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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)** The theoretical. **(c)** Geometry. **(d)** Algebra.

**2. Which name does NOT belong?**
**(a)** Blaise Pascal. **(b)** John Napier. **(c)** Renee Descartes. **(d)** Francois Viete

**3. Who encourages Newton during his studies at Cambridge?**
**(a)** Henry Briggs. **(b)** John Napier. **(c)** Henry Stokes. **(d)** Isaac Barrow.

**4. Which of the following was NOT a field in which Isaac Newton made enormous advances?**
**(a)** Physics. **(b)** Biology. **(c)** Optics. **(d)** Mathematics.

**5. Where does the center of mathematical thinking shift to after Italy?**
**(a)** To Germany and Russia. **(b)** To Turkey and Russia. **(c)** To Britian and Scotland. **(d)** To France and Britian.

## Short Answer Questions

**1.** What did Cantor develop?

**2.** Who else, besides Newton, independently discovered a calculus method?

**3.** What was most noticeable about Euler at a young age?

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

**5.** What hindered Euler's work as he grew older?

## Short Essay Questions

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

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

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

**4.** Give an example of a series who's sum is still unknown.

**5.** What was Gauss's major unpublished achievement in geometry?

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

**7.** Who was Georg Cantor, and what was significant about his work in mathematics?

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

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

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

This section contains 709 words(approx. 3 pages at 300 words per page) |