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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 Cantor define as the continuum?**
**(a)** Real numbers between 0 and 1. **(b)** The square root of any real number. **(c)** All imaginary numbers. **(d)** All imaginary and real numbers.

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

**3. How did Cantor finally prove his theory?**
**(a)** By extension of the Pythagorean Theorem. **(b)** By using basic algebra. **(c)** By refining and expanding set theory. **(d)** By extension of the infinite series.

**4. When was Euler born?**
**(a)** 1658. **(b)** 1796. **(c)** 1707. **(d)** 1903.

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

## Short Answer Questions

**1.** What was similar about both Euler and Gauss as children?

**2.** What did Cantor's work do to mathematics?

**3.** To how many decimal places did Newton determine the number for pi?

**4.** What concept did Dunham end his book with?

**5.** Who was Euler's teacher?

## Short Essay Questions

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

**2.** What was Gauss's major unpublished achievement in geometry?

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

**4.** Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

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

**6.** Explain why Eulers sum of Ï€Â²/6 was in some ways surprising.

**7.** Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

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

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

**10.** Describe who were Jakob and Johann Bernoulli.

This section contains 764 words(approx. 3 pages at 300 words per page) |