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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. Which of the following was a major part of Gauss' work in mathematics?
(a) Proofs on the area of a square.
(b) Simple proofs to demonstrate Bernoulli's series.
(c) Proofs to show that Archimedes' number theory was wrong.
(d) Elemental proofs related to the foundations of algebra.

2. What did Newton's calculus involve?
(a) Determining the volume of a sphere.
(b) Proving the cubic equation.
(c) Proving the existance of pi.
(d) Determining the area under a curve.

3. Where did George Cantor live in the 1860s and 1870s?
(a) Germany.
(b) Britian.
(c) Russia.
(d) Scotland.

4. In what area was Gauss especially interested?
(a) The elements of number theory.
(b) The elements of geometry.
(c) The proof of the infinite series.
(d) The circumference of Earth.

5. When was Euler born?
(a) 1658.
(b) 1796.
(c) 1707.
(d) 1903.

Short Answer Questions

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

2. What was Dunham central theorem for this chapter?

3. Which of the following was one of Gauss' early discoveries?

4. Which of the following was NOT a field in which Isaac Newton made enormous advances?

5. What did Cantor define as the continuum?

Short Essay Questions

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

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

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 What was Gauss's major unpublished achievement in geometry?

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

5. Describe Cantor's difficult personal life.

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

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

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

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. Give an example of a series who's sum is still unknown.

(see the answer keys)

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