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

Multiple Choice Questions

1. What was Dunham central theorem for this chapter?
(a) That there are other transfinite cardinals greater than c.
(b) That the area of a circle is fundamentally related to the square of its area.
(c) That the sum of a set of real numbers is finite.
(d) That the sum of an infintire series is always infinite.

2. What did British scholars accuse Leibniz of?
(a) Publishing Newton's work without his approval.
(b) Stealing Newton's Binomial theorem.
(c) Conspiring the death of Newton.
(d) Plagiarizing Newton's calculus method.

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

4. What was most noticeable about Euler at a young age?
(a) He had a remarkable memory.
(b) He was not very quick with arithmatic.
(c) He had an aptitude for literature.
(d) He was very athletic.

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

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

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

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

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

10. Which of the following was a major part of Gauss' work in mathematics?
(a) Proofs to show that Archimedes' number theory was wrong.
(b) Simple proofs to demonstrate Bernoulli's series.
(c) Elemental proofs related to the foundations of algebra.
(d) Proofs on the area of a square.

11. What did Gauss do with his best work?
(a) He published it.
(b) He gave it to his son to publish.
(c) He did not publish it.
(d) He gave it to his students.

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

13. What great theorem is presented by Dunham in this chapter?
(a) A theorem on infinite series published by Jakob Bernoulli.
(b) An improvement on Leibniz's caluclus as presented 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.

14. What was similar about both Euler and Gauss as children?
(a) They both were too poor to attend a Universtiy.
(b) They both showed incredible abilities in mathematics.
(c) They both were late to attend school.
(d) They both showed a desire to lead a simple life.

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

Short Answer Questions

1. How did Cantor finally prove his theory?

2. What did Euler prove about 2²ⁿ + 1?

3. Who were Johann and Jakob Bernoulli?

4. In his later life, what position did Isaac Newton hold?

5. To how many decimal places did Newton determine the number for pi?

(see the answer keys)

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