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. Who else, besides Newton, independently discovered a calculus method?
(a) John Napier.
(b) Pierre de Fermat.
(c) Gottfried Leibniz.
(d) Isaac Barrow.

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

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

4. What did Cantor develop?
(a) A method to factor very large composite 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 system to compare relative sizes of cardinal numbers.

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

6. Who was Euler's teacher?
(a) Isaac Newton.
(b) Johann Bernoulli.
(c) Jakob Bernoulli.
(d) Gottfried Leibniz.

7. 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.

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

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

10. When was Euler born?
(a) 1658.
(b) 1707.
(c) 1796.
(d) 1903.

11. Who, in modern day, is given credit for the calculus method?
(a) Newton,
(b) Both Newton and Leibniz.
(c) Leibniz.
(d) Johann Bernoulli.

12. Which of the following was one of Gauss' early discoveries?
(a) A method to simplify Newton's calulus.
(b) A proof that the Pythagorean Theorem was correct.
(c) A way to construct a regular 17-sided polygon.
(d) A demonstration of the sum of the series 1 + 1/2³ + 1/3³ + 1/4³ . . . 1/k³ . .

13. What was aleph naught?
(a) A symbol to represent the number of items in a set.
(b) A method to determine the sum of a series.
(c) A method to numerate terms.
(d) A symbol to state the sum of a series.

14. How did Cantor finally prove his theory?
(a) By extension of the Pythagorean Theorem.
(b) By refining and expanding set theory.
(c) By using basic algebra.
(d) By extension of the infinite series.

15. Where was Euler born?
(a) Germany.
(b) Denmark.
(c) Finland.
(d) Switzerland.

Short Answer Questions

1. What did George Cantor determine to be true of a set of rational numbers?

2. What did Gauss construct?

3. What did Cantor find after extending the continuum between 0 and 1 into two dimensions?

4. Which of the following demonstrates the successive squared denominator series?

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

(see the answer keys)

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