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 George Cantor determine to be true of a set of rational numbers?
(a) They are all composite numbers.
(b) They are denumerable.
(c) They are non-denumerable.
(d) They are all prime numbers.

2. What was aleph naught?
(a) A symbol to state the sum of a series.
(b) A method to determine the sum of a series.
(c) A method to numerate terms.
(d) A symbol to represent the number of items in a set.

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

4. What did Cantor's beliefs lead him to think?
(a) That he was God.
(b) That he was learning about the origins of God.
(c) That he was tapping into the nature of God by delving into the infinite.
(d) That he was seeing God when he worked on equations.

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

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

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

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

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

10. What concept did Dunham end his book with?
(a) Newton's method of calculus.
(b) Cantor and his voyage into the infinite.
(c) Heron's triangulated area.
(d) Archimedes and the infinite series.

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

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

13. What did most of 19th century mathematics focus on, as highlighted by Dunham?
(a) Geometry.
(b) The theoretical.
(c) The immediately practical.
(d) Algebra.

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

15. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 2 + 3 + 4 + 5. . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 1/2 + 3/4 + 4/5 . . .
(d) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .

Short Answer Questions

1. What did Cantor define as the continuum?

2. What were the main technique(s) that Euler used to find the sum of the series?

3. Which of the following did Dunham concentrate on as one of Newton's great advances?

4. What did mathematicians want to perfect in the mid-19th century?

5. Who, in modern day, is given credit for the calculus method?

(see the answer keys)

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