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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. Who, in modern day, is given credit for the calculus method?
(a) Newton,
(b) Leibniz.
(c) Both Newton and Leibniz.
(d) Johann Bernoulli.

2. What were the two types of transfinite cardinals defined by Cantor?
(a) אₒ and c.
(b) pi and אₒ.
(c) 1 and pi.
(d) c and pi.

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

4. What did George Cantor discover?
(a) A method to measure infinity.
(b) A way to compare the relative sizes of infinite sets.
(c) A method to measure a curved area.
(d) A way to determine the accuracy of a calculation.

5. What was most noticeable about Euler at a young age?
(a) He had a remarkable memory.
(b) He had an aptitude for literature.
(c) He was not very quick with arithmatic.
(d) He was very athletic.

Short Answer Questions

1. What did Cantor's cardinal numbers represent?

2. What did Euler prove about 2²ⁿ + 1?

3. Where was Euler born?

4. Who encourages Newton during his studies at Cambridge?

5. What did Newton's calculus involve?

Short Essay Questions

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

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

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

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

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 What was Gauss's major unpublished achievement in geometry?

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

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

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

9. Describe Cantor's difficult personal life.

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

(see the answer keys)

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