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

Multiple Choice Questions

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

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

3. How did Euler prove if the number 4,294,967,297 was prime or composite?
(a) He used his own rule of squares.
(b) He used Newton's calulus methods.
(c) He factored it.
(d) He divided it by 2.

4. What series was Euler most famous for?
(a) 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . .
(b) 1 + 1/2 + 3/4 + 4/5 . . .
(c) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(d) 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . .

5. What did Cantor's work do to mathematics?
(a) It forced the reexamination of set theory.
(b) It caused a reevaluation of basic algebra.
(c) It raised arguments on the origins of geometry.
(d) It caused much agreement among mathematicians on the use of calculus.

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

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

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

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

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

12. What sum did Euler find for the series?
(a) 1.
(b) π²/6
(c) The sum was infinite.
(d) 2.

13. Where was Euler born?
(a) Finland.
(b) Germany.
(c) Denmark.
(d) Switzerland.

14. What did Gauss construct?
(a) A system where the angles of a triangle add up to more 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 fewer than 180 degrees.

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

Short Answer Questions

1. Which word best describes Newton's childhood?

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

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

4. In what area was Gauss especially interested?

5. What did Cantor suspect about transfinite cardinals?

(see the answer keys)

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