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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 British scholars accuse Leibniz of?
(a) Publishing Newton's work without his approval.
(b) Conspiring the death of Newton.
(c) Stealing Newton's Binomial theorem.
(d) Plagiarizing Newton's calculus method.

2. What hindered Euler's work as he grew older?
(a) His increasing blindness.
(b) He had very bad arthritis.
(c) He had a stroke.
(d) His hearing was getting worse.

3. Where did Euler study at the age of 20?
(a) Oxford.
(b) University of Moscow.
(c) The Academy in St. Petersburg.
(d) Cambrigde.

4. In the Bernoulli's time, what was the current definition of a series?
(a) The sum of a never-ending series of terms.
(b) The sum of a finite series of terms.
(c) The finite sum of a divergent series.
(d) The infinite sum of a convergent series.

5. How did Euler prove if the number 4,294,967,297 was prime or composite?
(a) He factored it.
(b) He used Newton's calulus methods.
(c) He used his own rule of squares.
(d) He divided it by 2.

Short Answer Questions

1. Which of the following did Dunham concentrate on as one of Newton's great advances?

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

3. Who were Johann and Jakob Bernoulli?

4. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?

5. Where did George Cantor live in the 1860s and 1870s?

Short Essay Questions

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

2. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.

3. Describe who were Jakob and Johann Bernoulli.

4. Explain any methods used by Cantor that were unsuccessful.

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

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

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 What was Gauss's major unpublished achievement in geometry?

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

9. What great theorems and work of Newton did Dunham highlight?

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

(see the answer keys)

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