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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 George Cantor discover?
(a) A method to measure infinity.
(b) A way to compare the relative sizes of infinite sets.
(c) A method to measure a curved area.
(d) A way to determine the accuracy of a calculation.

2. What did Dunham describe as lacking from calculus previous to the mid-19th century?
(a) Foundations that link it to the principles of geometry.
(b) Description of the word "area."
(c) An explanation of non-Eulidean mathematics.
(d) Definitions of infinately large and small quantities.

3. Who encourages Newton during his studies at Cambridge?
(a) Henry Briggs.
(b) John Napier.
(c) Isaac Barrow.
(d) Henry Stokes.

4. What did mathematicians want to perfect in the mid-19th century?
(a) The method of finding the area under a curve.
(b) The method of finding the volume of spheres.
(c) The definition of pi.
(d) The definition of infinite.

5. Who eventually solved the sum of the successive squared denominator series?
(a) John Napier.
(b) Johann Bernoulli.
(c) Leonhard Euler.
(d) Jakob Bernoulli.

Short Answer Questions

1. What was aleph naught?

2. Which of the following demonstrates the successive squared denominator series?

3. Which of the following was NOT a field in which Isaac Newton made enormous advances?

4. Where was George Cantor born?

5. What did Cantor struggle with later in his life?

Short Essay Questions

1. Who was Georg Cantor, and what was significant about his work in mathematics?

2. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

3. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.

4. Describe what the Bernoullis discovered about series, and give an example.

5. What great theorems and work of Newton did Dunham highlight?

6. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

7. What was the great theorem of this chapter? Describe it briefly.

8. Explain any methods used by Cantor that were unsuccessful.

9. Describe the connection between Fermat and Euler's work.

10. Describe some of the characteristics of Leonhard Euler, and what made him successful.

(see the answer keys)

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