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Name: _________________________ | Period: ___________________ |

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

## Multiple Choice Questions

**1. In his later life, what position did Isaac Newton hold?**
**(a)** Angelican father. **(b)** Professor of philosophy in Paris. **(c)** Principle science advisor to Charles II. **(d)** Warden of the Mint.

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

**3. What hindered Euler's work as he grew older?**
**(a)** His increasing blindness. **(b)** His hearing was getting worse. **(c)** He had a stroke. **(d)** He had very bad arthritis.

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

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

**6. Where did Newton go to school before he went to Cambridge?**
**(a)** Charles II Grammar School. **(b)** The King's School. **(c)** Cambridge Prep. **(d)** Oxford Grammar School.

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

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

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

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

**11. What did Newton's calculus involve?**
**(a)** Determining the volume of a sphere. **(b)** Proving the existance of pi. **(c)** Proving the cubic equation. **(d)** Determining the area under a curve.

**12. What was the same about the series proposed by Leibniz and the series proposed by Bernoulli?**
**(a)** Both series were composed of successively smaller terms. **(b)** Both series were convergent. **(c)** Both series were composed of successively larger terms. **(d)** Both series were divergent.

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

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

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

## Short Answer Questions

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

**2.** Who was Euler's teacher?

**3.** Where did Euler study at the age of 20?

**4.** What did Gauss construct?

**5.** What did Cantor suspect about transfinite cardinals?

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