Journey Through Genius: The Great Theorems of Mathematics Test | Final Test - Easy

William Dunham (mathematician)
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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

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

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

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

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

5. What did Cantor struggle with later in his life?
(a) Blindness.
(b) Mental illness.
(c) Leukemia.
(d) Seizures.

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

7. What great theorem is presented by Dunham in this chapter?
(a) A theorem on series developed by Jakob and published by Johann Bernoulli.
(b) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
(c) A theorem on finite series developed by Johann Bernoulli.
(d) A theorem on infinite series published by Jakob Bernoulli.

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

9. What sum did Euler find for the series?
(a) The sum was infinite.
(b) 2.
(c) π²/6
(d) 1.

10. Which of the following was one of Gauss' early discoveries?
(a) A method to simplify Newton's calulus.
(b) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .
(c) A proof that the Pythagorean Theorem was correct.
(d) A way to construct a regular 17-sided polygon.

11. To how many decimal places did Newton determine the number for pi?
(a) Nine places.
(b) Twelve places.
(c) Eight places.
(d) Three places.

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

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

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

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

Short Answer Questions

1. Who encourages Newton during his studies at Cambridge?

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

3. What was aleph naught?

4. Which name does NOT belong?

5. What didn't Euler attempt?

(see the answer keys)

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