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This test consists of 15 multiple choice questions and 5 short answer questions.
Multiple Choice Questions
1. Where did Newton go to school before he went to Cambridge?
(a) Oxford Grammar School.
(b) Charles II Grammar School.
(c) The King's School.
(d) Cambridge Prep.
2. What did Cantor define as the continuum?
(a) All imaginary and real numbers.
(b) Real numbers between 0 and 1.
(c) All imaginary numbers.
(d) The square root of any real number.
3. What did Cantor struggle with later in his life?
(c) Mental illness.
4. Which of the following demonstrates the successive squared denominator series?
(a) 1 + 1/2 + 3/4 + 4/5 . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/4 + 1/9 + 1/16 . . .
(d) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
5. What did mathematicians want to perfect in the mid-19th century?
(a) The definition of infinite.
(b) The method of finding the area under a curve.
(c) The definition of pi.
(d) The method of finding the volume of spheres.
6. What was similar about both Euler and Gauss as children?
(a) They both showed a desire to lead a simple life.
(b) They both were too poor to attend a Universtiy.
(c) They both showed incredible abilities in mathematics.
(d) They both were late to attend school.
7. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a divergent series squared numbers.
(b) It's a convergent series of cubic numbers.
(c) It's a convergent series of triangular numbers.
(d) It's a divergent series with a sum of 2.
8. Who was Euler's teacher?
(a) Johann Bernoulli.
(b) Jakob Bernoulli.
(c) Isaac Newton.
(d) Gottfried Leibniz.
9. What was aleph naught?
(a) A method to determine the sum of a series.
(b) A method to numerate terms.
(c) A symbol to state the sum of a series.
(d) A symbol to represent the number of items in a set.
10. Which of the following was a major part of Gauss' work in mathematics?
(a) Simple proofs to demonstrate Bernoulli's series.
(b) Proofs on the area of a square.
(c) Elemental proofs related to the foundations of algebra.
(d) Proofs to show that Archimedes' number theory was wrong.
11. 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 infinity.
(d) The sum converges to a finite term.
12. What did Newton's calculus involve?
(a) Proving the existance of pi.
(b) Proving the cubic equation.
(c) Determining the volume of a sphere.
(d) Determining the area under a curve.
13. On who's work did Euler base his number theory?
14. Who else, besides Newton, independently discovered a calculus method?
(a) Gottfried Leibniz.
(b) John Napier.
(c) Pierre de Fermat.
(d) Isaac Barrow.
15. Which of the following is not denumerable, proven by Cantor's theorem?
(a) A set of rational numbers.
(b) A set of a geometric series.
(c) A set of imaginary numbers.
(d) A set of transcendental numbers.
Short Answer Questions
1. Where does the center of mathematical thinking shift to after Italy?
2. Which of the following is a quote from Bertrand Russell included by Dunham?
3. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
4. Which of the following was one of Gauss' early discoveries?
5. What great theorem is presented by Dunham in this chapter?
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