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

Multiple Choice Questions

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

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

3. What was Dunham central theorem for this chapter?
(a) That the sum of an infintire series is always infinite.
(b) That the sum of a set of real numbers is finite.
(c) That the area of a circle is fundamentally related to the square of its area.
(d) That there are other transfinite cardinals greater than c.

4. What did George Cantor discover?
(a) A way to determine the accuracy of a calculation.
(b) A method to measure infinity.
(c) A way to compare the relative sizes of infinite sets.
(d) A method to measure a curved area.

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

6. What hindered Euler's work as he grew older?
(a) His increasing blindness.
(b) He had very bad arthritis.
(c) His hearing was getting worse.
(d) He had a stroke.

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

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

9. Who encourages Newton during his studies at Cambridge?
(a) Henry Stokes.
(b) Isaac Barrow.
(c) Henry Briggs.
(d) John Napier.

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

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

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

13. Where was Euler born?
(a) Finland.
(b) Denmark.
(c) Switzerland.
(d) Germany.

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

15. How did Gauss feel about his best work?
(a) He was confident that his students would find it of great importance.
(b) He was unceratin if it would be accepted by his collegues.
(c) He was confident that it would change mathematics.
(d) He was uncertain if it was useful.

Short Answer Questions

1. In what area was Gauss especially interested?

2. Which phrase best describes Newton as a student at Cambridge?

3. Which of the following is a quote from Bertrand Russell included by Dunham?

4. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?

5. What concept did Dunham end his book with?

(see the answer keys)

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