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This test consists of 15 multiple choice questions and 5 short answer questions.
Multiple Choice Questions
1. What is true about real numbers between 0 and 1?
(a) They are denumerable,
(b) They are not denumerable.
(c) There is no set for these numbers.
(d) No sum can be determined.
2. How did Euler prove if the number 4,294,967,297 was prime or composite?
(a) He used Newton's calulus methods.
(b) He divided it by 2.
(c) He used his own rule of squares.
(d) He factored it.
3. Which of the following was a major part of Gauss' work in mathematics?
(a) Proofs on the area of a square.
(b) Proofs to show that Archimedes' number theory was wrong.
(c) Simple proofs to demonstrate Bernoulli's series.
(d) Elemental proofs related to the foundations of algebra.
4. Where was George Cantor born?
5. When was Euler born?
6. Who else, besides Newton, independently discovered a calculus method?
(a) Gottfried Leibniz.
(b) John Napier.
(c) Isaac Barrow.
(d) Pierre de Fermat.
7. What did most of 19th century mathematics focus on, as highlighted by Dunham?
(c) The theoretical.
(d) The immediately practical.
8. In his later life, what position did Isaac Newton hold?
(a) Professor of philosophy in Paris.
(b) Angelican father.
(c) Principle science advisor to Charles II.
(d) Warden of the Mint.
9. 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 more than 180 degrees.
(c) A system where the angles of a triangle add up to fewer than 180 degrees.
(d) A proof that demonstrates Newtonian physics.
10. Which phrase best describes Newton as a student at Cambridge?
(a) A highly praised genius.
(b) Quiet recluse of no intelligence.
(c) Tolerant, mildly interested in science.
(d) Unnoticed, but remarkable.
11. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
(a) That the set is infinite.
(b) That the set is still equal to c.
(c) That the set is equal to 1.
(d) That the series is infinite.
12. Where did George Cantor live in the 1860s and 1870s?
13. Who, in modern day, is given credit for the calculus method?
(b) Johann Bernoulli.
(d) Both Newton and Leibniz.
14. What did George Cantor determine to be true of a set of rational numbers?
(a) They are denumerable.
(b) They are all prime numbers.
(c) They are non-denumerable.
(d) They are all composite numbers.
15. Which word best describes Newton's childhood?
Short Answer Questions
1. What did Cantor struggle with later in his life?
2. Who were Johann and Jakob Bernoulli?
3. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
4. What did Newton's calculus involve?
5. Where does the center of mathematical thinking shift to after Italy?
This section contains 499 words
(approx. 2 pages at 300 words per page)