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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

**2. What did Cantor suspect about transfinite cardinals?**
**(a)** That the sum of the series is finite. **(b)** That there are transfinite cardinals much less than c. **(c)** That there are transfinite cardinals even greater than c. **(d)** That the sum of the series is infinite.

**3. In the Bernoulli's time, what was the current definition of a series?**
**(a)** The sum of a finite series of terms. **(b)** The finite sum of a divergent series. **(c)** The sum of a never-ending series of terms. **(d)** The infinite sum of a convergent series.

**4. 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)** Definitions of infinately large and small quantities. **(d)** An explanation of non-Eulidean mathematics.

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

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

**7. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?**
**(a)** That the set is still equal to c. **(b)** That the series is infinite. **(c)** That the set is equal to 1. **(d)** That the set is infinite.

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

**9. What was similar about both Euler and Gauss as children?**
**(a)** They both showed incredible abilities in mathematics. **(b)** They both were late to attend school. **(c)** They both were too poor to attend a Universtiy. **(d)** They both showed a desire to lead a simple life.

**10. What did Cantor struggle with later in his life?**
**(a)** Leukemia. **(b)** Mental illness. **(c)** Blindness. **(d)** Seizures.

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

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

**13. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?**
**(a)** The sum grows ever smaller. **(b)** The sum converges to a finite term. **(c)** The sum diverges to infinity. **(d)** The sum converges to infinity.

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

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

## Short Answer Questions

**1.** What did Cantor develop?

**2.** What did Gauss construct?

**3.** Which name does NOT belong?

**4.** Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

**5.** What concept did Dunham end his book with?

This section contains 576 words(approx. 2 pages at 300 words per page) |