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

## Multiple Choice Questions

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

**2. How did Gauss feel about his best work?**
**(a)** He was confident that it would change mathematics. **(b)** He was unceratin if it would be accepted by his collegues. **(c)** He was uncertain if it was useful. **(d)** He was confident that his students would find it of great importance.

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

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

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

**6. Where does the center of mathematical thinking shift to after Italy?**
**(a)** To Turkey and Russia. **(b)** To Britian and Scotland. **(c)** To France and Britian. **(d)** To Germany and Russia.

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

**8. 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 sum of a set of real numbers is finite. **(d)** That the area of a circle is fundamentally related to the square of its area.

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

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

**11. What were the two types of transfinite cardinals defined by Cantor?**
**(a)** Ã—ÂÃ¢â€šâ€™ and c. **(b)** 1 and pi. **(c)** pi and Ã—ÂÃ¢â€šâ€™. **(d)** c and pi.

**12. What did British scholars accuse Leibniz of?**
**(a)** Plagiarizing Newton's calculus method. **(b)** Conspiring the death of Newton. **(c)** Stealing Newton's Binomial theorem. **(d)** Publishing Newton's work without his approval.

**13. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?**
**(a)** 1 + 1/2 + 3/4 + 4/5 . . . **(b)** 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . . **(c)** 1 + 1/2 + 1/6 + 1/10 + 1/15 . . . **(d)** 1 + 2 + 3 + 4 + 5. . .

**14. How did Cantor finally prove his theory?**
**(a)** By extension of the infinite series. **(b)** By refining and expanding set theory. **(c)** By extension of the Pythagorean Theorem. **(d)** By using basic algebra.

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

## Short Answer Questions

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

**2.** What didn't Euler attempt?

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

**4.** What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

**5.** What series was Euler most famous for?

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