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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 Cantor define as the continuum?
(a) Real numbers between 0 and 1.
(b) The square root of any real number.
(c) All imaginary numbers.
(d) All imaginary and real numbers.
2. Who eventually solved the sum of the successive squared denominator series?
(a) Leonhard Euler.
(b) Jakob Bernoulli.
(c) John Napier.
(d) Johann Bernoulli.
3. How did Cantor finally prove his theory?
(a) By extension of the Pythagorean Theorem.
(b) By using basic algebra.
(c) By refining and expanding set theory.
(d) By extension of the infinite series.
4. When was Euler born?
5. What did Cantor struggle with later in his life?
(a) Mental illness.
Short Answer Questions
1. What was similar about both Euler and Gauss as children?
2. What did Cantor's work do to mathematics?
3. To how many decimal places did Newton determine the number for pi?
4. What concept did Dunham end his book with?
5. Who was Euler's teacher?
Short Essay Questions
1. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?
2. What was Gauss's major unpublished achievement in geometry?
3. Explain how Gottfried Leibniz was able to publish his method of calculus.
4. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.
5. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?
6. Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.
7. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?
8. What great theorems and work of Newton did Dunham highlight?
9. Describe the connection between Fermat and Euler's work.
10. Describe who were Jakob and Johann Bernoulli.
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