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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. The author states in Chapter 6, “Infinity’s Twin” that Carl Gauss realized that real and imaginary numbers could be what?
2. During what years did Georg Cantor live?
3. According to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians,” Jean le Rond d'Alembert had satisfied the mathematician's need for what?
4. The operation of finding the area under a curve is now called what, according to the author in Chapter 5, “Infinite Zeros and Infidel Mathematicians”?
5. The author asserts in Chapter 8, “Zero Hour at Ground Zero” that today astronomers estimate the universe as being how old?
Short Essay Questions
1. How did the field of quantum mechanics address the problem of zero in thermodynamics?
2. Who was Carl Gauss? What discovery did he make regarding imaginary numbers?
3. What discovery did Georg Cantor make regarding different types of infinities? How are these types defined?
4. How old is the universe estimated to be by astronomers today? How did they calculate this age?
5. 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?
6. What problem does zero present when calculating tangent lines? What is a tangent?
7. How many dimensions are required for string theory to work? How are these dimensions described in Chapter 8, “Zero Hour at Ground Zero”?
8. How did Max Planck address the problem of the ultraviolet catastrophe?
9. What are differential equations? Who first developed differential equations?
10. What problem do black holes present in physics, according to the author in Chapter 8, “Zero Hour at Ground Zero”?
Essay Topics
Write an essay for ONE of the following topics:
Essay Topic 1
Discuss the origins, history, and evolution of mathematics in ancient Egypt. How was geometry developed in Egypt? How did the Egyptians use mathematics in the creation of the pyramids? How did the Nile relate to their use of mathematics?
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
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?
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