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. In his later life, what position did Isaac Newton hold?
(a) Angelican father.
(b) Professor of philosophy in Paris.
(c) Principle science advisor to Charles II.
(d) Warden of the Mint.

2. How did Cantor finally prove his theory?
(a) By extension of the infinite series.
(b) By refining and expanding set theory.
(c) By extension of the Pythagorean Theorem.
(d) By using basic algebra.

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

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

5. What great theorem is presented by Dunham in this chapter?
(a) A theorem on infinite series published by Jakob Bernoulli.
(b) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
(c) A theorem on series developed by Jakob and published by Johann Bernoulli.
(d) A theorem on finite series developed by Johann Bernoulli.

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

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

8. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum diverges to infinity.
(b) The sum converges to infinity.
(c) The sum grows ever smaller.
(d) The sum converges to a finite term.

9. 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 divided it by 2.
(c) He used Newton's calulus methods.
(d) He factored it.

10. What didn't Euler attempt?
(a) A series where exponents are odd.
(b) A series starting with the number 1.
(c) A series where exponents are even.
(d) A series of sequencially smaller terms.

11. What did Newton's calculus involve?
(a) Determining the volume of a sphere.
(b) Proving the existance of pi.
(c) Proving the cubic equation.
(d) Determining the area under a curve.

12. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were composed of successively smaller terms.
(b) Both series were convergent.
(c) Both series were composed of successively larger terms.
(d) Both series were divergent.

13. Which of the following is a quote from Bertrand Russell included by Dunham?
(a) "Mathematics, rightly viewed, posses not only truth, but supreme beauty."
(b) "The study of mathematics is the study of the universe."
(c) "Matematicians are the gatekeepers of knowledge."
(d) "Mathematics is truth."

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

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

Short Answer Questions

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

2. Who was Euler's teacher?

3. Where did Euler study at the age of 20?

4. What did Gauss construct?

5. What did Cantor suspect about transfinite cardinals?

(see the answer keys)

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