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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. Who was Euler's teacher?**
**(a)** Johann Bernoulli. **(b)** Gottfried Leibniz. **(c)** Isaac Newton. **(d)** Jakob Bernoulli.

**2. What was most noticeable about Euler at a young age?**
**(a)** He was not very quick with arithmatic. **(b)** He was very athletic. **(c)** He had a remarkable memory. **(d)** He had an aptitude for literature.

**3. What did Dunham describe as lacking from calculus previous to the mid-19th century?**
**(a)** Description of the word "area." **(b)** Foundations that link it to the principles of geometry. **(c)** An explanation of non-Eulidean mathematics. **(d)** Definitions of infinately large and small quantities.

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

**5. Where did George Cantor live in the 1860s and 1870s?**
**(a)** Britian. **(b)** Scotland. **(c)** Russia. **(d)** Germany.

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

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

**8. How did Gauss feel about his best work?**
**(a)** He was uncertain if it was useful. **(b)** He was confident that his students would find it of great importance. **(c)** He was confident that it would change mathematics. **(d)** He was unceratin if it would be accepted by his collegues.

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

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

**11. What did Gauss do with his best work?**
**(a)** He gave it to his students. **(b)** He gave it to his son to publish. **(c)** He did not publish it. **(d)** He published it.

**12. What did Cantor's work do to mathematics?**
**(a)** It forced the reexamination of set theory. **(b)** It caused a reevaluation of basic algebra. **(c)** It caused much agreement among mathematicians on the use of calculus. **(d)** It raised arguments on the origins of geometry.

**13. Which phrase best describes Newton as a student at Cambridge?**
**(a)** Quiet recluse of no intelligence. **(b)** A highly praised genius. **(c)** Tolerant, mildly interested in science. **(d)** Unnoticed, but remarkable.

**14. What is true about the successive squared denominator series proposed by the Bernoullis?**
**(a)** The sum diverges into infinity. **(b)** The sum diverges. **(c)** The sum converges. **(d)** The sum converges to 2.

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

## Short Answer Questions

**1.** What did Cantor struggle with later in his life?

**2.** Which of the following demonstrates the successive squared denominator series?

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

**4.** In the Bernoulli's time, what was the current definition of a series?

**5.** Who, in modern day, is given credit for the calculus method?

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