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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 did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to infinity.
(b) The sum converges to a finite term.
(c) The sum diverges to infinity.
(d) The sum grows ever smaller.
2. What did George Cantor determine to be true of a set of rational numbers?
(a) They are non-denumerable.
(b) They are denumerable.
(c) They are all prime numbers.
(d) They are all composite numbers.
3. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?
(a) They are both less concern with reality.
(b) They are both fascinated on artificial images, such as photography.
(c) They are both becoming less abstract.
(d) They are both focused on realism.
4. What was aleph naught?
(a) A symbol to state the sum of a series.
(b) A method to numerate terms.
(c) A symbol to represent the number of items in a set.
(d) A method to determine the sum of a series.
5. Where was Euler born?
Short Answer Questions
1. What did Gauss construct?
2. Where was George Cantor born?
3. Which of the following demonstrates the successive squared denominator series?
4. What did Cantor's work do to mathematics?
5. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
Short Essay Questions
1. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?
2. Why did Euler start working on the sum of series?
3. Describe some of the characteristics of Leonhard Euler, and what made him successful.
4. What was Gauss's major unpublished achievement in geometry?
5. Describe some of Gauss's work.
6. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?
7. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.
8. What was the great theorem of this chapter? Describe it briefly.
9. Describe who were Jakob and Johann Bernoulli.
10. Describe the controversy that Newton was caught in with his publication of his calculus methods.
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