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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. Where was Euler born?**
**(a)** Germany. **(b)** Denmark. **(c)** Finland. **(d)** Switzerland.

**2. What did Cantor struggle with later in his life?**
**(a)** Leukemia. **(b)** Mental illness. **(c)** Blindness. **(d)** Seizures.

**3. What did Cantor develop?**
**(a)** A system to compare relative sizes of cardinal numbers. **(b)** A method to factor very large composite numbers. **(c)** A system to identify prime numbers of very large size. **(d)** A method to find the sum of a geometric series.

**4. Which of the following is not denumerable, proven by Cantor's theorem?**
**(a)** A set of transcendental numbers. **(b)** A set of rational numbers. **(c)** A set of a geometric series. **(d)** A set of imaginary numbers.

**5. What were the main technique(s) that Euler used to find the sum of the series?**
**(a)** Calculus methods. **(b)** Cubic equations. **(c)** Quadratic sums, **(d)** Trigonometry and basic algebra.

## Short Answer Questions

**1.** What did George Cantor discover?

**2.** What did British scholars accuse Leibniz of?

**3.** What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

**4.** What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

**5.** What did Gauss do with his best work?

## Short Essay Questions

**1.** Explain how Gottfried Leibniz was able to publish his method of calculus.

**2.** Describe the connection between Fermat and Euler's work.

**3.** What was Gauss's major unpublished achievement in geometry?

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

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

**6.** What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

**7.** Explain any methods used by Cantor that were unsuccessful.

**8.** Describe some of Gauss's work.

**9.** Describe the great theorem explained by Dunham in this chapter.

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

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