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

Multiple Choice Questions

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

2. In the Bernoulli's time, what was the current definition of a series?
(a) The sum of a finite series of terms.
(b) The infinite sum of a convergent series.
(c) The finite sum of a divergent series.
(d) The sum of a never-ending series of terms.

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

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

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

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

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

8. Which of the following was one of Gauss' early discoveries?
(a) A proof that the Pythagorean Theorem was correct.
(b) A way to construct a regular 17-sided polygon.
(c) A method to simplify Newton's calulus.
(d) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .

9. 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.

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

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

12. 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 tapping into the nature of God by delving into the infinite.
(d) That he was seeing God when he worked on equations.

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

14. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to infinity.
(b) The sum diverges to infinity.
(c) The sum grows ever smaller.
(d) The sum converges to a finite term.

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

Short Answer Questions

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

2. Where was Euler born?

3. What sum did Euler find for the series?

4. Who were Johann and Jakob Bernoulli?

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

(see the answer keys)

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