Mathematics is a language. It is the language of our universe. Every shred of existing evidence points to a mathematical design of the known universe in which we exist. Be you a creationist or an evolutionist, your existence, and your survival are guided by mathematical principles and laws.
Since the time of Pythagoras (c. 550 B.C.), humans have created the magnificent language of mathematics in attempts to understand the world in which they existed. The language has been modified and changed over a period of two thousand years. Today, we know considerably more mathematics than did the Pythagoreans, Galileo, Newton, and even Einstein. But, we know the language needs further development. As modern as we think we are, one hundred years from now our descendants will see us from a historical standpoint as being relatively primitive. They will know considerably more mathematics than we know at the present time. You cannot expect to be very successful in a study of mathematics if you simply see it as a set of unchanging rules and laws. Mathematics is not a static discipline. It is forever changing, and forever being discovered.
As you begin this course, try to appreciate mathematics as a language. Like any language, it has basic definitions and rules. It is important to understand (not memorize) the basics. Obviously, if you don't learn the basics, the language becomes difficult to learn an appreciate. Try to get yourself to realize that mathematics is the language of our universe. If you develop a good attitude and appreciation for this magnificent academic discipline, learning can be both fun and rewarding.
You are studying a branch of mathematics called algebra. The word algebra comes from an Arabic word aljabr, which appeared in the title of a mathematics book Hisab aljabr w' almuqabaleh, written by alKhwarizmi around 825. Loosely translated, the book title means "the science of reunion and reduction." A loose translation of aljabr means "to balance." There are other translations, but I like this one because in modern algebra we solve equations by a balancing process. As a simple example, consider the equation
x + 3 = 15
If we think of this equation as being balanced around the = symbol (think of a seesaw), we preserve the balance if we subtract 3 from each side of the = symbol. If we do this, we solve the equation, obtaining
x = 12
OK, you already know some of the language of mathematics. Let's get ready to learn a lot more. Since math is a language, communication in problem solving is important. Below are four examples that stress communication. Note that the last two problems stress the order of operations. This is extremely important. Among many other things, your calculator follows the order of operations in performing computations. If you don't "communicate" properly with your calculator, you many not get the results you are supposed to get. The basic hierarchy of operations is as follows:
(1) Exponents
(2) Multiplication and division in order from left to right.
(3) Addition and subtraction in order from left to right.
You can use parentheses () to alter the order of operations, if necessary. For instance, 10/2 + 3 = 5 + 3 = 8, while 10/(2 + 3) = 10/5 = 2.
Problem: Evaluate 5(x2) + x^{2} when x = 6.
Solution (with communication):
If x = 6, then 5(x2) + x^{2} = 5(62) + 6^{2} = 5(4) + 36 = 20 + 36 = 56. 
Problem: Simplify the expression
3(24x)  2(x4).
Solution (with communication):
3(24x)  2(x4) = 6  12x 2x + 8 = 14  14x.

Problem: Evaluate 12  8x4  14/7.
Solution (with communication):
12  8x4  14/7 = 12  32  2 = 20  2 = 22. 
Problem: Evaluate 20/2^{2}  8/(1+3) + 5x3^{2}.
Solution (with communication):
20/2^{2}  8/(1+3) + 5x3^{2 }= 20/4  8/4 + 5x9 = 5  2 + 45 = 48. 