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

2. To how many decimal places did Newton determine the number for pi?
(a) Three places.
(b) Eight places.
(c) Nine places.
(d) Twelve places.

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

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

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

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

7. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?
(a) Both series were convergent.
(b) Both series were composed of successively larger terms.
(c) Both series were composed of successively smaller terms.
(d) Both series were divergent.

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

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

10. What did Gauss do with his best work?
(a) He did not publish it.
(b) He gave it to his son to publish.
(c) He gave it to his students.
(d) He published it.

11. What was most noticeable about Euler at a young age?
(a) He had a remarkable memory.
(b) He was very athletic.
(c) He was not very quick with arithmatic.
(d) He had an aptitude for literature.

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

13. On who's work did Euler base his number theory?
(a) Newton's.
(b) Bernoulli's.
(c) Leibniz's.
(d) Fermat's.

14. Which of the following was a major part of Gauss' work in mathematics?
(a) Elemental proofs related to the foundations of algebra.
(b) Simple proofs to demonstrate Bernoulli's series.
(c) Proofs on the area of a square.
(d) Proofs to show that Archimedes' number theory was wrong.

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

Short Answer Questions

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

2. Where was Euler born?

3. What was Dunham central theorem for this chapter?

4. What great theorem is presented by Dunham in this chapter?

5. Which of the following was NOT a field in which Isaac Newton made enormous advances?

(see the answer keys)

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