# Mathematics in Non-Math Courses

In introductory courses such as chemistry, economics, political science, and psychology, you will often see discussions of examples and topics that require an understanding of concepts in mathematics such as algebra. The examples below are taken directly from different economics textbooks and they demonstrate the kinds of skills that you will be required to use in many non-math introductory courses.

### Example

 Production costs are divided into fixed costs and variable costs. All production costs fall within these two categories, so total costs (TC) equal total fixed costs (TFC) plus total variable costs (TVC), or TC = TFC + TVC From: Byrns, R. T. & Stone, G. W. (1995) Microeconomics (p. 171). New York: Harper Collins College Publishers

The example above demonstrates the use of basic algebra skills in economics. Without the ability to substitute values for the variables, or the ability to evaluate this equation, there would be no meaning to this paragraph or equation.

Below is a more complex linear equation that relates the yield of lumber to maintenance of land.

### Example

 For this forestry example, b = 10,000, m = 1,000, and the equation is: y = 1,000x + 10,000 where: y    =    annual yield of lumber in board feet x    =    hours of annual maintenance per acre, and 10,000    =    the intercept [the value of y (board feet annually) when x (maintenance) is zero]. To find the harvest rate for each maintenance level, just multiply each possible value of x by 1,000 and add 10,000. From: Byrns, R. T. & Stone, G. W. (1995) Microeconomics (p. 171). New York: Harper Collins College Publishers

This algebra review will provide you with the skills necessary to evaluate the two examples on the previous page, and to solve each equation for any variable.

The skills you will learn in this book are to:

• Define algebra.
• Recognize when an algebraic statement is an algebraic term, expression, or equation.
• Use exponential notation.
• Apply addition, subtraction, multiplication, and division in algebraic terms.
• Apply addition, subtraction, multiplication, and division to algebraic expressions.
• Apply the rules of grouping symbols to algebraic expressions.
• Apply the order of operations to algebraic expressions.
• Evaluate algebraic expressions.
• Solve equations by isolating variables through the use of addition, subtraction, multiplication, and division.
• Check that solutions are correct by the use of substitution.
• Isolate one variable in a multivariate equation.
• Substitute a constant, term, or expression for a variable.
• Use substitution techniques to solve systems of equations.
• Use the addition/subtraction techniques to solve systems of equations.

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