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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. Lord Kelvin is well known for determining the correct value of absolute zero. Absolute zero is approximately what temperature Celsius?

2. Absolute zero has no energy and is unattainable for what reason?

3. How is the Planck relation expressed?

4. According to the author in Chapter 7, “Absolute Zeros,” thermodynamics led physicists to believe that light was not a particle but what?

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

Short Essay Questions

1. What was discovered by Albert Einstein’s solution to the photoelectric effect?

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

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

4. What problems were encountered in calculus with zero? How did zero apply to the physical world, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

5. What is expressed through the Rayleigh-Jeans law? How does this law relate to zero?

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

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

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

9. How did Max Planck address the problem of the ultraviolet catastrophe?

10. What problem does zero present when calculating tangent lines? What is a tangent?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Discuss the biography and the mathematical and philosophical contributions of Archimedes of Syracuse. How did Archimedes first encounter the infinite? How did this discovery influence his work and the work of mathematicians after him?

Essay Topic 2

Discuss the work of Sir Isaac Newton, Gottfried Wilhelm Leibniz, Johannes Kepler, and the origins and development of calculus. When did Newton and Leibniz independently create calculus? What conflict occurred between the two? When did this conflict end?

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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