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

2. Who was Euler's teacher?
(a) Isaac Newton.
(b) Gottfried Leibniz.
(c) Jakob Bernoulli.
(d) Johann Bernoulli.

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

4. What is true about real numbers between 0 and 1?
(a) There is no set for these numbers.
(b) They are denumerable,
(c) No sum can be determined.
(d) They are not denumerable.

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

6. What were the two types of transfinite cardinals defined by Cantor?
(a) 1 and pi.
(b) אₒ and c.
(c) pi and אₒ.
(d) c and pi.

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

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

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

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

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

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

13. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?
(a) They are both fascinated on artificial images, such as photography.
(b) They are both less concern with reality.
(c) They are both focused on realism.
(d) They are both becoming less abstract.

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

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

Short Answer Questions

1. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

2. What did British scholars accuse Leibniz of?

3. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

4. What did Cantor struggle with later in his life?

5. What did Euler prove about 2²ⁿ + 1?

(see the answer keys)

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