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

2. What did Gauss construct?
(a) A system where the angles of a triangle add up to more than 180 degrees.
(b) A system where the angles of a triangle add up to fewer than 180 degrees.
(c) A proof that demonstrates Newtonian physics.
(d) A proof that demonstrated the circumference of Earth.

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

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

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

6. What did Cantor's beliefs lead him to think?
(a) That he was learning about the origins of God.
(b) That he was God.
(c) That he was seeing God when he worked on equations.
(d) That he was tapping into the nature of God by delving into the infinite.

7. Which of the following did Dunham concentrate on as one of Newton's great advances?
(a) Quintic theorem.
(b) Binomial theorem.
(c) Area of a sphere.
(d) Quadratic equation.

8. What did Euler's sum surprisingly connect?
(a) The area under a curve.
(b) The area of squares and the area of circles.
(c) The squares of area and square roots.
(d) The circumference of a circle and right triangles.

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

10. Who, in modern day, is given credit for the calculus method?
(a) Johann Bernoulli.
(b) Leibniz.
(c) Newton,
(d) Both Newton and Leibniz.

11. What did most of 19th century mathematics focus on, as highlighted by Dunham?
(a) Geometry.
(b) The theoretical.
(c) Algebra.
(d) The immediately practical.

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

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

14. What did Dunham describe as lacking from calculus previous to the mid-19th century?
(a) An explanation of non-Eulidean mathematics.
(b) Definitions of infinately large and small quantities.
(c) Foundations that link it to the principles of geometry.
(d) Description of the word "area."

15. Where did George Cantor live in the 1860s and 1870s?
(a) Russia.
(b) Scotland.
(c) Britian.
(d) Germany.

Short Answer Questions

1. Where was George Cantor born?

2. Which word best describes Newton's childhood?

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

4. How did Cantor finally prove his theory?

5. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?

(see the answer keys)

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