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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. Which phrase best describes Newton as a student at Cambridge?
(a) Unnoticed, but remarkable.
(b) Quiet recluse of no intelligence.
(c) Tolerant, mildly interested in science.
(d) A highly praised genius.

2. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were divergent.
(b) Both series were composed of successively larger terms.
(c) Both series were composed of successively smaller terms.
(d) Both series were convergent.

3. What did Cantor's cardinal numbers represent?
(a) Finite series.
(b) Sets of all imaginary numbers.
(c) Infinite sets.
(d) Series of prime numbers.

4. What were the main technique(s) that Euler used to find the sum of the series?
(a) Quadratic sums,
(b) Cubic equations.
(c) Calculus methods.
(d) Trigonometry and basic algebra.

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

Short Answer Questions

1. What did Cantor's beliefs lead him to think?

2. Which word best describes Newton's childhood?

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

4. What were the two types of transfinite cardinals defined by Cantor?

5. Who was Euler's teacher?

Short Essay Questions

1. Describe who were Jakob and Johann Bernoulli.

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

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

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

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

6. Describe Newton's days in Cambridge and what he eventually came to discover.

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

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

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

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

(see the answer keys)

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