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

Multiple Choice Questions

1. What great theorem is presented by Dunham in this chapter?
(a) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
(b) A theorem on infinite series published by Jakob Bernoulli.
(c) A theorem on finite series developed by Johann Bernoulli.
(d) A theorem on series developed by Jakob and published by Johann Bernoulli.

2. What is true about the successive squared denominator series proposed by the Bernoullis?
(a) The sum diverges into infinity.
(b) The sum diverges.
(c) The sum converges.
(d) The sum converges to 2.

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

4. Where did Euler study at the age of 20?
(a) Cambrigde.
(b) Oxford.
(c) The Academy in St. Petersburg.
(d) University of Moscow.

5. What hindered Euler's work as he grew older?
(a) His hearing was getting worse.
(b) He had a stroke.
(c) He had very bad arthritis.
(d) His increasing blindness.

6. 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 + 2 + 3 + 4 + 5. . .
(c) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(d) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .

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

8. Which of the following was NOT a field in which Isaac Newton made enormous advances?
(a) Mathematics.
(b) Physics.
(c) Optics.
(d) Biology.

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

10. When was Euler born?
(a) 1707.
(b) 1796.
(c) 1658.
(d) 1903.

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

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

13. Which phrase best describes Newton as a student at Cambridge?
(a) Unnoticed, but remarkable.
(b) Quiet recluse of no intelligence.
(c) Tolerant, mildly interested in science.
(d) A highly praised genius.

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

15. What did George Cantor discover?
(a) A method to measure infinity.
(b) A way to determine the accuracy of a calculation.
(c) A method to measure a curved area.
(d) A way to compare the relative sizes of infinite sets.

Short Answer Questions

1. How did Euler prove if the number 4,294,967,297 was prime or composite?

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

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

4. Which of the following was a major part of Gauss' work in mathematics?

5. What did Cantor suspect about transfinite cardinals?

(see the answer keys)

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