# Mathematics for Business and Social Sciences

Written by: Kathryn Bollinger (Texas A&M University) and Vanessa Coffelt (Texas A&M University)

Mathematics for Business and Social Sciences was published in August of 2020. The textook, written by Kathryn Bollinger and Venessa Coffelt is currently being used at Texas A&M University.

From the course and textbook description: “Topics covered include application of common algebraic functions, including polynomial, exponential, logarithmic and rational, to problems in business, economics and the social sciences; includes mathematics of finance, including simple and compound interest and annuities; systems of linear equations; matrices; linear programming; and probability, including expected value.”

Students should have completed high school algebra I and II along with geometry. Additionally, each chapter in the textbook begins with a list of topics students should have proficiency with. For example, chapter 1 suggests students be familiar with:

• Simplifying Fractions
• Decimals
• Properties of Real Numbers
• Using Variables and Algebraic Symbols Simplifying Expressions
• Translating an English Phrase to an Algebraic Expression or Equation Solving Linear Equations with One Variable
• Using Problem-Solving Strategies

The textbook includes an appendix that covers a number of these topics. We would also recommend that you check out our section of high school algebra textbooks and precalculus textbooks to find more in-depth coverage of these topics.

Mathematics for Business and Social Sciences contains the answers to ALL of the practice questions and exercises. It is a great resource for self-study or to supplement a different textbook.

#### 1 Matrices

1.1  Basic Matrix Operations

Multiplying a Matrix by a Scalar
Transposing a Matrix
Matrix Equality
ApplyingBasicMatrixOperations

#### 2 Linear Models and Systems of LinearEquations

2.1 Review of Lines

Plotting Ordered Pairs in the Cartesian Coordinate System
Graphing Linear Equations by Plotting Points
Graphing Linear Equations using Technology
Writing a Linear Equation
Finding x-intercepts and y-intercepts
Interpreting Slope

2.2  Modeling with Linear Functions

Defining a Linear Function
Modeling with Linear Functions

2.3  Systems of Two Equations in Two Unknowns

Identifying Solutions to Linear Equations
Solving Systems of Two Linear Equations in Two Unknowns
Relating Solutions of Systems to Business Applications

2.4  Setting Up and Solving Systems of Linear Equations

Setting up Systems of Linear Equations
Converting between Systems and Augmented Matrices
Solving Systems using Gauss-Jordan Elimination
Solving Systems using Gauss-Jordan Elimination with Technology.

Chapter Review

#### 3 LinearProgramming

3.1  Setting Up Linear Programming Problems

Linear Programming Problems

3.2  Graphing Systems of Linear Inequalities in Two Variables

Graphing Linear Inequalities
Graphing Systems of Linear Inequalities
Determining the Types of Solutions Sets and Corner Points

3.3  Graphical Solution of Linear Programming Problems

3.4  Simplex Method

Performing the Simplex Method on a Standard Maximization Problem
Comparing the Simplex Method and the Method of Corners
Applying the Simplex Method to Real-World Scenarios

Chapter Review

#### 4 BasicProbabilityandApplications

4.1  Mathematical Experiments

Defining a Sample Space and Events
Operating on Events

4.2  Basics of Probability

Defining Probability
Constructing Probability Distributions

4.3  Rules of Probability

Computing a Probability Using a Probability Distribution
Applying the Rules of Probability

4.4  Probability Distributions and Expected Value

Defining a Random Variable
Computing Expected Value Chapter Review

#### 5 Functions

5.1  Relations and Functions

Writing Interval Notation
Differentiating Between a Relation and a Function
Using Function Notation

5.2  Polynomial Functions

DescribingPolynomialFunctions

5.3  Rational Functions

Describing Rational Functions
Combining and Simplifying Rational Expressions
Computing the Difference Quotient

Defining Power Functions
Computing Domains of Algebraic Functions
Rationalizing Numerators and Denominators

5.5  Piecewise-Defined Functions

Describing Piecewise-Defined Functions
Domain of a Piecewise-Defined Function
Graphs of Piecewise-Defined Functions
Real-World Applications

5.6  Exponential Functions

Reviewing Laws of Exponents
Describing Exponential Functions
Computing Domain
Solving Equations Involving Exponential Expressions
Applying Exponential Functions to Real-World Applications

5.7  Combining and Transforming Functions

Transforming Parent Functions
Performing Function Arithmetic
Finding the Composition of Functions

5.8 Inverse Functions and Logarithms

Defining an Inverse Function
Defining Logarithmic Functions
Properties of Logarithmic Functions
Computing the Domain of a Logarithmic Function
Using Algebraic Properties of Logarithms
Applying Exponential and Logarithmic Functions

Chapter Review

#### 6 Mathematical Finance

6.1  Interest and Effective Rates

Working with Simple Interest
Working with Compound Interest
Comparing Interest Rates

6.2  Annuities, Sinking Funds, and Amortization

Understanding Annuities Involving Deposits
Understanding Annuities Involving Withdrawals
Understanding Loans
Understanding Amortization
Summarizing Finance Problems

Chapter Review

#### A Appendix

A.1  Number Sense

Introduction to Whole Numbers
Integers
Fractions
Simplifying Fractions
Decimals Integer Exponents and Scientific Notation
The Real Numbers .
Properties of Real Numbers
Systems of Time Measurement

A.2  Introduction to Algebra

Using Variables and Algebraic Symbols
Simplifying Expressions
Evaluating an Expression
Translating an English Phrase to an Algebraic Expression or Equation
Solving Linear Equations with One Variable
Using Problem-Solving Strategies
Graphing Inequalities on the Number Line and Interval Notation
Solving Inequalities using the Addition and Subtraction Properties of Inequality
Solving Inequalities using the Multiplication and Division Properties of Inequality

A.3  Introduction to Algebraic Expressions

Describing Polynomials
Evaluating a Polynomial for a Given Value
Simplifying Expressions with Exponents
Multiplying Polynomials
Observing Special Products
Simplifying Expressions Involving Quotients and Exponents
Dividing Monomials
Simplifying Rational Expressions
Evaluating Rational Expressions
Dividing a Polynomial by a Monomial
Simplifying Variable Expressions with Roots
Simplifying Expressions with Rational Exponents
Rationalizing a Two-Term Denominator

A.4  Factoring

Greatest Common Factor
Factor by Grouping
Factoring Differences of Squares

Solving Quadratic Equations Using the Zero Product Property
Completing the Square of a Binomial Expression
Solving Quadratic Equations of the Form x2 +bx+c = 0 by Completing the Square
Solving Quadratic Equations of the form ax2 + bx + c = 0 by Completing the Square
Identifying the Most Appropriate Method to Use to Solve a Quadratic Equation