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This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

**1. What did George Cantor determine to be true of a set of rational numbers?**
**(a)** They are all composite numbers. **(b)** They are denumerable. **(c)** They are non-denumerable. **(d)** They are all prime numbers.

**2. What was aleph naught?**
**(a)** A symbol to state the sum of a series. **(b)** A method to determine the sum of a series. **(c)** A method to numerate terms. **(d)** A symbol to represent the number of items in a set.

**3. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?**
**(a)** The statement was a composite number. **(b)** The statement was a prime number. **(c)** The statement was not a prime number. **(d)** The statement was a perfect number.

**4. What did Cantor's beliefs lead him to think?**
**(a)** That he was God. **(b)** That he was learning about the origins of God. **(c)** That he was tapping into the nature of God by delving into the infinite. **(d)** That he was seeing God when he worked on equations.

**5. What did Gauss do with his best work?**
**(a)** He published it. **(b)** He did not publish it. **(c)** He gave it to his son to publish. **(d)** He gave it to his students.

**6. Where did Newton go to school before he went to Cambridge?**
**(a)** The King's School. **(b)** Cambridge Prep. **(c)** Charles II Grammar School. **(d)** Oxford Grammar School.

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

**8. What great theorem is presented by Dunham in this chapter?**
**(a)** An improvement on Leibniz's caluclus as presented by Jakob Bernoulli. **(b)** A theorem on finite series developed by Johann Bernoulli. **(c)** A theorem on series developed by Jakob and published by Johann Bernoulli. **(d)** A theorem on infinite series published by Jakob Bernoulli.

**9. Where did George Cantor live in the 1860s and 1870s?**
**(a)** Scotland. **(b)** Russia. **(c)** Germany. **(d)** Britian.

**10. What concept did Dunham end his book with?**
**(a)** Newton's method of calculus. **(b)** Cantor and his voyage into the infinite. **(c)** Heron's triangulated area. **(d)** Archimedes and the infinite series.

**11. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?**
**(a)** Both series were divergent. **(b)** Both series were composed of successively smaller terms. **(c)** Both series were composed of successively larger terms. **(d)** Both series were convergent.

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

**13. What did most of 19th century mathematics focus on, as highlighted by Dunham?**
**(a)** Geometry. **(b)** The theoretical. **(c)** The immediately practical. **(d)** Algebra.

**14. Which of the following was one of Gauss' early discoveries?**
**(a)** A proof that the Pythagorean Theorem was correct. **(b)** A method to simplify Newton's calulus. **(c)** A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . **(d)** A way to construct a regular 17-sided polygon.

**15. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?**
**(a)** 1 + 2 + 3 + 4 + 5. . . **(b)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . . **(c)** 1 + 1/2 + 3/4 + 4/5 . . . **(d)** 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .

## Short Answer Questions

**1.** What did Cantor define as the continuum?

**2.** What were the main technique(s) that Euler used to find the sum of the series?

**3.** Which of the following did Dunham concentrate on as one of Newton's great advances?

**4.** What did mathematicians want to perfect in the mid-19th century?

**5.** Who, in modern day, is given credit for the calculus method?

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