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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. Who were Johann and Jakob Bernoulli?

2. What did George Cantor discover?

3. What did Newton's calculus involve?

4. What did British scholars accuse Leibniz of?

5. What did Cantor define as the continuum?

Short Essay Questions

1. Describe some of Gauss's work.

2. Describe who were Jakob and Johann Bernoulli.

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

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

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

6. Describe Cantor's difficult personal life.

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

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

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

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

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Compare Pythagoras's proof of the Pythagorean Theorem and how Heron's formula for triangular area can be used as an alternative proof of the Pythagorean theorem. What are the common assumptions in both proofs? What components of each proof are different?

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

Write an essay to describe what was known about mathematics and geometry before and in the time of Thales.

Part 1) Describe what we know about geometry before Thales.

Part 2) In what ways were mathematics and geometry used before Thales?

Part 3) Explain what we know about Thales' work. How did it advance mathematics?

(see the answer keys)

This section contains 847 words (approx. 3 pages at 300 words per page) View a FREE sample