzzles remain unsolved today?

(see the answer keys)

This section contains 910 words (approx. 4 pages at 300 words per page) View a FREE sample