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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 Euler's sum surprisingly connect?**
**(a)** The circumference of a circle and right triangles. **(b)** The area of squares and the area of circles. **(c)** The squares of area and square roots. **(d)** The area under a curve.

**2. Which word best describes Newton's childhood?**
**(a)** Troubled. **(b)** Hard. **(c)** Simple. **(d)** Cold.

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

**4. What did Gauss construct?**
**(a)** A proof that demonstrated the circumference of Earth. **(b)** A system where the angles of a triangle add up to more than 180 degrees. **(c)** A proof that demonstrates Newtonian physics. **(d)** A system where the angles of a triangle add up to fewer than 180 degrees.

**5. On who's work did Euler base his number theory?**
**(a)** Newton's. **(b)** Bernoulli's. **(c)** Leibniz's. **(d)** Fermat's.

## Short Answer Questions

**1.** In what area was Gauss especially interested?

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

**3.** What was Dunham central theorem for this chapter?

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

**5.** What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

## Short Essay Questions

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

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

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

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

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

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

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

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

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

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

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