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

Multiple Choice Questions

1. What did Cantor's beliefs lead him to think?
(a) That he was tapping into the nature of God by delving into the infinite.
(b) That he was learning about the origins of God.
(c) That he was seeing God when he worked on equations.
(d) That he was God.

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

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

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

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

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

7. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?
(a) They are both fascinated on artificial images, such as photography.
(b) They are both becoming less abstract.
(c) They are both less concern with reality.
(d) They are both focused on realism.

8. Who was Euler's teacher?
(a) Gottfried Leibniz.
(b) Isaac Newton.
(c) Johann Bernoulli.
(d) Jakob Bernoulli.

9. Which name does NOT belong?
(a) Blaise Pascal.
(b) John Napier.
(c) Francois Viete
(d) Renee Descartes.

10. In what area was Gauss especially interested?
(a) The elements of geometry.
(b) The proof of the infinite series.
(c) The circumference of Earth.
(d) The elements of number theory.

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

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

13. What did most of 19th century mathematics focus on, as highlighted by Dunham?
(a) The theoretical.
(b) Algebra.
(c) The immediately practical.
(d) Geometry.

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

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

Short Answer Questions

1. What hindered Euler's work as he grew older?

2. What did Dunham describe as lacking from calculus previous to the mid-19th century?

3. How did Cantor finally prove his theory?

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

5. What sum did Euler find for the series?

(see the answer keys)

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