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

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

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

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

5. Where did Euler study at the age of 20?
(a) The Academy in St. Petersburg.
(b) Oxford.
(c) University of Moscow.
(d) Cambrigde.

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

7. Where was George Cantor born?
(a) Switzerland.
(b) Germany.
(c) Britian.
(d) Russia.

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

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

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

11. Where does the center of mathematical thinking shift to after Italy?
(a) To Britian and Scotland.
(b) To Turkey and Russia.
(c) To Germany and Russia.
(d) To France and Britian.

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

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

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

15. 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 all prime numbers.
(d) They are non-denumerable.

Short Answer Questions

1. Which word best describes Newton's childhood?

2. Who else, besides Newton, independently discovered a calculus method?

3. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

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

5. What did Cantor's beliefs lead him to think?

(see the answer keys)

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