Mathematical modeling involves finding and applying mathematical equations that model some finite aspect of the world. For example, real estate agents and appraisers with an understanding of finite math might estimate the value of a house by applying an equation containing the square footage of the house and the neighborhood's average price per square foot. Business owners with a background in finite math can predict whether they will make more money by charging a large monthly fee or a smaller monthly fee with add-on user fees.
Matrices are collections of numbers or symbols organized into columns and rows. The multiplication table, and tables that show distances between cities, are well-known examples. Matrices also can be used to represent robots and computer-generated images. The numbers in the matrix describe attributes, such as the color and location of each point on the surface of the robot or image. Once you have the matrix, you can manipulate the robot or image by applying finite math to the matrix.
Linear programming is a set of techniques for finding optimal points in a group of linear equations -- equations which can be graphed as straight lines. The techniques are used in engineering applications to find the conditions that maximize stability or minimize weight. Linear programming also is used in business applications that involve maximizing profits and minimizing costs. For example, a business owner could plot the cost of materials as one line, the cost of labor as another line, and the cost of the building and equipment as a third line. When the three lines are plotted on the same axes, the intersection of the lines would indicate where costs are minimized and profits are maximized.
Combinatorics is the art of counting the finite number of ways things can be combined. Typical problems are: If an item comes in 15 different colors, how many ways can two differently-colored items be packaged together? How many different ways can 24 students in a classroom line up for a fire drill? How many different five-letter words can be created from 26 English letters; how would that number change if a letter could not occur twice in a word; how would it change if a word must contain at least one vowel?
Probability is the science of assigning likelihoods to future events. If the likelihood of an event occurring is zero, the event definitely will not happen. If the likelihood of an event is one, then it definitely will happen. The higher the likelihood of an event, the more likely the event is to occur. Probability theory provides mathematical techniques for assigning likelihoods to events, and therefore provides one way to deal intelligently with future events. A typical probability application would be to compute the likelihood of surviving a tornado based on past experience. For example, say a community contained 1,000 people, and 900 of them survived the last tornado. If no modifications were made to the town and a second tornado having the same strength as the first hits the town, the likelihood of survival is 0.9.
Logic is usually a topic in a finite math class for computer science students. Computer programming languages deal with a finite number of options. For example, "if, then, else" structures offer two options: one that occurs when the if condition is satisfied, and one that occurs when it is not satisfied. Similarly, computer switching circuits and gates that rely on Boolean logic contain a finite number of inputs and outputs. It would be difficult to understand the rest of computer science without a solid foundation in the kind of logic covered in a finite math class.