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. Where was Euler born?
(a) Germany.
(b) Denmark.
(c) Finland.
(d) Switzerland.

2. What did Cantor struggle with later in his life?
(a) Leukemia.
(b) Mental illness.
(c) Blindness.
(d) Seizures.

3. What did Cantor develop?
(a) A system to compare relative sizes of cardinal numbers.
(b) A method to factor very large composite numbers.
(c) A system to identify prime numbers of very large size.
(d) A method to find the sum of a geometric series.

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

5. What were the main technique(s) that Euler used to find the sum of the series?
(a) Calculus methods.
(b) Cubic equations.
(c) Quadratic sums,
(d) Trigonometry and basic algebra.

Short Answer Questions

1. What did George Cantor discover?

2. What did British scholars accuse Leibniz of?

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

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

5. What did Gauss do with his best work?

Short Essay Questions

1. Explain how Gottfried Leibniz was able to publish his method of calculus.

2. Describe the connection between Fermat and Euler's work.

3. What was Gauss's major unpublished achievement in geometry?

4. Describe what the Bernoullis discovered about series, and give an example.

5. What was the great theorem of this chapter? Describe it briefly.

6. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?

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

8. Describe some of Gauss's work.

9. Describe the great theorem explained by Dunham in this chapter.

10. What were the two transfinite cardinals discovered by Cantor, and what method did he use to determine them?

(see the answer keys)

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