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 was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were composed of successively smaller terms.
(b) Both series were divergent.
(c) Both series were convergent.
(d) Both series were composed of successively larger terms.

2. In what area was Gauss especially interested?
(a) The elements of geometry.
(b) The elements of number theory.
(c) The circumference of Earth.
(d) The proof of the infinite series.

3. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
(a) That the set is equal to 1.
(b) That the set is infinite.
(c) That the set is still equal to c.
(d) That the series is infinite.

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

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

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

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

8. What did Cantor's cardinal numbers represent?
(a) Series of prime numbers.
(b) Sets of all imaginary numbers.
(c) Infinite sets.
(d) Finite series.

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

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

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

12. Who were Johann and Jakob Bernoulli?
(a) Twin brothers and students of Newton.
(b) Cousins and students with Newton at Cambridge.
(c) Cousins and students with Leibniz in Paris.
(d) Brothers and students of Leibniz.

13. 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.

14. Which of the following is not denumerable, proven by Cantor's theorem?
(a) A set of rational numbers.
(b) A set of imaginary numbers.
(c) A set of a geometric series.
(d) A set of transcendental numbers.

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

Short Answer Questions

1. Where was Euler born?

2. How did Euler prove if the number 4,294,967,297 was prime or composite?

3. Which name does NOT belong?

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

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

(see the answer keys)

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