View a FREE sample

This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. What did British scholars accuse Leibniz of?
(a) Stealing Newton's Binomial theorem.
(b) Plagiarizing Newton's calculus method.
(c) Publishing Newton's work without his approval.
(d) Conspiring the death of Newton.

2. What was Dunham central theorem for this chapter?
(a) That the area of a circle is fundamentally related to the square of its area.
(b) That the sum of an infintire series is always infinite.
(c) That there are other transfinite cardinals greater than c.
(d) That the sum of a set of real numbers is finite.

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

4. 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 set is infinite.
(c) That the series is infinite.
(d) That the set is equal to 1.

5. What great theorem is presented by Dunham in this chapter?
(a) A theorem on finite series developed by Johann Bernoulli.
(b) An improvement on Leibniz's caluclus as presented by Jakob Bernoulli.
(c) A theorem on infinite series published by Jakob Bernoulli.
(d) A theorem on series developed by Jakob and published by Johann Bernoulli.

6. 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 divergent series squared numbers.
(c) It's a convergent series of triangular numbers.
(d) It's a convergent series of cubic numbers.

7. Which of the following is not denumerable, proven by Cantor's theorem?
(a) A set of rational numbers.
(b) A set of imaginary numbers.
(c) A set of a geometric series.
(d) A set of transcendental numbers.

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

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

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

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

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

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

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

Short Answer Questions

1. What did Newton's calculus involve?

2. Who were Johann and Jakob Bernoulli?

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

4. What is true about the successive squared denominator series proposed by the Bernoullis?

5. Who encourages Newton during his studies at Cambridge?

(see the answer keys)

This section contains 641 words (approx. 3 pages at 300 words per page) View a FREE sample