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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 Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to a finite term.
(b) The sum converges to infinity.
(c) The sum grows ever smaller.
(d) The sum diverges to infinity.
2. What did Gauss do with his best work?
(a) He did not publish it.
(b) He gave it to his son to publish.
(c) He gave it to his students.
(d) He published it.
3. Which of the following was one of Gauss' early discoveries?
(a) A proof that the Pythagorean Theorem was correct.
(b) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .
(c) A way to construct a regular 17-sided polygon.
(d) A method to simplify Newton's calulus.
4. Which word best describes Newton's childhood?
5. Who was Euler's teacher?
(a) Gottfried Leibniz.
(b) Jakob Bernoulli.
(c) Isaac Newton.
(d) Johann Bernoulli.
Short Answer Questions
1. What didn't Euler attempt?
2. Who encourages Newton during his studies at Cambridge?
3. What did mathematicians want to perfect in the mid-19th century?
4. What did British scholars accuse Leibniz of?
5. What great theorem is presented by Dunham in this chapter?
Short Essay Questions
1. What was Gauss's major unpublished achievement in geometry?
2. Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.
3. Describe Newton's days in Cambridge and what he eventually came to discover.
4. What was the great theorem of this chapter? Describe it briefly.
5. Why did Euler start working on the sum of series?
6. Describe some of the characteristics of Leonhard Euler, and what made him successful.
7. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.
8. Describe what the Bernoullis discovered about series, and give an example.
9. Describe the great theorem explained by Dunham in this chapter.
10. What great theorems and work of Newton did Dunham highlight?
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