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Über dieses Buch

This text aims to show that mathematics is useful to virtually everyone. And it seeks to accomplish this by offering the reader plenty of practice in elementary mathematical computations motivated by real-world problems. The prerequisite for this book is a little algebra and geometry-nothing more than entrance requirements at most colleges. I hope that users-especially those who "don't like math"-will complete the course with greater confidence in their ability to solve practical problems (without seeking help from someone who is "good at math"). Here is a sampler of some of the problems to be encountered: I. If a U. S. dollar were worth 1. 15 Canadian dollars, what would a Canadian dollar be worth in U. S. money? 2. If the tax rates are reduced 5% one year and then 10% in each of the next 2 years (as they were between 1981 and 1984), what is the overall reduction for the 3 years? 3. An automobile cooling system contains 10 liters ofa mixture of water and antifreeze which is 25% antifreeze. How much of this should be drained out and replaced with pure antifreeze so that the resulting 10 liters will be 40% antifreeze? 4. If you drive halfway at 30 mph and the rest of the distance at 50 mph, what is your average speed for the entire trip? 5. A tank storing solar heated water stands unmolested in a room having an approximately constant temperature of 80°F.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Arithmetic Review

Abstract
Hardly any “practical” mathematics can be done at an elementary level unless one is comfortable with arithmetic.
R. D. Driver

Chapter 2. Prime Numbers and Fractions

Abstract
Given a large integer, how can one determine whether or not it is divisible by the prime numbers 2, or 3, or 5, or other numbers?
R. D. Driver

Chapter 3. The Pythagorean Theorem and Square Roots

Abstract
By about 2000 b.c. the Egyptians knew (or believed) that if a right triangle had legs of lengths 3 and 4 units, then the hypotenuse—the side opposite the right angle—had a length of 5 units.
R. D. Driver

Chapter 4. Elementary Equations

Abstract
Many day-to-day problems can be solved most easily with the aid of a little elementary algebra. Examples in this chapter will treat currency exchanges, speed and distance problems, mixtures, levers, and conversions between Celsius and Fahrenheit.
R. D. Driver

Chapter 5. Quadratic Polynomials and Equations

Abstract
The equation 2x + 4 = 7 is called a “linear” equation. This type of problem arose repeatedly in Chapter 4.
R. D. Driver

Chapter 6. Powers and Geometric Sequences

Abstract
What do pyramid clubs, hot cups of coffee, gambling outcomes, and inflation rates have in common? Consider the following specific problems.
(a)
If each recipient of a certain chain letter dutifully delivers copies of the same letter to just five other persons in 1 week, how many people will be involved in the first 8 weeks?
 
(b)
A cup of coffee in a room where the temperature is 70°F cools from 190°F to 130°F in 6 minutes. How much longer will it take to cool down to 85°F?
 
(c)
Assume you have $100 for gambling at the roulette wheel, and at each spin of the wheel you bet half the money you then have on red, which is an “even-money” bet. Thus you win or lose the amount of your bet. If you win 10 times and lose 10 times will you end up ahead or behind or even?
 
(d)
If the Consumer Price Index rises 1% per month for 12 months, what is its rise for the entire year?
 
R. D. Driver

Chapter 7. Areas and Volumes

Abstract
Try to answer the following questions:
(a)
If a 10-inch pizza costs $3.00, what should a 15-inch pizza cost?
 
(b)
If a flower pot 1 foot deep and 1 foot in diameter holds 5 gallons, what would be the capacity of a similar pot 2 feet deep and 2 feet in diameter?
 
(c)
How much more water will flow through a 5/8-inch garden hose than through a 1/2-inch hose (assuming the same pressure and length)?
 
(d)
How many dimes can be placed flat on the face of a half-dollar with none overlapping each other or extending off the edge of the half-dollar?
 
R. D. Driver

Chapter 8. Galilean Relativity

Abstract
This chapter considers a variety of problems involving relationships between moving objects—a plane flying in moving air, a horn sounding on a moving train or car, a police radar speed trap, and the basics of sailing.
R. D. Driver

Chapter 9. Special Relativity

Abstract
The theory of relativity, due primarily to H. A. Lorentz in the 1890s and Albert Einstein in the early 1900s, revolutionized scientific thinking. This chapter gives a brief introduction to the ideas of “special relativity”—the subject of a 1905 paper by Einstein. The special theory of relativity considers the viewpoints of different observers moving with constant velocities, as in the previous chapter. But the key postulate and the conclusions will now be quite different and, for most people, surprising.
R. D. Driver

Chapter 10. Binary Arithmetic

Abstract
Thousands of years before recorded history, herdskeepers kept track of their cattle or sheep by means of notches on a “tally stick.” More efficient notations for the concepts “one,” “two,” “three,” were developed by the ancient Egyptians, Romans, Chinese, and others. And these eventually evolved into the familiar decimal notation.
R. D. Driver

Chapter 11. Sets and Counting

Abstract
This brief chapter provides the prerequisites for Chapter 12 on probability and Chapter 13 on cardinality. For these topics one needs some acquaintance with the mathematical notation for sets.
R. D. Driver

Chapter 12. Probability

Abstract
Almost everyone uses the language and ideas of probability:
  • “There is a 20% chance of rain tomorrow.”
  • “The probability that the baby will be a boy is slightly more than half.”
  • “What is the probability of passing this course?”
R. D. Driver

Chapter 13. Cardinality

Abstract
This chapter is not easily “justified” in terms of day-to-day applications. It will not help you deal with compound interest, lay out the foundation for a house, decide which pizza is the better buy, appraise the risks of smoking, or judge the feasibility of civil defense plans.
R. D. Driver

Backmatter

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