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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

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

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

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

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

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

**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 the same about the series proposed by Leibniz and the series proposed by Bernoulli?**
**(a)** Both series were convergent. **(b)** Both series were composed of successively larger terms. **(c)** Both series were composed of successively smaller terms. **(d)** Both series were divergent.

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

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

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

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

**12. What did Gauss construct?**
**(a)** A system where the angles of a triangle add up to more than 180 degrees. **(b)** A proof that demonstrated the circumference of Earth. **(c)** A system where the angles of a triangle add up to fewer than 180 degrees. **(d)** A proof that demonstrates Newtonian physics.

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

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

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

## Short Answer Questions

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

**2.** Where was Euler born?

**3.** What was Dunham central theorem for this chapter?

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

**5.** Which of the following was NOT a field in which Isaac Newton made enormous advances?

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