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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 as lacking from calculus previous to the mid-19th century?
(a) An explanation of non-Eulidean mathematics.
(b) Definitions of infinately large and small quantities.
(c) Foundations that link it to the principles of geometry.
(d) Description of the word "area."

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

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

4. Who eventually solved the sum of the successive squared denominator series?
(a) John Napier.
(b) Jakob Bernoulli.
(c) Leonhard Euler.
(d) Johann Bernoulli.

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

6. How did Cantor finally prove his theory?
(a) By refining and expanding set theory.
(b) By extension of the Pythagorean Theorem.
(c) By extension of the infinite series.
(d) By using basic algebra.

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

8. Where did Newton go to school before he went to Cambridge?
(a) Charles II Grammar School.
(b) The King's School.
(c) Oxford Grammar School.
(d) Cambridge Prep.

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

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

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

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

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

14. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?
(a) Nobody has determined the sum.
(b) 0.
(c) 2.
(d) Infinity.

15. In the Bernoulli's time, what was the current definition of a series?
(a) The finite sum of a divergent series.
(b) The sum of a never-ending series of terms.
(c) The sum of a finite series of terms.
(d) The infinite sum of a convergent series.

Short Answer Questions

1. What is true about the successive squared denominator series proposed by the Bernoullis?

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

3. What did Cantor suspect about transfinite cardinals?

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

5. Which of the following was NOT a field in which Isaac Newton made enormous advances?

(see the answer keys)

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