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

**2. What is one proof that Euler was able to prove?**
**(a)** "little Fermat theorem." **(b)** Bernoulli's principle of lift. **(c)** Newton's method of calculus. **(d)** Descartes' number theory.

**3. In his later life, what position did Isaac Newton hold?**
**(a)** Principle science advisor to Charles II. **(b)** Warden of the Mint. **(c)** Angelican father. **(d)** Professor of philosophy in Paris.

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

**5. What is true about real numbers between 0 and 1?**
**(a)** There is no set for these numbers. **(b)** No sum can be determined. **(c)** They are not denumerable. **(d)** They are denumerable,

## Short Answer Questions

**1.** What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?

**2.** Which of the following was NOT a field in which Isaac Newton made enormous advances?

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

**4.** Where does the center of mathematical thinking shift to after Italy?

**5.** What did George Cantor determine to be true of a set of rational numbers?

## Short Essay Questions

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

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

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

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

**5.** What was Gauss's major unpublished achievement in geometry?

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

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

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

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

This section contains 808 words(approx. 3 pages at 300 words per page) |