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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 determine the accuracy of a calculation. **(c)** A way to compare the relative sizes of infinite sets. **(d)** A method to measure a curved area.

**2. What didn't Euler attempt?**
**(a)** A series where exponents are even. **(b)** A series where exponents are odd. **(c)** A series starting with the number 1. **(d)** A series of sequencially smaller terms.

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

**4. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?**
**(a)** They are both less concern with reality. **(b)** They are both fascinated on artificial images, such as photography. **(c)** They are both becoming less abstract. **(d)** They are both focused on realism.

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

## Short Answer Questions

**1.** Where did Euler study at the age of 20?

**2.** Which of the following was one of Gauss' early discoveries?

**3.** How did Euler prove if the number 4,294,967,297 was prime or composite?

**4.** What did Euler prove about 2²ⁿ + 1?

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

## Short Essay Questions

**1.** Describe Newton's days in Cambridge and what he eventually came to discover.

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

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

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

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

**6.** Describe the controversy that Newton was caught in with his publication of his calculus methods.

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

**8.** Describe Cantor's difficult personal life.

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

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

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