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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. Where did Newton go to school before he went to Cambridge?**
**(a)** Oxford Grammar School. **(b)** Charles II Grammar School. **(c)** The King's School. **(d)** Cambridge Prep.

**2. What did Cantor define as the continuum?**
**(a)** All imaginary and real numbers. **(b)** Real numbers between 0 and 1. **(c)** All imaginary numbers. **(d)** The square root of any real number.

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

**4. Which of the following demonstrates the successive squared denominator series?**
**(a)** 1 + 1/2 + 3/4 + 4/5 . . . **(b)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . . **(c)** 1 + 1/4 + 1/9 + 1/16 . . . **(d)** 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .

**5. What did mathematicians want to perfect in the mid-19th century?**
**(a)** The definition of infinite. **(b)** The method of finding the area under a curve. **(c)** The definition of pi. **(d)** The method of finding the volume of spheres.

**6. 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 too poor to attend a Universtiy. **(c)** They both showed incredible abilities in mathematics. **(d)** They both were late to attend school.

**7. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?**
**(a)** It's a divergent series squared numbers. **(b)** It's a convergent series of cubic numbers. **(c)** It's a convergent series of triangular numbers. **(d)** It's a divergent series with a sum of 2.

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

**9. What was aleph naught?**
**(a)** A method to determine the sum of a series. **(b)** A method to numerate terms. **(c)** A symbol to state the sum of a series. **(d)** A symbol to represent the number of items in a set.

**10. Which of the following was a major part of Gauss' work in mathematics?**
**(a)** Simple proofs to demonstrate Bernoulli's series. **(b)** Proofs on the area of a square. **(c)** Elemental proofs related to the foundations of algebra. **(d)** Proofs to show that Archimedes' number theory was wrong.

**11. 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.

**12. What did Newton's calculus involve?**
**(a)** Proving the existance of pi. **(b)** Proving the cubic equation. **(c)** Determining the volume of a sphere. **(d)** Determining the area under a curve.

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

**14. Who else, besides Newton, independently discovered a calculus method?**
**(a)** Gottfried Leibniz. **(b)** John Napier. **(c)** Pierre de Fermat. **(d)** Isaac Barrow.

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

## Short Answer Questions

**1.** Where does the center of mathematical thinking shift to after Italy?

**2.** Which of the following is a quote from Bertrand Russell included by Dunham?

**3.** What was true when Euler used n = 5 in the statement 2²ⁿ + 1?

**4.** Which of the following was one of Gauss' early discoveries?

**5.** What great theorem is presented by Dunham in this chapter?

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