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

2. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a convergent series of cubic numbers.
(b) It's a divergent series squared numbers.
(c) It's a divergent series with a sum of 2.
(d) It's a convergent series of triangular numbers.

3. What did Euler's sum surprisingly connect?
(a) The circumference of a circle and right triangles.
(b) The area under a curve.
(c) The area of squares and the area of circles.
(d) The squares of area and square roots.

4. Who encourages Newton during his studies at Cambridge?
(a) Henry Stokes.
(b) John Napier.
(c) Henry Briggs.
(d) Isaac Barrow.

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

Short Answer Questions

1. Which of the following was a major part of Gauss' work in mathematics?

2. Who were Johann and Jakob Bernoulli?

3. Which of the following is a quote from Bertrand Russell included by Dunham?

4. Where was George Cantor born?

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

Short Essay Questions

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

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

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

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 What was Gauss's major unpublished achievement in geometry?

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

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

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

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

9. Describe Cantor's difficult personal life.

10. Describe some of Gauss's work.

(see the answer keys)

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