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

Multiple Choice Questions

1. What did George Cantor determine to be true of a set of rational numbers?
(a) They are all composite numbers.
(b) They are non-denumerable.
(c) They are denumerable.
(d) They are all prime numbers.

2. What did mathematicians want to perfect in the mid-19th century?
(a) The definition of infinite.
(b) The method of finding the volume of spheres.
(c) The method of finding the area under a curve.
(d) The definition of pi.

3. Where was George Cantor born?
(a) Russia.
(b) Germany.
(c) Britian.
(d) Switzerland.

4. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were convergent.
(b) Both series were composed of successively smaller terms.
(c) Both series were composed of successively larger terms.
(d) Both series were divergent.

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

6. On who's work did Euler base his number theory?
(a) Newton's.
(b) Leibniz's.
(c) Bernoulli's.
(d) Fermat's.

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

8. What was aleph naught?
(a) A method to determine the sum of a series.
(b) A symbol to represent the number of items in a set.
(c) A symbol to state the sum of a series.
(d) A method to numerate terms.

9. Who, in modern day, is given credit for the calculus method?
(a) Both Newton and Leibniz.
(b) Newton,
(c) Johann Bernoulli.
(d) Leibniz.

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

11. What were the main technique(s) that Euler used to find the sum of the series?
(a) Quadratic sums,
(b) Cubic equations.
(c) Calculus methods.
(d) Trigonometry and basic algebra.

12. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
(a) That the series is infinite.
(b) That the set is equal to 1.
(c) That the set is still equal to c.
(d) That the set is infinite.

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

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

15. Which of the following did Dunham concentrate on as one of Newton's great advances?
(a) Quadratic equation.
(b) Binomial theorem.
(c) Quintic theorem.
(d) Area of a sphere.

Short Answer Questions

1. Where did Newton go to school before he went to Cambridge?

2. What did Gauss do with his best work?

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

4. What did Cantor define as the continuum?

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

(see the answer keys)

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