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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 most of 19th century mathematics focus on, as highlighted by Dunham?
(a) The immediately practical.
(d) The theoretical.
2. What is one proof that Euler was able to prove?
(a) "little Fermat theorem."
(b) Bernoulli's principle of lift.
(c) Newton's method of calculus.
(d) Descartes' number theory.
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 as the same between artistic movements and mathematical studies in the 19th century?
(a) They are both becoming less abstract.
(b) They are both fascinated on artificial images, such as photography.
(c) They are both less concern with reality.
(d) They are both focused on realism.
5. What is true about real numbers between 0 and 1?
(a) There is no set for these numbers.
(b) No sum can be determined.
(c) They are not denumerable.
(d) They are denumerable,
Short Answer Questions
1. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
2. Which of the following was NOT a field in which Isaac Newton made enormous advances?
3. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
4. Where does the center of mathematical thinking shift to after Italy?
5. What did George Cantor determine to be true of a set of rational numbers?
Short Essay Questions
1. Describe the controversy that Newton was caught in with his publication of his calculus methods.
2. What great theorems and work of Newton did Dunham highlight?
3. Describe Newton's days in Cambridge and what he eventually came to discover.
4. Explain how Gottfried Leibniz was able to publish his method of calculus.
5. What was Gauss's major unpublished achievement in geometry?
6. Describe Cantor's difficult personal life.
7. Describe the connection between Fermat and Euler's work.
8. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?
9. Describe who were Jakob and Johann Bernoulli.
10. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?
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