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

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

3. What did Euler prove about 2²ⁿ + 1?
(a) That the statement is always a prime number.
(b) That the statment is sometimes prime and sometimes composite.
(c) That the statement is always a composite number.
(d) That the statement is neither prime nor composite.

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

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

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

7. What did Cantor's beliefs lead him to think?
(a) That he was tapping into the nature of God by delving into the infinite.
(b) That he was God.
(c) That he was learning about the origins of God.
(d) That he was seeing God when he worked on equations.

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

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

10. Where did George Cantor live in the 1860s and 1870s?
(a) Britian.
(b) Scotland.
(c) Russia.
(d) Germany.

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

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

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

14. What did Cantor develop?
(a) A system to compare relative sizes of cardinal numbers.
(b) A method to find the sum of a geometric series.
(c) A system to identify prime numbers of very large size.
(d) A method to factor very large composite numbers.

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

Short Answer Questions

1. Who was Euler's teacher?

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

3. Who encourages Newton during his studies at Cambridge?

4. What did most of 19th century mathematics focus on, as highlighted by Dunham?

5. Which of the following did Dunham concentrate on as one of Newton's great advances?

(see the answer keys)

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