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Mary Jane Sterling
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Published:
May 15, 2018

Finite Math For Dummies

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Overview

Use mathematical analysis in the real world

Finite math takes everything you've learned in your previous math courses and brings them together into one course with a focus on organizing and analyzing information, creating mathematical models for approaching business decisions, using statistics principles to understand future states, and applying logic to data organization.

Finite Math For Dummies tracks to a typical college-level course designed for business, computer

science, accounting, and other non-math majors, and is the perfect supplement to help you score high!

  • Organize and analyze information
  • Apply calculation principles to real-world problems
  • Use models for business calculations
  • Supplement your coursework with step-by-step example problems

If you’re not a math person or just want to brush up on your skills to get a better grade, Finite Math For Dummies is your ticket to scoring higher!

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About The Author

Mary Jane Sterling is the author of Algebra I For Dummies, Algebra Workbook For Dummies, and many other For Dummies books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.

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CHEAT SHEET

When performing the many types of computations found in Finite Math topics, it’s helpful to have some numbers, notations, distributions, and listings right at hand.Pascal's triangleWhen performing computations in problems involving probability and statistics, it’s often helpful to have the binomial coefficients found in Pascal’s triangle.
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Articles from
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In a typical finite math course, you will have many opportunities to study games that involve chance—where you can’t control the play results, but you can be informed about the possibilities.The following three examples use Bunco, a lottery, and a poker hand to explore these opportunities and their probabilities.
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A common situation when doing probability problems is having to determine the patterns of heads-and-tails, boys-and-girls, true-or-false arrangements. When there are two choices, there are 2n ways that they can occur. The following refer to Heads-or-Tails in a coin-flipping situation but can be adapted to any binomial arrangement.
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In a finite mathematics course, you may be asked to solve algebra problems using different forms of the same linear equation—for example, slope-intercept versus standard.You can change from one form of a linear equation to another by using basic algebra. The choice of the form of the line—whether slope-intercept or standard—just depends on the particular process being performed.
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When studying logic in your finite mathematics course, you will probably work with truth tables. A truth table is a visual representation of all the possible combinations of truth values for a given compound statement.Two types of connectives that you often see in a compound statement are conjunctions and disjunctions, represented by ∧ and ∨, respectively.
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Matrices are very handy to have around when you’re solving certain finite math problems. Matrices are simple structures that you can use to change the format of mathematical statements to make them more usable and understandable.Two matrices are equal to one another if they are exactly the same size and have exactly the same elements in exactly the same places.
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Calculation & Analysis

Factorial
Factorial
The factorial operation says to multiply the designated number by every positive integer smaller than that number.n! = n (n – 1) (n – 2) 3 2 1When using the operation in the formulas for the number of permutations or combinations of n things taken k at a time, factorial values need to be inserted into the numerator and denominator of the fraction.
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When performing the many types of computations found in Finite Math topics, it’s helpful to have some numbers, notations, distributions, and listings right at hand.Pascal's triangleWhen performing computations in problems involving probability and statistics, it’s often helpful to have the binomial coefficients found in Pascal’s triangle.
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Finite math applies many basic mathematical processes to real-world problems. For example, have you ever been called a “chicken” for not being willing to jump off the diving board or stick your finger in the hot cocoa? You probably didn’t realize that this is a classic in game theory and has been immortalized in the movie Rebel without a Cause.
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The classic prisoner’s dilemma is a popular problem in game theory, and so you may encounter it in a finite math course. The prisoner’s dilemma has many other applications, but it is probably best described with the following situation.Two gang members are arrested and put into two separate rooms for questioning.
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On a finite math exam, you may be asked to analyze an argument with a visual approach using an Euler diagram. This pictorial technique is used to check to see whether an argument is valid. An argument can be classified as either valid or invalid. A valid argument occurs in situations where if the premises are true, then the conclusion must also be true.
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If your finite math instructor asks you to analyze a compound statement, you can try using a truth table to do this. Not every topic in a discussion can be turned into a compound statement and analyzed for its truth that way, but using logic and truth values is a good technique to use when possible.Consider the compound statementWhen constructing a truth table, you start with the basic p and q columns.
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Finite math starts with the basic mathematical processes and draws in all the applications that make the processes usable in the real world. A valuable tool that you’ll learn about in your finite math course is matrices, which help you to organize your data.A classic problem that can be handled with matrices involves temperature distribution—how the different temperatures at points on a surface are affected by the temperatures closest to them.
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A big part of finite math involves working through financial problems. Some of these problems may seem complex—like calculating the monthly deposits required to maintain a sinking fund. Fortunately, there’s a special formula you can use to find the answer.A sinking fund is usually used to accumulate money to fund a future expense or a way to retire a debt.
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In a finite math course, you will encounter a range of financial problems, such as how to calculate an annuity. An annuity consists of regular payments into an account that earns interest.You can use a formula to figure out how much you need to contribute to it, for how long, and, most importantly, how much will be in your account when you want to start using the money.
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In a finite math course, you’ll often be asked to use mathematical formulas to solve real-world problems. A good example of this is calculating the starting value of an annuity.Say that you’re planning an around-the-world-trip, and your big concern is how to fund this adventure. One way is to have a fund from which you can withdraw a certain amount of money at regular intervals and have just enough money when you’re finished, where the fund goes down to zero.
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When you encounter a matrix problem in finite math, a nice way to illustrate the transition from one state to another is to use a transition diagram. The different states are represented by circles, and the probability of going from one state to another is shown by using curves with arrows.The transition diagram in the following figure shows how an insurance company classifies its drivers: no accidents, one accident, or two or more accidents.
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In a finite mathematics course, you may be asked to solve a financial problem using a linear equation. The basic business model is Profit = Revenue – Cost. If revenue is equal to cost, then the profit is 0. That’s called the break-even point.Consider the We Are Jeans store. It costs the business $29 to make a pair of jeans.
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Graphing linear functions and inequalities has a place in finite mathematics. A system of inequalities contains lots of points—each of them satisfying the statement of one or more inequalities.You can test different points to see which system is satisfied, often one at a time. Or you can look at a graph that gives you the overall view of the solutions.
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If you take a course in finite math, you’ll learn how to apply basic mathematical processes to financial problems. For example, if you want to maximize your results with a limited budget, you can use linear programming to get the most bang for your buck.For example, say that you have a new 60-gallon aquarium and want to stock it with tetras and marbled headstanders.
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You will definitely encounter probability or chance problems in a finite math course. One way you can solve these problems is to organize the data visually in probability trees.For example, say that you’re doing a market survey concerning pizza establishments and the preferences of consumers. You went to Dominick’s Den, Pizza House, and Mama Joe’s interviewing an equal number of people at each establishment.
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If your finite math instructor asks you to predict the likelihood of an action repeating over time, you may need to use a transition matrix to do this. A transition matrix consists of a square matrix that gives the probabilities of different states going from one to another.With a transition matrix, you can perform matrix multiplication and determine trends, if there are any, and make predications.
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A matrix is a useful structure that you can use in a variety of finite math problems to change the format of mathematical statements to make them more usable and understandable.A matrix is nothing more (or nothing less) than a rectangular arrangement of numbers or letters or other items. You can use matrices to organize data by month, person, age group, company, and so on.
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As with many areas and topics in finite mathematics, there is a very special and specific vocabulary that goes along with game theory. Here are some important and useful terms that you should know. Payoff matrix: A matrix whose elements represent all the amounts won or lost by the row player. Payoff: An amount showing as an element in the payoff matrix, which indicates the amount gained or lost by the row player.
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Calculation & Analysis

Matrix Notation
Matrix Notation
Matrices are rectangular arrangements of elements. The dimension of a matrix is given with m × n where m is the number of rows and n is the number of columns. The elements are identified with subscripts giving the row, j, and column, k, shown as ajk for the elements of a matrix A.When multiplying the matrices, the number of rows in the first matrix has to equal the number of columns in the second.
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When performing computations in problems involving probability and statistics, it’s often helpful to have the binomial coefficients found in Pascal’s triangle. These numbers are the results of finding combinations of n things taken k at a time. For quick reference, the first ten rows of the triangle are shown.
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If your finite math instructor asks you to solve a linear inequality, you can use most of the same rules that you’d use when solving linear equations. There are two huge exceptions, however, which you’ll learn about here.The following list shows all the rules you need to know when performing operations on inequalities.
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Finite math teaches you how to use basic mathematic processes to solve problems in business and finance. For example, you can use linear programming to stay within a budget.When you’re dealing with money, you want a maximum value if you’re receiving cash. But if you’re on a tight budget and have to watch those pennies, then you’re concerned with minimizing your expenses.
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If your finite math instructor asks you to solve a system of linear equations, one approach is to use elimination. For example, if you’re asked to solve a system of three linear equations in three unknowns, elimination is the best way to do this.To solve the problem, you have to pick which variable to eliminate first.
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In a finite mathematics course, you can expect to run into a lot of problems that involve systems of linear equations. When you’re working with a system of three or more linear equations, you’ll find that using substitution to solve the system involves one variable in terms of another in terms of another, and so on.
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Most of the applications in finite math that involve mathematical statements are of the linear variety. You can use an augmented matrix to solve a system of linear equations in two variables. For example, say you start with these two equations:To solve this system, you would follow these steps: Write each equation in the same format, with variables in the same order in each, and all set equal to the constant.
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