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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

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

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

3. Who eventually solved the sum of the successive squared denominator series?
(a) Jakob Bernoulli.
(b) John Napier.
(c) Johann Bernoulli.
(d) Leonhard Euler.

4. What were the two types of transfinite cardinals defined by Cantor?
(a) c and pi.
(b) 1 and pi.
(c) pi and אₒ.
(d) אₒ and c.

5. 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.

Short Answer Questions

1. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?

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

3. What didn't Euler attempt?

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

5. What did Cantor define as the continuum?

Short Essay Questions

1. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

2. Give an example of a series who's sum is still unknown.

3. What was the great theorem of this chapter? Describe it briefly.

4. Describe Cantor's difficult personal life.

5. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

6. Explain how Gottfried Leibniz was able to publish his method of calculus.

7. Describe who were Jakob and Johann Bernoulli.

8. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.

9. What was Gauss's major unpublished achievement in geometry?

10. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

(see the answer keys)

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