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

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

Multiple Choice Questions

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

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

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

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

5. What series was Euler most famous for?
(a) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(b) 1 + 1/2 + 3/4 + 4/5 . . .
(c) 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . . .
(d) 1 + 1/4 + 1/9 + 1/16 . . . + 1/k² . . .

Short Answer Questions

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

2. What did Dunham describe as lacking from calculus previous to the mid-19th century?

3. What did Gauss construct?

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

5. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?

(see the answer keys)

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