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

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

**3. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?**
**(a)** They are both focused on realism. **(b)** They are both less concern with reality. **(c)** They are both fascinated on artificial images, such as photography. **(d)** They are both becoming less abstract.

**4. What didn't Euler attempt?**
**(a)** A series starting with the number 1. **(b)** A series where exponents are odd. **(c)** A series of sequencially smaller terms. **(d)** A series where exponents are even.

**5. What was Dunham central theorem for this chapter?**
**(a)** That there are other transfinite cardinals greater than c. **(b)** That the sum of an infintire series is always infinite. **(c)** That the area of a circle is fundamentally related to the square of its area. **(d)** That the sum of a set of real numbers is finite.

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

**7. Which of the following did Dunham concentrate on as one of Newton's great advances?**
**(a)** Quintic theorem. **(b)** Binomial theorem. **(c)** Area of a sphere. **(d)** Quadratic equation.

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

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

**10. Who, in modern day, is given credit for the calculus method?**
**(a)** Johann Bernoulli. **(b)** Leibniz. **(c)** Newton, **(d)** Both Newton and Leibniz.

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

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

**13. Who were Johann and Jakob Bernoulli?**
**(a)** Brothers and students of Leibniz. **(b)** Cousins and students with Leibniz in Paris. **(c)** Twin brothers and students of Newton. **(d)** Cousins and students with Newton at Cambridge.

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

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

## Short Answer Questions

**1.** Where was George Cantor born?

**2.** Which word best describes Newton's childhood?

**3.** What is true about real numbers between 0 and 1?

**4.** How did Cantor finally prove his theory?

**5.** What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

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