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This test consists of 15 multiple choice questions and 5 short answer questions.

## Multiple Choice Questions

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

**2. What concept did Dunham end his book with?**
**(a)** Cantor and his voyage into the infinite. **(b)** Newton's method of calculus. **(c)** Heron's triangulated area. **(d)** Archimedes and the infinite series.

**3. What did Cantor's cardinal numbers represent?**
**(a)** Sets of all imaginary numbers. **(b)** Finite series. **(c)** Series of prime numbers. **(d)** Infinite sets.

**4. To how many decimal places did Newton determine the number for pi?**
**(a)** Three places. **(b)** Twelve places. **(c)** Nine places. **(d)** Eight places.

**5. Where did Euler study at the age of 20?**
**(a)** The Academy in St. Petersburg. **(b)** Oxford. **(c)** University of Moscow. **(d)** Cambrigde.

**6. What series was Euler most famous for?**
**(a)** 1 + 1/2 + 3/4 + 4/5 . . . **(b)** 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . . **(c)** 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . . **(d)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .

**7. Where was George Cantor born?**
**(a)** Switzerland. **(b)** Germany. **(c)** Britian. **(d)** Russia.

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

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

**10. In what area was Gauss especially interested?**
**(a)** The circumference of Earth. **(b)** The elements of number theory. **(c)** The elements of geometry. **(d)** The proof of the infinite series.

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

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

**13. Which of the following is not denumerable, proven by Cantor's theorem?**
**(a)** A set of a geometric series. **(b)** A set of transcendental numbers. **(c)** A set of imaginary numbers. **(d)** A set of rational numbers.

**14. How did Euler prove if the number 4,294,967,297 was prime or composite?**
**(a)** He used his own rule of squares. **(b)** He factored it. **(c)** He used Newton's calulus methods. **(d)** He divided it by 2.

**15. What did George Cantor determine to be true of a set of rational numbers?**
**(a)** They are denumerable. **(b)** They are all composite numbers. **(c)** They are all prime numbers. **(d)** They are non-denumerable.

## Short Answer Questions

**1.** Which word best describes Newton's childhood?

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

**3.** What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

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

**5.** What did Cantor's beliefs lead him to think?

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