Journey Through Genius: The Great Theorems of Mathematics Test | Final Test - Medium

William Dunham (mathematician)
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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

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

2. What sum did Euler find for the series?
(a) π²/6
(b) The sum was infinite.
(c) 1.
(d) 2.

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

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

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

Short Answer Questions

1. What did Dunham describe as lacking from calculus previous to the mid-19th century?

2. What did British scholars accuse Leibniz of?

3. Which of the following demonstrates the successive squared denominator series?

4. Where does the center of mathematical thinking shift to after Italy?

5. Where did Newton go to school before he went to Cambridge?

Short Essay Questions

1. What great theorems and work of Newton did Dunham highlight?

2. Describe the controversy that Newton was caught in with his publication of his calculus methods.

3. Describe some of the characteristics of Leonhard Euler, and what made him successful.

4. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

5. Describe Cantor's difficult personal life.

6. Describe what mathematical and artistic movements are focused on in the second half of the 19th century.

7. Describe who were Jakob and Johann Bernoulli.

8. Summarize in a few sentences, what types of number sets did Cantor prove to be denumerable and non-denumerable.

9. Describe some of Gauss's work.

10. Explain any methods used by Cantor that were unsuccessful.

(see the answer keys)

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