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

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

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

4. Which of the following demonstrates the successive squared denominator series?
(a) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(b) 1 + 1/4 + 1/9 + 1/16 . . .
(c) 1 + 1/2 + 3/4 + 4/5 . . .
(d) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .

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

6. In what area was Gauss especially interested?
(a) The elements of number theory.
(b) The proof of the infinite series.
(c) The circumference of Earth.
(d) The elements of geometry.

7. What is one proof that Euler was able to prove?
(a) Newton's method of calculus.
(b) Descartes' number theory.
(c) Bernoulli's principle of lift.
(d) "little Fermat theorem."

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

9. What were the two types of transfinite cardinals defined by Cantor?
(a) c and pi.
(b) 1 and pi.
(c) pi and אₒ.
(d) אₒ and c.

10. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?
(a) 1 + 1/2 + 1/3 + 1/4 + 1/5 . . . 1/1000 . . .
(b) 1 + 1/2 + 1/6 + 1/10 + 1/15 . . .
(c) 1 + 2 + 3 + 4 + 5. . .
(d) 1 + 1/2 + 3/4 + 4/5 . . .

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

12. Who eventually solved the sum of the successive squared denominator series?
(a) Leonhard Euler.
(b) Jakob Bernoulli.
(c) Johann Bernoulli.
(d) John Napier.

13. What hindered Euler's work as he grew older?
(a) His increasing blindness.
(b) He had a stroke.
(c) He had very bad arthritis.
(d) His hearing was getting worse.

14. What was described as true about the series 1 + 1/2 + 1/6 + 1/10 + 1/15 + 1/21?
(a) It's a divergent series with a sum of 2.
(b) It's a convergent series of cubic numbers.
(c) It's a convergent series of triangular numbers.
(d) It's a divergent series squared numbers.

15. Which of the following is a quote from Bertrand Russell included by Dunham?
(a) "Matematicians are the gatekeepers of knowledge."
(b) "Mathematics is truth."
(c) "Mathematics, rightly viewed, posses not only truth, but supreme beauty."
(d) "The study of mathematics is the study of the universe."

Short Answer Questions

1. In his later life, what position did Isaac Newton hold?

2. When was Euler born?

3. Which of the following was one of Gauss' early discoveries?

4. What is the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ ... 1/k³ . . .?

5. Who was Euler's teacher?

(see the answer keys)

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