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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. How did Cantor finally prove his theory?
(a) By refining and expanding set theory.
(b) By using basic algebra.
(c) By extension of the infinite series.
(d) By extension of the Pythagorean Theorem.
2. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
(b) Nobody has determined the sum.
3. Which of the following demonstrates the successive squared denominator series?
(a) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(b) 1 + 1/4 + 1/9 + 1/16 . . .
(c) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .
4. In his later life, what position did Isaac Newton hold?
(a) Angelican father.
(b) Warden of the Mint.
(c) Principle science advisor to Charles II.
(d) Professor of philosophy in Paris.
5. What did Cantor's cardinal numbers represent?
(a) Sets of all imaginary numbers.
(b) Infinite sets.
(c) Finite series.
(d) Series of prime numbers.
Short Answer Questions
1. What did Euler's sum surprisingly connect?
2. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
3. Which of the following was one of Gauss' early discoveries?
4. Where was Euler born?
5. What is true about the successive squared denominator series proposed by the Bernoullis?
Short Essay Questions
1. What was Gauss's major unpublished achievement in geometry?
2. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.
3. Describe the connection between Fermat and Euler's work.
4. Who was Georg Cantor, and what was significant about his work in mathematics?
5. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?
6. Describe Newton's days in Cambridge and what he eventually came to discover.
7. Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.
8. Describe who were Jakob and Johann Bernoulli.
9. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?
10. Describe what the Bernoullis discovered about series, and give an example.
This section contains 800 words
(approx. 3 pages at 300 words per page)