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

Multiple Choice Questions

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

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

3. In his later life, what position did Isaac Newton hold?
(a) Warden of the Mint.
(b) Professor of philosophy in Paris.
(c) Principle science advisor to Charles II.
(d) Angelican father.

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

5. What did Euler prove about 2²ⁿ + 1?
(a) That the statment is sometimes prime and sometimes composite.
(b) That the statement is always a composite number.
(c) That the statement is always a prime number.
(d) That the statement is neither prime nor composite.

6. 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.

7. Which word best describes Newton's childhood?
(a) Troubled.
(b) Simple.
(c) Hard.
(d) Cold.

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

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

10. Where did George Cantor live in the 1860s and 1870s?
(a) Germany.
(b) Russia.
(c) Britian.
(d) Scotland.

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

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

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

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

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

Short Answer Questions

1. What was similar about both Euler and Gauss as children?

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

3. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

4. On who's work did Euler base his number theory?

5. What did George Cantor determine to be true of a set of rational numbers?

(see the answer keys)

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