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) Leukemia.
(b) Seizures.
(c) Blindness.
(d) Mental illness.

2. 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) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
(d) A theorem on infinite series published by Jakob Bernoulli.

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

4. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?
(a) That the set is infinite.
(b) That the set is equal to 1.
(c) That the series is infinite.
(d) That the set is still equal to c.

5. What is true about real numbers between 0 and 1?
(a) They are not denumerable.
(b) They are denumerable,
(c) There is no set for these numbers.
(d) No sum can be determined.

6. 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.

7. What did Dunham describe about the following series 1 + 2 + 3 + 4. . .?
(a) The sum converges to a finite term.
(b) The sum diverges to infinity.
(c) The sum converges to infinity.
(d) The sum grows ever smaller.

8. What was similar about both Euler and Gauss as children?
(a) They both were too poor to attend a Universtiy.
(b) They both were late to attend school.
(c) They both showed a desire to lead a simple life.
(d) They both showed incredible abilities in mathematics.

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

10. Where did Newton go to school before he went to Cambridge?
(a) Oxford Grammar School.
(b) Charles II Grammar School.
(c) Cambridge Prep.
(d) The King's School.

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

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

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

14. Which of the following was NOT a field in which Isaac Newton made enormous advances?
(a) Mathematics.
(b) Biology.
(c) Optics.
(d) Physics.

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

Short Answer Questions

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

2. What concept did Dunham end his book with?

3. What did Cantor's work do to mathematics?

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

5. What was Dunham central theorem for this chapter?

(see the answer keys)

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