|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 George Cantor discover?
(a) A method to measure infinity.
(b) A way to determine the accuracy of a calculation.
(c) A way to compare the relative sizes of infinite sets.
(d) A method to measure a curved area.
2. What didn't Euler attempt?
(a) A series where exponents are even.
(b) A series where exponents are odd.
(c) A series starting with the number 1.
(d) A series of sequencially smaller terms.
3. What were the main technique(s) that Euler used to find the sum of the series?
(a) Trigonometry and basic algebra.
(b) Cubic equations.
(c) Calculus methods.
(d) Quadratic sums,
4. 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.
5. What did most of 19th century mathematics focus on, as highlighted by Dunham?
(b) The theoretical.
(c) The immediately practical.
Short Answer Questions
1. Where did Euler study at the age of 20?
2. Which of the following was one of Gauss' early discoveries?
3. How did Euler prove if the number 4,294,967,297 was prime or composite?
4. What did Euler prove about 2²ⁿ + 1?
5. Who was Euler's teacher?
Short Essay Questions
1. Describe Newton's days in Cambridge and what he eventually came to discover.
2. What was the great theorem of this chapter? Describe it briefly.
3. Describe some of Gauss's work.
4. Describe what the Bernoullis discovered about series, and give an example.
5. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.
6. Describe the controversy that Newton was caught in with his publication of his calculus methods.
7. What great theorems and work of Newton did Dunham highlight?
8. Describe Cantor's difficult personal life.
9. Explain how Gottfried Leibniz was able to publish his method of calculus.
10. Describe the great theorem explained by Dunham in this chapter.
This section contains 930 words
(approx. 4 pages at 300 words per page)