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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 is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
(a) Nobody has determined the sum.
2. Who encourages Newton during his studies at Cambridge?
(a) Henry Briggs.
(b) John Napier.
(c) Henry Stokes.
(d) Isaac Barrow.
3. Which of the following was a major part of Gauss' work in mathematics?
(a) Elemental proofs related to the foundations of algebra.
(b) Proofs on the area of a square.
(c) Simple proofs to demonstrate Bernoulli's series.
(d) Proofs to show that Archimedes' number theory was wrong.
4. What did Cantor struggle with later in his life?
(b) Mental illness.
5. What is one proof that Euler was able to prove?
(a) Descartes' number theory.
(b) Newton's method of calculus.
(c) "little Fermat theorem."
(d) Bernoulli's principle of lift.
Short Answer Questions
1. What was Dunham central theorem for this chapter?
2. What were the main technique(s) that Euler used to find the sum of the series?
3. What did Cantor's work do to mathematics?
4. Which of the following is not denumerable, proven by Cantor's theorem?
5. What did George Cantor determine to be true of a set of rational numbers?
Short Essay Questions
1. Describe what the Bernoullis discovered about series, and give an example.
2. Why did Euler start working on the sum of series?
3. Describe who were Jakob and Johann Bernoulli.
4. Who was Georg Cantor, and what was significant about his work in mathematics?
5. Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.
6. Describe the connection between Fermat and Euler's work.
7. Describe Newton's days in Cambridge and what he eventually came to discover.
8. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?
9. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?
10. Describe some of Gauss's work.
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