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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. What rule in calculus uses derivatives to help evaluate limits involving indeterminate forms?

2. In the photoelectric effect, electrons are emitted from solids, liquids or gases when they do what?

3. When was Bernhard Riemann born?

4. The author states in Chapter 6, “Infinity’s Twin” that Carl Gauss realized that real and imaginary numbers could be what?

5. Carl Gauss referred to mathematics as what?

Short Essay Questions

1. How does the elimination of zero help general relativity theory, according to the author in Chapter 8, “Zero Hour at Ground Zero”?

2. How did l’Hopital address the problem of zero, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

3. How is string theory described by the author in Chapter 8, “Zero Hour at Ground Zero”?

4. How did the field of quantum mechanics address the problem of zero in thermodynamics?

5. Who devised the concept of a limit in calculus? What problems did the limit solve?

6. What are differential equations? Who first developed differential equations?

7. How old is the universe estimated to be by astronomers today? How did they calculate this age?

8. Who discovered “absolute zero”? How is absolute zero defined in Chapter 7, “Absolute Zeros”?

9. How did the discovery of imaginary numbers affect the study of algebra?

10. How were Georg Cantor’s mathematical principles applied to his theology? Who disagreed with his vision and why?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Discuss the life and work of Zeno of Elea. What philosophical and mathematical discoveries did Zeno make? What is the definition of paradox? What paradox of Zeno’s is discussed in the book?

Essay Topic 2

Describe and discuss the biography and works of Leonardo Fibonacci during the Middle Ages, and Fibonacci’s influence in spreading the Hindu–Arabic numeral system in Europe. What is the Fibonacci number sequence? What works did Fibonacci write?

Essay Topic 3

Discuss Guillaume de l'Hôpital, Bishop Berkeley, and l'Hôpital's rule. How are derivatives used to evaluate limits involving indeterminate forms under l'Hôpital's rule? How did these advancements deal with the problem of zero?

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