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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.** Carl Gauss referred to mathematics as what?

**2.** The Rayleigh–Jeans law revealed an important error in physics theory of its time. The law predicted an energy output that diverges towards infinity as wavelength approaches what?

**3.** Johannes Kepler used calculus to determine that planets had what, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?

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

**5.** Georg Cantor is best known as the inventor of what fundamental theory in mathematics?

## Short Essay Questions

**1.** Who was Carl Gauss? What discovery did he make regarding imaginary numbers?

**2.** What are differential equations? Who first developed differential equations?

**3.** 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?

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

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

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

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

**8.** 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”?

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

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

## Essay Topics

Write an essay for ONE of the following topics:

### Essay Topic 1

Discuss the biography, works, and mathematical developments of Mohammed ibn-Musa al-Khowarizmi. When was his work, Compendious Book on Calculation by Completion and Balancing completed? What did this work entail?

### Essay Topic 2

Describe and discuss the origins and history of mathematics within Islamic culture. When was the House of Wisdom built? Who first coined the term “algebra”? When was the term coined?

### Essay Topic 3

Describe and discuss the advancements made in mathematics, music, and philosophy by Pythagoras. What is the Pythagorean Theorem? When was it developed? What were the beliefs of the Pythagoreans?

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