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

2. Which word best describes Newton's childhood?
(a) Troubled.
(b) Hard.
(c) Simple.
(d) Cold.

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

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

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

Short Answer Questions

1. In what area was Gauss especially interested?

2. What did Cantor define as the continuum?

3. What was Dunham central theorem for this chapter?

4. What were the main technique(s) that Euler used to find the sum of the series?

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

Short Essay Questions

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

2. Describe some of Gauss's work.

3. Describe the controversy that Newton was caught in with his publication of his calculus methods.

4. Describe Newton's days in Cambridge and what he eventually came to discover.

5. What great theorems and work of Newton did Dunham highlight?

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

7. Explain why Eulers sum of π²/6 was in some ways surprising.

8. Where did the center of mathematical thinking shift to in the !7th Century, and who are the major scholars of this time period?

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

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

(see the answer keys)

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