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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. When did Sir Isaac Newton live?

2. The mass of an electron is represented by what fraction in comparison with the mass of a proton?

3. The author asserts in Chapter 8, “Zero Hour at Ground Zero” that today astronomers estimate the universe as being how old?

4. Quantum mechanics eliminated zero in classical thermodynamics by removing what, according to the author in Chapter 7, “Absolute Zeros”?

5. When was Lord Kelvin born?

Short Essay Questions

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

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

3. How are electrons described in Chapter 8, “Zero Hour at Ground Zero”?

4. What problem do black holes present in physics, according to the author in Chapter 8, “Zero Hour at Ground Zero”?

5. How many dimensions are required for string theory to work? How are these dimensions described in Chapter 8, “Zero Hour at Ground Zero”?

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

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

8. What does the author say thermodynamics has taught us in Chapter 7, “Absolute Zeros”?

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

10. The author states in Chapter 6, “Infinity’s Twin” that before imaginary numbers could be accepted, several developments had to occur. Which was the first?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

Define and discuss imaginary numbers and their impact on algebra and mathematic philosophy. Who discovered imaginary numbers and when? How do imaginary numbers behave in comparison to real numbers?

Essay Topic 2

Discuss the mathematical influences of Copernicus and Nicholas of Cusa during the Renaissance. How did Copernicus’s model of the universe differ from the Aristotelian model? What became of Copernicus and Nicholas of Cusa?

Essay Topic 3

Describe and discuss the work and discoveries of René Descartes, and the development of the Cartesian coordinate system. How did the Cartesian coordinate system affect geometry and algebra? How did Descartes relate his mathematical discoveries to his philosophies and theological beliefs?

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