|Name: _________________________||Period: ___________________|
This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.
Multiple Choice Questions
1. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 2 + 3 + 4 + 5. . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/2 + 3/4 + 4/5 . . .
(d) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
2. What did Euler prove about 2²ⁿ + 1?
(a) That the statement is always a prime number.
(b) That the statment is sometimes prime and sometimes composite.
(c) That the statement is neither prime nor composite.
(d) That the statement is always a composite number.
3. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a composite number.
(b) The statement was a prime number.
(c) The statement was not a prime number.
(d) The statement was a perfect number.
4. Where did Euler study at the age of 20?
(a) University of Moscow.
(d) The Academy in St. Petersburg.
5. What did George Cantor determine to be true of a set of rational numbers?
(a) They are all prime numbers.
(b) They are denumerable.
(c) They are all composite numbers.
(d) They are non-denumerable.
Short Answer Questions
1. Who else, besides Newton, independently discovered a calculus method?
2. What great theorem is presented by Dunham in this chapter?
3. What did Euler's sum surprisingly connect?
4. What did Cantor define as the continuum?
5. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
Short Essay Questions
1. Describe the connection between Fermat and Euler's work.
2. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?
3. What was Gauss's major unpublished achievement in geometry?
4. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.
5. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.
6. What great theorems and work of Newton did Dunham highlight?
7. Describe the great theorem explained by Dunham in this chapter.
8. Describe Newton's days in Cambridge and what he eventually came to discover.
9. Describe Cantor's difficult personal life.
10. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.
This section contains 851 words
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