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Many students have had experiences with mathematics that left them unhappy about the subject. However, most students do not realize that mathematics is really a straight forward subject that can easily be learned if it is logically presented to a student. Students often encounter difficulties when they study mathematics because usually they are not presented with sufficient overview, or background material to help them understand the math. Another reason that students often have trouble when they study mathematics is that they are not shown what they can do with the math after they learn it. The purpose of this overview is to provide to students a means for overcoming these difficulties. The theme behind this is that of presenting the central reasons why mathematics is studied, why it was originally developed and how it satisfies man's needs. Before we go into the details of mathematics, let us look at some of the reasons why people want to learn about something in the first place.

- Learning is important because it can provide a framework of knowledge from which a person can extract inferences, or conclusions from given data, to gain understand of an occurrence or difficult problem. People know from their experiences that gaining knowledge helps them to solve problems. Learning helps a person know about things and, therefore, helps the person to understand what to do to make things right when they have gone wrong.

Mathematical symbols can

Mathematics can be used to predict the outcome of events and phenomena. For this reason mathematics can be called

For example, a customer can find out how many items she can afford to buy at the grocery store by adding the prices of the items needed before she goes to the store. Then, when she actually gets to the store she can have confidence that the items she picks out will not exceed the cost for them at the check-out counter. If the customer's math is correct, the customer is not going to be embarrassed at the check-out counter because the items' total to more than the customer has money for.

In like manner, when people at NASA decided to send some astronauts to the moon, they performed all the math calculations that allowed them to infer, or conclude from the facts and premises, what would happen during the moon voyage. Then, when the systems were built and sent off into space, the space ship systems performed exactly as the math predicted.

As a third example, by doing some simple calculations a carpenter can conclude and, thereby, predict how many 2 by 4' studs he will need to construct a frame for a house. If his calculations are right, he knows how many studs to order from his distributor and how much they will cost him before he starts construction of the house.

As a final example, a floor covering installer, by measuring the area, i.e., the length and width of a floor, can accurately determine how many floor tiles are required to cover the floor. Thus, from his conclusion, he knows how many to purchase when he goes to his distributor for materials.

If, indeed, mathematics is a science of prediction, then, upon becoming aware of this, most people would want to learn mathematics so that they could use it to help them predict what is going to occur before it happens! This is surely be an important resource for people to possess. When people are surrounded in a world environment in which they don't have the power to see around a corner, or instinctively know what sizes of beams are needed to hold up a building that they want to construct, it is little wonder that they become interested in mathematics - a field of study that helps them to uncover solutions to problems they otherwise could not solve.

If math is really a subject that can be used to predict the outcome of an event before it occurs - then, upon realizing this, most students would have a strong interest in math. Most people want to be able to have more control over their lives and their environment. This is probably the main reason people take the time to learn anything. This is the reason why the old masters who discovered math took such an intense interest in the subject. It helped them to better understand their world so that they could better handle the problems they encounter! Thus, a conscientious person will want to learn mathematics so as to become more practical in his/her affairs, and have more control over his/her environment.

With the above understood, let us delve a bit deeper into what mathematics can do for us. Whether we thought about it or not everything around us has been there when we were just born. Light, sound, matter, electricity, velocity, acceleration, impact, momentum and distance have existed since the beginning of time. We didn't understand what heat was so Pierre Laplace (1749-1827) analyzed what it was and wrote his famous Laplace's equation which effectively tells how a heat field pattern will distribute itself in, say, a frying pan or an oven. Remember, it can be important to know this because sometimes, because of variations in conductivity, a hot frying pan can have high temperatures on some areas of its surface and lower temperatures on other areas of the same surface. So, if a person is trying to cook something on a hot frying pan some parts of the food may burn and other parts of the same food may not brown up properly. These temperature variations also can hold for an oven. Some sections of an oven can be considerably hotter than other sections of the same oven. These are circumstances that we should be aware of. Why? Well, try to serve burned food to a customer in a restaurant - or to your mate. The point here is that the properties of heat were in existence since time immemorial. Laplace's equation was developed to help us understand how the heat patterns look when heat travels through something hot like a frying pan or an oven. Later people using Laplace's equation brought out an important insight when they showed that the electric field patterns from electric charges resembles the heat field patterns when positive and negative electric charges are replaced by corresponding hot and cold bodies.

Light and radio waves were here millions of years ago. When James Clerk Maxwell discovered the curl and divergence relationships between magnetic and electric fields and expressed them in his very famous Maxwell's equations, he developed the mathematical foundation that made radio, TV and communications possible. Electromagnetic waves were here for millions of years. So, Maxwell's equations were developed to help

By now the reader should be getting the idea that a background in mathematics can help a person to better understand the world he/she is living in. The next question that arises is "Who cares?" Well, there are some people who are intrigued over the things and phenomena in the world and how they work. Some people are intrigued by the fact that they can study the heat field patterns in a frying pan or an oven and use that knowledge to prepare first-class fried foods and cakes. Some people are intrigued by the fact that they can study how an electronic amplifier can be altered to become an oscillator which, in turn, can be connected to an antenna, that will send a replica of a voice across the ocean to Portugal. There are people who want to use their lives to achieve results for the benefit of others. There are people who want to live the rich life, a life filled with intrigue, a life in which a person has confidence in his/her abilities, and the power to control the factors in one's environment, as opposed to the poor life, wherein one is content doing nothing. This overview was written for students who wish to take positive steps to find out about things so they might better understand the factors that they will have to contend with in their personal and working lives.

One essential point is clear: a large part of intermediate and advanced college mathematics had its origin from people trying to understand and interpret mechanical vibrations and their corresponding wave motions. This means that a quick way to learn mathematics is to learn the principles of wave motion. Once the concepts of wave motion are understood, the mathematics that describes the wave motion obvious. Readers should be aware of this fact: Those students who studied math by rote, i.e., by memorizing formulas and methods, i.e., without attention to meaning, have been at a great disadvantage when it came time to apply the mathematics they learned. On the other hand, those students who were presented a cogent theory of math with attention to the meaning of the principles from which the mathematics was originally derived, namely the study of wave motion, had a superb advantage when it came to understanding and applying college level mathematics. When students had something to which they could relate the mathematics, they were in a superior position to use the math to solve practical problems.

The following section, entitled "Introduction to Applied Mathematics", is intended to provide students with a sound understanding of the first basic and main subject behind the principles of practical or applied mathematics The theory of waves is the main subject that is behind a large amount of mathematics presented in college. From a study of this subject students can more easily understand the underlying concepts and relationship of mathematics to the real world problems. Mathematic is the science of prediction and a tool to help us.

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