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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. What did most of 19th century mathematics focus on, as highlighted by Dunham?
(a) Geometry.
(b) The immediately practical.
(c) Algebra.
(d) The theoretical.

2. What did Cantor's beliefs lead him to think?
(a) That he was God.
(b) That he was tapping into the nature of God by delving into the infinite.
(c) That he was learning about the origins of God.
(d) That he was seeing God when he worked on equations.

3. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to infinity.
(b) The sum grows ever smaller.
(c) The sum converges to a finite term.
(d) The sum diverges to infinity.

4. Who was Euler's teacher?
(a) Gottfried Leibniz.
(b) Jakob Bernoulli.
(c) Isaac Newton.
(d) Johann Bernoulli.

5. Who else, besides Newton, independently discovered a calculus method?
(a) John Napier.
(b) Isaac Barrow.
(c) Gottfried Leibniz.
(d) Pierre de Fermat.

Short Answer Questions

1. Where was Euler born?

2. Where did Newton go to school before he went to Cambridge?

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

4. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

5. When was Euler born?

Short Essay Questions

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

2. Describe some of Gauss's work.

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

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

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

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

7. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

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

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

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

(see the answer keys)

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