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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

**2. What sum did Euler find for the series?**
**(a)** 1. **(b)** π²/6 **(c)** 2. **(d)** The sum was infinite.

**3. What did Euler prove about 2²ⁿ + 1?**
**(a)** That the statement is always a prime number. **(b)** That the statment is sometimes prime and sometimes composite. **(c)** That the statement is always a composite number. **(d)** That the statement is neither prime nor composite.

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

**5. Which of the following is a quote from Bertrand Russell included by Dunham?**
**(a)** "Matematicians are the gatekeepers of knowledge." **(b)** "Mathematics, rightly viewed, posses not only truth, but supreme beauty." **(c)** "The study of mathematics is the study of the universe." **(d)** "Mathematics is truth."

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

**7. What did Cantor's beliefs lead him to think?**
**(a)** That he was tapping into the nature of God by delving into the infinite. **(b)** That he was God. **(c)** That he was learning about the origins of God. **(d)** That he was seeing God when he worked on equations.

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

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

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

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

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

**13. What did George Cantor discover?**
**(a)** A method to measure infinity. **(b)** A way to determine the accuracy of a calculation. **(c)** A method to measure a curved area. **(d)** A way to compare the relative sizes of infinite sets.

**14. What did Cantor develop?**
**(a)** A system to compare relative sizes of cardinal numbers. **(b)** A method to find the sum of a geometric series. **(c)** A system to identify prime numbers of very large size. **(d)** A method to factor very large composite numbers.

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

## Short Answer Questions

**1.** Who was Euler's teacher?

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

**3.** Who encourages Newton during his studies at Cambridge?

**4.** What did most of 19th century mathematics focus on, as highlighted by Dunham?

**5.** Which of the following did Dunham concentrate on as one of Newton's great advances?

This section contains 528 words(approx. 2 pages at 300 words per page) |