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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. In the Bernoulli's time, what was the current definition of a series?
(a) The finite sum of a divergent series.
(b) The infinite sum of a convergent series.
(c) The sum of a finite series of terms.
(d) The sum of a never-ending series of terms.
2. What did Cantor's cardinal numbers represent?
(a) Infinite sets.
(b) Sets of all imaginary numbers.
(c) Finite series.
(d) Series of prime numbers.
3. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was not a prime number.
(b) The statement was a composite number.
(c) The statement was a prime number.
(d) The statement was a perfect number.
4. In his later life, what position did Isaac Newton hold?
(a) Professor of philosophy in Paris.
(b) Warden of the Mint.
(c) Angelican father.
(d) Principle science advisor to Charles II.
5. What did Euler prove about 2²ⁿ + 1?
(a) That the statment is sometimes prime and sometimes composite.
(b) That the statement is neither prime nor composite.
(c) That the statement is always a prime number.
(d) That the statement is always a composite number.
Short Answer Questions
1. Which name does NOT belong?
2. Who eventually solved the sum of the successive squared denominator series?
3. What did Gauss construct?
4. What did Dunham describe as lacking from calculus previous to the mid-19th century?
5. Where was George Cantor born?
Short Essay Questions
1. What was the great theorem of this chapter? Describe it briefly.
2. Give an example of a series who's sum is still unknown.
3. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.
4. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?
5. Why did Euler start working on the sum of series?
6. Describe who were Jakob and Johann Bernoulli.
7. Describe some of Gauss's work.
8. Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.
9. What was Gauss's major unpublished achievement in geometry?
10. What great theorems and work of Newton did Dunham highlight?
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