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

2. Which of the following did Dunham concentrate on as one of Newton's great advances?
(a) Quadratic equation.
(b) Binomial theorem.
(c) Quintic theorem.
(d) Area of a sphere.

3. Where was Euler born?
(a) Finland.
(b) Denmark.
(c) Germany.
(d) Switzerland.

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

5. Which word best describes Newton's childhood?
(a) Simple.
(b) Cold.
(c) Troubled.
(d) Hard.

Short Answer Questions

1. Who encourages Newton during his studies at Cambridge?

2. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?

3. Where did Euler study at the age of 20?

4. Who, in modern day, is given credit for the calculus method?

5. Which of the following demonstrates the successive squared denominator series?

Short Essay Questions

1. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

2. Describe who were Jakob and Johann Bernoulli.

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

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

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

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

7. Why did Euler start working on the sum of series?

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

9. Describe some of Gauss's work.

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

(see the answer keys)

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