|Name: _________________________||Period: ___________________|
This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.
Multiple Choice Questions
1. What did Cantor's cardinal numbers represent?
(a) Infinite sets.
(b) Sets of all imaginary numbers.
(c) Finite series.
(d) Series of prime numbers.
2. What is true about the successive squared denominator series proposed by the Bernoullis?
(a) The sum diverges.
(b) The sum diverges into infinity.
(c) The sum converges to 2.
(d) The sum converges.
3. In his later life, what position did Isaac Newton hold?
(a) Principle science advisor to Charles II.
(b) Warden of the Mint.
(c) Angelican father.
(d) Professor of philosophy in Paris.
4. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to a finite term.
(b) The sum diverges to infinity.
(c) The sum grows ever smaller.
(d) The sum converges to infinity.
5. What didn't Euler attempt?
(a) A series of sequencially smaller terms.
(b) A series starting with the number 1.
(c) A series where exponents are even.
(d) A series where exponents are odd.
Short Answer Questions
1. Which of the following is not denumerable, proven by Cantor's theorem?
2. On who's work did Euler base his number theory?
3. What did George Cantor discover?
4. Which word best describes Newton's childhood?
5. Which phrase best describes Newton as a student at Cambridge?
Short Essay Questions
1. Describe the great theorem explained by Dunham in this chapter.
2. What was the great theorem of this chapter? Describe it briefly.
3. Describe Cantor's difficult personal life.
4. Give an example of a series who's sum is still unknown.
5. Describe some of the characteristics of Leonhard Euler, and what made him successful.
6. Describe Newton's days in Cambridge and what he eventually came to discover.
7. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.
8. Describe what the Bernoullis discovered about series, and give an example.
9. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?
10. Describe some of Gauss's work.
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