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

Multiple Choice Questions

1. What series was Euler most famous for?
(a) 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . .
(b) 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . .
(c) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .

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

3. Where did Euler study at the age of 20?
(a) University of Moscow.
(b) The Academy in St. Petersburg.
(c) Cambrigde.
(d) Oxford.

4. What did Newton's calculus involve?
(a) Proving the existance of pi.
(b) Determining the area under a curve.
(c) Determining the volume of a sphere.
(d) Proving the cubic equation.

5. Who else, besides Newton, independently discovered a calculus method?
(a) Isaac Barrow.
(b) John Napier.
(c) Pierre de Fermat.
(d) Gottfried Leibniz.

6. 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.

7. What did Cantor define as the continuum?
(a) All imaginary and real numbers.
(b) Real numbers between 0 and 1.
(c) The square root of any real number.
(d) All imaginary numbers.

8. Which phrase best describes Newton as a student at Cambridge?
(a) Tolerant, mildly interested in science.
(b) Unnoticed, but remarkable.
(c) Quiet recluse of no intelligence.
(d) A highly praised genius.

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

10. Which of the following was NOT a field in which Isaac Newton made enormous advances?
(a) Physics.
(b) Optics.
(c) Mathematics.
(d) Biology.

11. What is one proof that Euler was able to prove?
(a) Bernoulli's principle of lift.
(b) "little Fermat theorem."
(c) Newton's method of calculus.
(d) Descartes' number theory.

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

13. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a perfect number.
(b) The statement was not a prime number.
(c) The statement was a composite number.
(d) The statement was a prime number.

14. What did Cantor develop?
(a) A system to compare relative sizes of cardinal numbers.
(b) A method to factor very large composite numbers.
(c) A method to find the sum of a geometric series.
(d) A system to identify prime numbers of very large size.

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

Short Answer Questions

1. Where did George Cantor live in the 1860s and 1870s?

2. What great theorem is presented by Dunham in this chapter?

3. What did Cantor's beliefs lead him to think?

4. What did British scholars accuse Leibniz of?

5. What were the main technique(s) that Euler used to find the sum of the series?

(see the answer keys)

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