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) Principle science advisor to Charles II.
(b) Professor of philosophy in Paris.
(c) Warden of the Mint.
(d) Angelican father.

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

3. Which of the following was one of Gauss' early discoveries?
(a) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .
(b) A method to simplify Newton's calulus.
(c) A proof that the Pythagorean Theorem was correct.
(d) A way to construct a regular 17-sided polygon.

4. On who's work did Euler base his number theory?
(a) Fermat's.
(b) Bernoulli's.
(c) Newton's.
(d) Leibniz's.

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

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

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

8. Who were Johann and Jakob Bernoulli?
(a) Cousins and students with Leibniz in Paris.
(b) Brothers and students of Leibniz.
(c) Twin brothers and students of Newton.
(d) Cousins and students with Newton at Cambridge.

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

10. What did George Cantor discover?
(a) A method to measure infinity.
(b) A method to measure a curved area.
(c) A way to compare the relative sizes of infinite sets.
(d) A way to determine the accuracy of a calculation.

11. In the Bernoulli's time, what was the current definition of a series?
(a) The sum of a finite series of terms.
(b) The sum of a never-ending series of terms.
(c) The infinite sum of a convergent series.
(d) The finite sum of a divergent series.

12. What did Gauss do with his best work?
(a) He gave it to his son to publish.
(b) He gave it to his students.
(c) He published it.
(d) He did not publish it.

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

14. What was aleph naught?
(a) A method to determine the sum of a series.
(b) A method to numerate terms.
(c) A symbol to state the sum of a series.
(d) A symbol to represent the number of items in a set.

15. How did Gauss feel about his best work?
(a) He was confident that it would change mathematics.
(b) He was unceratin if it would be accepted by his collegues.
(c) He was confident that his students would find it of great importance.
(d) He was uncertain if it was useful.

Short Answer Questions

1. Who, in modern day, is given credit for the calculus method?

2. What is true about the successive squared denominator series proposed by the Bernoullis?

3. Which phrase best describes Newton as a student at Cambridge?

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

5. What is true about real numbers between 0 and 1?

(see the answer keys)

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