Quantitative Literacy: Essential Mathematics for Everyday Life, School, and Work

Edition: 1

Copyright: 2022

Pages: 356

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$81.04 USD

ISBN 9781792491559

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This book develops quantitative literacy by teaching the mathematical concepts and reasoning needed to interpret information, solve problems, and make informed decisions. Topics include number systems, arithmetic, algebra, fractions, ratios, proportional reasoning, decimals, percentages, measurement, probability, statistics, data analysis, functions, linear regression, and correlation. The text concludes with applications to personal finance, including interest, saving, retirement planning, credit, and loans, emphasizing the practical use of mathematics in everyday life.

CHAPTER 1 Introduction and Preview
Why Quantitative Literacy Matters 
Reading and Interpreting Quantitative Information
Using Quantitative Concepts and Methods to Solve a Problem 
Using Quantitative Concepts and Methods to Support an Argument 
The Role of Mathematics in Quantitative Literacy 
Problems
CHAPTER 2 Types of Numbers
Whole Numbers 
Fractions
Negative Numbers 
Number Terminology
The Ordering of the Real Numbers
Problems
CHAPTER 3 Whole Number Arithmetic 
The Concept of Addition
The Concept of Subtraction
Counting Using the Inclusion-Exclusion Principle
The Concept of Multiplication
Counting the Number of Ways to Perform a Multi-Step Process
The Concept of Division
Remainders in Division
Problems
CHAPTER 4 More Arithmetic and Some Algebra
Variables and Variable Expressions
Equations 
Some Algebraic Properties of Addition and Multiplication 
Even and Odd Numbers Revisited 
Arithmetic and Algebra with Positive and Negative Numbers
Multiplicative Inverses and Division
Positive Integer Exponents
Combining Operations
Solving Equations
Solving an Equation Containing More than One Variable 
Problems
CHAPTER 5 Fractions, Ratios, and Proportional Reasoning 
Fractions Revisited
Multiplying Fractions
Equivalent Fractions
Reducing Fractions
Multiplying Fractions Revisited 
Dividing Fractions 
Adding and Subtracting Fractions 
Ratios
Proportions 
Proportional Reasoning
Problems
CHAPTER 6 Rational and Irrational Numbers
Square Roots and Cube Roots
Rational Numbers and Irrational Numbers
Triangles
Right Triangles and the Pythagorean Theorem
The Circumference and Area of a Circle 
Problems
CHAPTER 7 Place Value and Decimals
Base Ten Representation of Whole Numbers
Base Two (Binary) Representation of Whole Numbers
Zero and Negative Exponents
Decimal Fractions
Rounding Numbers
Representing Rational and Irrational Numbers in Decimal Form
Scientific Notation
Problems
CHAPTER 8 Working with Percentages
Percentages
Percentages and Rounding
Absolute and Relative Change 
Percentage Points vs. Percentages 
Absolute and Relative Difference
Index Numbers
Problems
CHAPTER 9 Measurement Units 
Converting Units of Measurement
The Metric System
Rates 
Converting Units of Area and Volume
Density and Concentration 
Measurements Expressed in Scientific Notation
Approximation, Measurement Error, and Error Propagation 
Problems
CHAPTER 10 Probability 
Experiments, Outcomes, and Sample Spaces 
Events of a Sample Space
The Complement of an Event
The Intersection of Events
The Union of Events 
Using Venn Diagrams to Depict Events within a Sample Space
Assigning Probabilities 
Equally Likely Outcomes
The Complement Rule
The General Addition Rule
Conditional Probability 
Problems
CHAPTER 11 Data and Statistics 
Data, Populations, and Samples
Issues in Sampling: Representativeness and Bias
Randomized Sampling 
Variables: Quantitative and Categorical
Organizing and Displaying Categorical Data
Grouping Quantitative Data
Histograms 
Using Desmos to Make a Histogram 
Misleading Graphical Displays
Dotplots
Outliers
Measures of Center for Quantitative Data 
Weighted Averages 
Measuring How Quantitative Data Values Are Spread Out
The Range
Measuring Spread Relative to the Mean: The Standard Deviation
Standardizing Data Values
Measures of Relative Location
Measuring Spread Relative to the Median: The Interquartile Range 
Identifying Outliers
Boxplots 
Problems
CHAPTER 12 Modeling Relationships between Quantitative Variables
Ordered Pairs and the Coordinate Plane
Methods for Representing Quantitative Relationships 
Linear Functions
Piecewise-Defined Functions
Average Rate of Change
Exponential Functions 
Problems
CHAPTER 13 Linear Regression and Correlation
Nondeterministic Relationships and Regression Analysis
Scatterplots 
The Line of Best Fit 
Extrapolation 
Linear Correlation 
Correlation vs. Causation 
Problems
CHAPTER 14 Personal Finance
Simple and Compound Interest
Saving Money: Bank Accounts and Certificates of Deposit 
Sums of Consecutive Powers
Saving for Retirement 
Withdrawing Money in Retirement 
Credit Cards
Installment Loans
Problems

Michael J. Cullinane

Mike Cullinane is a Professor of Mathematics at Keene State College. He earned his B.S., M.S., and Ph.D. in Mathematics from the University of New Hampshire and previously served on the faculty at North Carolina Wesleyan College. His professional interests include topology, mathematical analysis, mathematical proof, and undergraduate mathematics education. His work includes research publications, presentations at regional and national conferences, and experience teaching mathematics at both the undergraduate and graduate levels.

This book develops quantitative literacy by teaching the mathematical concepts and reasoning needed to interpret information, solve problems, and make informed decisions. Topics include number systems, arithmetic, algebra, fractions, ratios, proportional reasoning, decimals, percentages, measurement, probability, statistics, data analysis, functions, linear regression, and correlation. The text concludes with applications to personal finance, including interest, saving, retirement planning, credit, and loans, emphasizing the practical use of mathematics in everyday life.

CHAPTER 1 Introduction and Preview
Why Quantitative Literacy Matters 
Reading and Interpreting Quantitative Information
Using Quantitative Concepts and Methods to Solve a Problem 
Using Quantitative Concepts and Methods to Support an Argument 
The Role of Mathematics in Quantitative Literacy 
Problems
CHAPTER 2 Types of Numbers
Whole Numbers 
Fractions
Negative Numbers 
Number Terminology
The Ordering of the Real Numbers
Problems
CHAPTER 3 Whole Number Arithmetic 
The Concept of Addition
The Concept of Subtraction
Counting Using the Inclusion-Exclusion Principle
The Concept of Multiplication
Counting the Number of Ways to Perform a Multi-Step Process
The Concept of Division
Remainders in Division
Problems
CHAPTER 4 More Arithmetic and Some Algebra
Variables and Variable Expressions
Equations 
Some Algebraic Properties of Addition and Multiplication 
Even and Odd Numbers Revisited 
Arithmetic and Algebra with Positive and Negative Numbers
Multiplicative Inverses and Division
Positive Integer Exponents
Combining Operations
Solving Equations
Solving an Equation Containing More than One Variable 
Problems
CHAPTER 5 Fractions, Ratios, and Proportional Reasoning 
Fractions Revisited
Multiplying Fractions
Equivalent Fractions
Reducing Fractions
Multiplying Fractions Revisited 
Dividing Fractions 
Adding and Subtracting Fractions 
Ratios
Proportions 
Proportional Reasoning
Problems
CHAPTER 6 Rational and Irrational Numbers
Square Roots and Cube Roots
Rational Numbers and Irrational Numbers
Triangles
Right Triangles and the Pythagorean Theorem
The Circumference and Area of a Circle 
Problems
CHAPTER 7 Place Value and Decimals
Base Ten Representation of Whole Numbers
Base Two (Binary) Representation of Whole Numbers
Zero and Negative Exponents
Decimal Fractions
Rounding Numbers
Representing Rational and Irrational Numbers in Decimal Form
Scientific Notation
Problems
CHAPTER 8 Working with Percentages
Percentages
Percentages and Rounding
Absolute and Relative Change 
Percentage Points vs. Percentages 
Absolute and Relative Difference
Index Numbers
Problems
CHAPTER 9 Measurement Units 
Converting Units of Measurement
The Metric System
Rates 
Converting Units of Area and Volume
Density and Concentration 
Measurements Expressed in Scientific Notation
Approximation, Measurement Error, and Error Propagation 
Problems
CHAPTER 10 Probability 
Experiments, Outcomes, and Sample Spaces 
Events of a Sample Space
The Complement of an Event
The Intersection of Events
The Union of Events 
Using Venn Diagrams to Depict Events within a Sample Space
Assigning Probabilities 
Equally Likely Outcomes
The Complement Rule
The General Addition Rule
Conditional Probability 
Problems
CHAPTER 11 Data and Statistics 
Data, Populations, and Samples
Issues in Sampling: Representativeness and Bias
Randomized Sampling 
Variables: Quantitative and Categorical
Organizing and Displaying Categorical Data
Grouping Quantitative Data
Histograms 
Using Desmos to Make a Histogram 
Misleading Graphical Displays
Dotplots
Outliers
Measures of Center for Quantitative Data 
Weighted Averages 
Measuring How Quantitative Data Values Are Spread Out
The Range
Measuring Spread Relative to the Mean: The Standard Deviation
Standardizing Data Values
Measures of Relative Location
Measuring Spread Relative to the Median: The Interquartile Range 
Identifying Outliers
Boxplots 
Problems
CHAPTER 12 Modeling Relationships between Quantitative Variables
Ordered Pairs and the Coordinate Plane
Methods for Representing Quantitative Relationships 
Linear Functions
Piecewise-Defined Functions
Average Rate of Change
Exponential Functions 
Problems
CHAPTER 13 Linear Regression and Correlation
Nondeterministic Relationships and Regression Analysis
Scatterplots 
The Line of Best Fit 
Extrapolation 
Linear Correlation 
Correlation vs. Causation 
Problems
CHAPTER 14 Personal Finance
Simple and Compound Interest
Saving Money: Bank Accounts and Certificates of Deposit 
Sums of Consecutive Powers
Saving for Retirement 
Withdrawing Money in Retirement 
Credit Cards
Installment Loans
Problems

Michael J. Cullinane

Mike Cullinane is a Professor of Mathematics at Keene State College. He earned his B.S., M.S., and Ph.D. in Mathematics from the University of New Hampshire and previously served on the faculty at North Carolina Wesleyan College. His professional interests include topology, mathematical analysis, mathematical proof, and undergraduate mathematics education. His work includes research publications, presentations at regional and national conferences, and experience teaching mathematics at both the undergraduate and graduate levels.