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

2. What was most noticeable about Euler at a young age?
(a) He was not very quick with arithmatic.
(b) He was very athletic.
(c) He had a remarkable memory.
(d) He had an aptitude for literature.

3. 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) An explanation of non-Eulidean mathematics.
(d) Definitions of infinately large and small quantities.

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

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

6. To how many decimal places did Newton determine the number for pi?
(a) Eight places.
(b) Nine places.
(c) Three places.
(d) Twelve places.

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

8. How did Gauss feel about his best work?
(a) He was uncertain if it was useful.
(b) He was confident that his students would find it of great importance.
(c) He was confident that it would change mathematics.
(d) He was unceratin if it would be accepted by his collegues.

9. What were the main technique(s) that Euler used to find the sum of the series?
(a) Cubic equations.
(b) Trigonometry and basic algebra.
(c) Calculus methods.
(d) Quadratic sums,

10. How did Euler prove if the number 4,294,967,297 was prime or composite?
(a) He divided it by 2.
(b) He factored it.
(c) He used Newton's calulus methods.
(d) He used his own rule of squares.

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

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

13. Which phrase best describes Newton as a student at Cambridge?
(a) Quiet recluse of no intelligence.
(b) A highly praised genius.
(c) Tolerant, mildly interested in science.
(d) Unnoticed, but remarkable.

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

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

Short Answer Questions

1. What did Cantor struggle with later in his life?

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

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

4. In the Bernoulli's time, what was the current definition of a series?

5. Who, in modern day, is given credit for the calculus method?

(see the answer keys)

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