Finite Mathematics
Topic outline

Welcome to Finite Mathematics [CMAT 1313]!
Course Introduction
This Finite Mathematics [CMAT 1313] course adheres to the scope and sequence of a onesemester Finite Mathematics course. The course description provided is the from the statewide common course information.Course Description: Systems of linear equations, matrices, and matrix algebra; linear inequalities; linear programming; counting techniques: permutations and combinations; probability; basic concepts in financial mathematics (annuities
included); and an introduction to statisticsUpon successful completion of this course, the student will be able to:
 Demonstrate mastery of review topics from college algebra.
 Solve systems of linear equations and inequalities by graphing, algebraically, and with matrices.
 Solve linear programming problems.
 Use Venn Diagrams to solve problems with sets and the relationship between sets.
 Apply rules of symbolic logic to assess the validity of logical arguments.
 Use basic counting principles, including combinations and permutations, to solve problems.
 Recognize and solve simple interest, compound interest, and annuities.
 Organize and interpret data in scenarios involving descriptive or inferential statistics.
Adopting instructors can embed a welcome video or add additional text here.Structure of the CourseThe course includes 8 content Modules which covers each of the 8 chapters in the textbook (provided link). Each module includes a brief introduction text with module learning objectives, links to the corresponding Pressbook sections, additional resources (video lessons), homework assignments in MyOpenMath, a Quiz in MyOpenMath, and a Q&A discussion forum for that Module. There are additional modules for smaller Exams, a Midterm Exam, and/or Final Exam.
Navigating the Course
This course is set up in Modules covering various topics which may be accessed from the course navigation menu on the left or by scrolling below. Modules may be collapsed in the menu and in the body of the course to minimize scrolling. Many items are required and may be marked as completed automatically when the activity has been submitted (the broken check box), but others will be marked as done by the student (the solid check box).
Please move through the items below and continue through the Learner Support and Getting Started modules before moving on to Module 1. Be sure to check for announcements and due dates to stay on track.Adopting instructors can embed a navigation video or add additional text here.
This course and its contents are licensed under a Creative Commons Attribution 4.0 International License by LOUIS: The Louisiana Library Network, except where otherwise noted.Adopting instructors should edit the About Your Instructor and Office Hours Information pages in this Module. 
Adopting instructors should edit all pages in this Module  as per their own Institution's policies.

This module contains all the items you should review and complete before you begin Module 1. Before moving on, be sure to:
 Check the News and Announcements Forum
 Read the Course Syllabus
 Introduce yourself to the class
 Read the instructions for the Q & A Forum
Good luck in the course!
Use this forum to tell us a little about yourself and your interests. Some topic ideas:
 What is your field of study/research interest or concentration?
 What are you most interested in learning about in this class and why?
 Have you ever taken an online class before?
 Any other information you would like to share with your classmates, such as special interests or activities.
Post a picture! We look forward to meeting you.

Use this forum to ask your instructor any questions you have about the course. You may post at any time, and your instructor will respond here. Be as specific as possible.
Please keep in mind that others can see your posts, so do not post any personal information. If you have questions about your grade, please email your instructor directly. You can expect a response to posts and emails within [X] hours. [Recommendation is 24 hours MF, next business day on weekends.]
Subscription should be set to Auto.

Use this forum to tell us a little about yourself and your interests. Some topic ideas:
 What is your field of study/research interest or concentration?
 What are you most interested in learning about in this class and why?
 Have you ever taken an online class before?
 Any other information you would like to share with your classmates, such as special interests or activities.
Post a picture! We look forward to meeting you.

Use this forum to ask your instructor any questions you have about the course. You may post at any time, and your instructor will respond here. Be as specific as possible.
Please keep in mind that others can see your posts, so do not post any personal information. If you have questions about your grade, please email your instructor directly. You can expect a response to posts and emails within [X] hours. [Recommendation is 24 hours MF, next business day on weekends.]
Subscription should be set to Auto.
 Check the News and Announcements Forum

Imagine being a pilot, but not just any pilot—a drone pilot. Drones, or unmanned aerial vehicles, are devices that can be flown remotely. They contain sensors that can relay information to a command center where the pilot is located. Larger drones can also carry cargo. In the near future, several companies hope to use drones to deliver materials and piloting a drone will become an important career. Law enforcement and the military are using drones rather than send personnel into dangerous situations.
Building and piloting a drone requires the ability to program a set of actions, including taking off, turning, and landing. This, in turn, requires the use of linear equations. In this chapter, you will explore linear equations, develop a strategy for solving them, and relate them to realworld situations.
Image Caption: This drone is flying high in the sky while its pilot remains safely on the ground. (credit: “Unsplash” / Pixabay)
(Content & Image Source: Chapter 2 Introduction, Intermediate Algebra, Lynn Marecek and Andrea Mathis, OpenStax, CC BY 4.0 License)
Upon completion of this module, you will be able to:1.1 Use a General Strategy to Solve Linear Equations Solve linear equations using a general strategy
 Classify equations
 Solve equations with fraction or decimal coefficients
1.2 Solve a Formula for a Specific Variable
 Solve a formula for a specific variable
1.3 Graph Linear Equations in Two Variables Plot points in a rectangular coordinate system
 Graph a linear equation by plotting points
 Graph vertical and horizontal lines
 Find the x and yintercepts
 Graph a line using the intercepts
1.4 Slope of a Line Find the slope of a line
 Graph a line given a point and the slope
 Graph a line using its slope and intercept
 Choose the most convenient method to graph a line
 Graph and interpret applications of slope–intercept
 Use slopes to identify parallel and perpendicular lines
 Read the Module 1 Introduction (see above)
 Read Sections 1.1  1.4 of Chapter 1: Linear Equations in Finite Mathematics (links to each Section provided below)
 Watch the Videos provided in the Video Lessons pages for each Section (links provided below)
 Complete the MyOpenMath Homework Assignments for each Section (links provided below)  These are graded!
 Complete the MyOpenMath Quiz for Chapter 1 (link provided below)  This is graded!
 Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
 Post in the Chapter 1 Q&A Discussion Forum  link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.
Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.

A matrix is a 2 dimensional array of numbers arranged in rows and columns. Matrices provide a method of organizing, storing, and working with mathematical information. Matrices have an abundance of applications and use in the real world. Matrices provide a useful tool for working with models based on systems of linear equations. We’ll use matrices in this chapter to solve systems of linear equations with several variables.
Matrices are used in encryption and in economic modelling. They are also used in optimization problems such as maximizing profit or revenue, or minimizing cost. Matrices are used in business for scheduling, routing transportation and shipments, and managing inventory. Just about any application that collects and manages data can apply matrices. Use of matrices has grown as the availability of data in many areas of life and business has increased. They are important tools for organizing data and solving problems in all fields of science, from physics and chemistry, to biology and genetics, to meteorology, and economics.
Computer science analyzes diagrams of networks to understand how things are connected to each other, such as relationships between people on a social website, and relationships between results in line search and how people link from one website to another. The mathematics to work with network diagrams comprise the field of “graph theory”; it relies on matrices to organize the information in the graphs that diagram connections and associations in a network. For example, if you use Facebook or LinkedIn, or other social media sites, these sites use network graphs and matrices to organize your relationships with other users.
Image Caption: In computer science, matrix mathematics lies behind animation of images in movies and video games. (Image Source: "Monitor, Binary, Binary system image.", Pixabay, Creative Commons Zero (CC0) license)
(Content Source: 2.1: Introduction to Matrices, Applied Finite Mathematics, Sekhon and Bllom, LibreTexts, CC BY License)
Upon completion of this module, you will be able to:2.1 Systems of Equations Solve linear systems using graphing
 Solve linear systems using substitution
 Solve linear systems using elimination (addition)
 Classify systems as independent, inconsistent, or dependent
 Solve linear systems in 3 variables
2.2 Solving Systems Using Matrices Write a system of equations as an augmented matrix.
 Use a matrix and rowreduction (Gaussian elimination) to solve a system of equations.
 Interpret the solutions from an augmented matrix.
 Recognize dependent and inconsistent systems of equations.
2.3 Matrix Operations Identify the dimensions of a matrix
 Identify the entries of a matrix
 Add and subtract matrices
 Calculate a scaler multiple of a matrix
 Multiply matrices
2.4 Solving Systems with Inverses Find the inverse of 2x2 and 3x3 matrices
 Use the formula for 2x2 matrices
 Use augmenting for 2x2 and 3x3 matrices
 Use the inverse to solve a system of equations
To achieve these objectives: Read the Module 2 Introduction (see above)
 Read Sections 2.1  2.4 of Chapter 2: Matrices in Finite Mathematics (links to each Section provided below)
 Watch the Videos provided in the Video Lessons pages for each Section (links provided below)
 Complete the MyOpenMath Homework Assignments for each Section (links provided below)  These are graded!
 Complete the MyOpenMath Quiz for Chapter 2 (link provided below)  This is graded!
 Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
 Post in the Chapter 2 Q&A Discussion Forum  link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.

In this module you will take your Exam 1 .
Read the Exam 1 Information and Instructions page carefully and take note of any special submission guidelines.
Upon completion of this module, you will have: Read and viewed the Exam 1 Information and Instructions page
 Scheduled your exam with the proctoring service [if applicable, delete if not needed]
 Post in the Exam 1 Q&A Discussion Forum  link provided below.
 Prepared for and submitted your Exam 1 [revise as needed]
 Uploaded your work in the Exam 1 Work Upload Assignment using the submission link below.
Attribution of image: ("Math, Numbers, Number image. Free for use." Pixabay.com. https://pixabay.com/photos/mathnumbersnumbercounting5247958/)Adopting instructors: Edit the Exam 1 Information and Instructions page.

A company produces a basic and premium version of its product. The basic version requires 20 minutes of assembly and 15 minutes of painting. The premium version requires 30 minutes of assembly and 30 minutes of painting. If the company has staffing for 3,900 minutes of assembly and 3,300 minutes of painting each week. How many items can then produce within the limits of their staffing?
Notice this problem is different than the question we asked in the first section, since we are no longer concerned about fully utilizing staffing, we are only interested in what is possible. Just as we created equations in the first section, we can now create inequalities, since we know the hours used in production needs to be less than or equal to the hours available. This leads to two inequalities that we can graph to find the solution. In the solution set we can see the solution to the system of equations. The solution set shows that if the company is willing to not fully utilize the staffing, there are many other possible combinations of products they could produce.
The techniques we will use in this chapter are key to a branch of mathematics called linear programming, which is used extensively in business.
Image Caption: A photo of a 3d printing technology. (Image Source: "Printer, 3d, Technology image.", Pixabay, Creative Commons Zero (CC0) license)
(Content Source: Systems of Equations and Linear Programming, BUSI1915 – Fundamentals of Business Mathematics, OER Lab, CC BYNCSA 4.0 License)
Upon completion of this module, you will be able to:
3.1 Inequalities in One Variable Solve linear inequalities
 Solve compound inequalities
3.2 Graph Linear Inequalities in Two Variables Verify solutions to an inequality in two variables.
 Recognize the relation between the solutions of an inequality and its graph.
 Graph linear inequalities in two variables
 Solve applications using linear inequalities in two variables
3.3 Linear Programming Write an objective function.
 Determine a feasible region for a system of linear inequalities.
 Solve linear programming problems graphically.
To achieve these objectives: Read the Module 3 Introduction (see above)
 Read Sections 3.1  3.3 of Chapter 3: Linear Programming in Finite Mathematics (links to each Section provided below)
 Watch the Videos provided in the Video Lessons pages for each Section (links provided below)
 Complete the MyOpenMath Homework Assignments for each Section (links provided below)  These are graded!
 Complete the MyOpenMath Quiz for Chapter 3 (link provided below)  This is graded!
 Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
 Post in the Chapter 3 Q&A Discussion Forum  link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.

The topic of money management is a broad and sometimes complex one. Ultimately, personal money management involves managing both our debt and also our savings and investments.
In 2021, the average American had consumer debt balance of $96,371. Nearly $100,000 per person. And less than 25% of Americans are debt free. Consumer debt can include mortgages, credit cards, as well as student loans. A key question all consumers should consider is how to manage debt and not become overburdened by it. The first step is to create a budget, which puts earnings into perspective, indicating what we can, and cannot, afford. A budget also entails setting aside certain funds for savings and investment, which help us achieve our short and longterm goals.
Creating a budget requires an understanding of how money—debt and savings—works. Initially, percentages and interest need to be understood. They drive most of what happens with debt and savings. With that understanding, discussions of buying a house, a car, or incurring credit card debt can be addressed from a financial perspective. All the while, retirement is waiting. Preparing for retirement involves saving and saving earlier rather than later. The power of compound interest is on full display when saving early.
This chapter covers some of the basics of money management: percentages, interest, savings, investments, annuities, and loans.
Image Caption: Financial health helps you realize your goals. (credit: modification of work "Budget and Bills" by Alabama Extension/Flickr, Public Domain)
(Content & Source: Chapter 6 Introduction, Contemporary Mathematics, Donna Kirk, OpenStax, CC BY 4.0 License)
Upon completion of this module, you will be able to:4.1 Simple and Compound Interest Calculate simple interest
 Calculate annual percentage rate
 Calculate compound interest
 Calculate annual percentage yield
4.2 Annuities Find the future value of an annuity
 Find deposits needed to fund an annuity
 Find the interest earned
4.3 Payout Annuities Find the present value of an annuity (principal required)
 Find the payments that can be made from a payout annuity
4.4 Loans Find the amount of a loan given the payments
 Find the payments required given the loan amount
 Find the remaining balance of a loan
4.5 Multistage Finance Problems Recognize the type of finance problem given a situation
 Breaking complex finance problems into smaller, simpler pieces
To achieve these objectives: Read the Module 4 Introduction (see above)
 Read Sections 4.1  4.5 of Chapter 4: Finance in Finite Mathematics (links to each Section provided below)
 Watch the Videos provided in the Video Lessons pages for each Section (links provided below)
 Complete the MyOpenMath Homework Assignments for each Section (links provided below)  These are graded!
 Complete the MyOpenMath Quiz for Chapter 4 (link provided below)  This is graded!
 Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
 Post in the Chapter 4 Q&A Discussion Forum  link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.