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

2. What did mathematicians want to perfect in the mid-19th century?
(a) The method of finding the volume of spheres.
(b) The definition of infinite.
(c) The definition of pi.
(d) The method of finding the area under a curve.

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

4. Which phrase best describes Newton as a student at Cambridge?
(a) Quiet recluse of no intelligence.
(b) A highly praised genius.
(c) Tolerant, mildly interested in science.
(d) Unnoticed, but remarkable.

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

6. What did Euler's sum surprisingly connect?
(a) The area under a curve.
(b) The circumference of a circle and right triangles.
(c) The area of squares and the area of circles.
(d) The squares of area and square roots.

7. What did Gauss construct?
(a) A system where the angles of a triangle add up to fewer than 180 degrees.
(b) A proof that demonstrates Newtonian physics.
(c) A proof that demonstrated the circumference of Earth.
(d) A system where the angles of a triangle add up to more than 180 degrees.

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

9. What did British scholars accuse Leibniz of?
(a) Conspiring the death of Newton.
(b) Publishing Newton's work without his approval.
(c) Plagiarizing Newton's calculus method.
(d) Stealing Newton's Binomial theorem.

10. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a divergent series with a sum of 2.
(b) It's a convergent series of triangular numbers.
(c) It's a divergent series squared numbers.
(d) It's a convergent series of cubic numbers.

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

12. What did Cantor define as the continuum?
(a) The square root of any real number.
(b) All imaginary numbers.
(c) All imaginary and real numbers.
(d) Real numbers between 0 and 1.

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

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

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

Short Answer Questions

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

2. How did Cantor finally prove his theory?

3. When was Euler born?

4. What sum did Euler find for the series?

5. Where was Euler born?

(see the answer keys)

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