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 is true about the successive squared denominator series proposed by the Bernoullis?
(a) The sum converges.
(b) The sum converges to 2.
(c) The sum diverges into infinity.
(d) The sum diverges.

2. What did Cantor suspect about transfinite cardinals?
(a) That the sum of the series is finite.
(b) That there are transfinite cardinals much less than c.
(c) That there are transfinite cardinals even greater than c.
(d) That the sum of the series is infinite.

3. In the Bernoulli's time, what was the current definition of a series?
(a) The sum of a finite series of terms.
(b) The finite sum of a divergent series.
(c) The sum of a never-ending series of terms.
(d) The infinite sum of a convergent series.

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

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

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

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

8. What did George Cantor determine to be true of a set of rational numbers?
(a) They are all prime numbers.
(b) They are denumerable.
(c) They are all composite numbers.
(d) They are non-denumerable.

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

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

11. What did Cantor's work do to mathematics?
(a) It caused a reevaluation of basic algebra.
(b) It forced the reexamination of set theory.
(c) It raised arguments on the origins of geometry.
(d) It caused much agreement among mathematicians on the use of calculus.

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

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

14. Where was George Cantor born?
(a) Switzerland.
(b) Britian.
(c) Russia.
(d) Germany.

15. Where did Euler study at the age of 20?
(a) The Academy in St. Petersburg.
(b) Oxford.
(c) Cambrigde.
(d) University of Moscow.

Short Answer Questions

1. What did Cantor develop?

2. What did Gauss construct?

3. Which name does NOT belong?

4. Which of the following is a series that the Bernoullis proposed did not converge on a finite sum?

5. What concept did Dunham end his book with?

(see the answer keys)

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