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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 using basic algebra.
(b) By extension of the infinite series.
(c) By refining and expanding set theory.
(d) By extension of the Pythagorean Theorem.
2. What did Gauss construct?
(a) A proof that demonstrates Newtonian physics.
(b) A system where the angles of a triangle add up to more than 180 degrees.
(c) A proof that demonstrated the circumference of Earth.
(d) A system where the angles of a triangle add up to fewer than 180 degrees.
3. To how many decimal places did Newton determine the number for pi?
(a) Twelve places.
(b) Eight places.
(c) Three places.
(d) Nine places.
4. What is one proof that Euler was able to prove?
(a) Newton's method of calculus.
(b) "little Fermat theorem."
(c) Bernoulli's principle of lift.
(d) Descartes' number theory.
5. What did Euler's sum surprisingly connect?
(a) The area of squares and the area of circles.
(b) The area under a curve.
(c) The squares of area and square roots.
(d) The circumference of a circle and right triangles.
Short Answer Questions
1. Where does the center of mathematical thinking shift to after Italy?
2. Which of the following demonstrates the successive squared denominator series?
3. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
4. What sum did Euler find for the series?
5. What did George Cantor determine to be true of a set of rational numbers?
Short Essay Questions
1. Describe who were Jakob and Johann Bernoulli.
2. What great theorems and work of Newton did Dunham highlight?
3. Describe the great theorem explained by Dunham in this chapter.
4. Describe the controversy that Newton was caught in with his publication of his calculus methods.
5. What was Gauss's major unpublished achievement in geometry?
6. Explain any methods used by Cantor that were unsuccessful.
7. Describe what the Bernoullis discovered about series, and give an example.
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. Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.
10. Give an example of a series who's sum is still unknown.
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