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

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

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

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

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

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

7. What was true when Euler used n = 5 in the statement 2²ⁿ + 1?
(a) The statement was a perfect number.
(b) The statement was a composite number.
(c) The statement was a prime number.
(d) The statement was not a prime number.

8. What did Cantor's work do to mathematics?
(a) It caused a reevaluation of basic algebra.
(b) It raised arguments on the origins of geometry.
(c) It caused much agreement among mathematicians on the use of calculus.
(d) It forced the reexamination of set theory.

9. What was Dunham central theorem for this chapter?
(a) That the sum of an infintire series is always infinite.
(b) That the area of a circle is fundamentally related to the square of its area.
(c) That there are other transfinite cardinals greater than c.
(d) That the sum of a set of real numbers is finite.

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

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

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

13. Where does the center of mathematical thinking shift to after Italy?
(a) To Britian and Scotland.
(b) To Germany and Russia.
(c) To France and Britian.
(d) To Turkey and Russia.

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

15. What did Dunham describe as the same between artistic movements and mathematical studies in the 19th century?
(a) They are both becoming less abstract.
(b) They are both focused on realism.
(c) They are both less concern with reality.
(d) They are both fascinated on artificial images, such as photography.

Short Answer Questions

1. What did Cantor define as the continuum?

2. In what area was Gauss especially interested?

3. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

4. Which word best describes Newton's childhood?

5. When was Euler born?

(see the answer keys)

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