|Name: _________________________||Period: ___________________|
This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.
Multiple Choice Questions
1. What is true about real numbers between 0 and 1?
(a) They are denumerable,
(b) There is no set for these numbers.
(c) No sum can be determined.
(d) They are not denumerable.
2. Where was Euler born?
3. Who was Euler's teacher?
(a) Isaac Newton.
(b) Gottfried Leibniz.
(c) Johann Bernoulli.
(d) Jakob Bernoulli.
4. What did Cantor develop?
(a) A system to compare relative sizes of cardinal numbers.
(b) A method to factor very large composite numbers.
(c) A system to identify prime numbers of very large size.
(d) A method to find the sum of a geometric series.
5. What did Newton's calculus involve?
(a) Determining the area under a curve.
(b) Determining the volume of a sphere.
(c) Proving the cubic equation.
(d) Proving the existance of pi.
Short Answer Questions
1. What did Cantor's cardinal numbers represent?
2. Who eventually solved the sum of the successive squared denominator series?
3. Which word best describes Newton's childhood?
4. Where does the center of mathematical thinking shift to after Italy?
5. Which of the following was NOT a field in which Isaac Newton made enormous advances?
Short Essay Questions
1. What was Gauss's major unpublished achievement in geometry?
2. Describe the connection between Fermat and Euler's work.
3. Explain what was the definition of a series before the Bernoullis, and give examples of what was known.
4. Describe some of the characteristics of Leonhard Euler, and what made him successful.
5. Describe what the Bernoullis discovered about series, and give an example.
6. Why did Euler start working on the sum of series?
7. What was Euler able to prove about 2²ⁿ + 1? Why was this a great accomplishment?
8. Give an example of a series who's sum is still unknown.
9. Describe Newton's days in Cambridge and what he eventually came to discover.
10. Describe who were Jakob and Johann Bernoulli.
This section contains 715 words
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