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

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

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

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

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

6. How did Euler prove if the number 4,294,967,297 was prime or composite?
(a) He used Newton's calulus methods.
(b) He factored it.
(c) He used his own rule of squares.
(d) He divided it by 2.

7. What is true about the successive squared denominator series proposed by the Bernoullis?
(a) The sum diverges.
(b) The sum converges.
(c) The sum diverges into infinity.
(d) The sum converges to 2.

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

9. Which of the following demonstrates the successive squared denominator series?
(a) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(b) 1 + 1/2 + 3/4 + 4/5 . . .
(c) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(d) 1 + 1/4 + 1/9 + 1/16 . . .

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

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

12. 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.

13. What was most noticeable about Euler at a young age?
(a) He had a remarkable memory.
(b) He was very athletic.
(c) He was not very quick with arithmatic.
(d) He had an aptitude for literature.

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

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

Short Answer Questions

1. What did Cantor develop?

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

3. What did Cantor's cardinal numbers represent?

4. What did Cantor define as the continuum?

5. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

(see the answer keys)

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