Because the course textbook is still in development, the navigation links are not live on the book's website. This page provides direct links to each of the chapters we'll use in class this semester; please get in touch if you find any links to be broken.

Chapter 1: Introduction to Problem-Solving and Deductive Reasoning

• Introduction to Problem-Solving
  In this section, we introduce Pólya's method and work through one detailed example, previewing the methods to be worked throughout the rest of the chapter.

• Exploring Pólya's Method
  In this section we go through several problem-solving examples in some detail in order to illustrate the importance of each individual step of Pólya's method.

• Estimation in Problem-Solving
  Part of the planning phase of problem-solving should be identifying the types of answers that one expects to find at the end; and when we start with questions that ask us to find numerical solutions, it is especially helpful to have an idea about the approximate values we would expect to see. In this section we talk about incorporating estimation into the problem-solving process.

• Inductive and Deductive Reasoning
  Inductive and deductive reasoning are different ways of approaching mathematical problem-solving that we use all the time without realizing it. In this section we provide definitions for these concepts, and we consider some examples to highlight the value of each approach in different situations.

  • Inductive Reasoning Strategies
    In this section, we explore using inductive reasoning to make predictions about complex or large sets.

  • Deductive Reasoning Strategies
    In this section, we explore using Euler diagrams to determine and evaluate consequences of simple logical statements.

Chapter 2: Whole Numbers

• • Whole Numbers
    This section introduces the concept of numerals and specifically whole numbers. Number lines are introduced as a graphical representation of numbers, and the importance of place value is emphasized.

  • Rounding Whole Numbers
    Rounding is an important tool in approximating and estimating and particularly useful when looking back and checking the reasonableness of your answers. In this section, rounding for whole numbers is explained.

  • Addition and Subtraction of Whole Numbers
    This section explains the process of adding and subtracting with whole numbers, emphasizing the role of place value in the development of the common algorithm.

  • Multiplication of Whole Numbers
    This section explains the typical algorithm for multiplying multi-digit whole numbers and defines some of the key properties of multiplication.

  • Division of Whole Numbers
    This section describes division with whole numbers both as a concept and explains the process of division. The phrase "long division" is often used as a name for the standard division algorithm.

  • Exponents and Square Roots
    This is a short section describing whole numbers raised to whole number exponents and roots of whole numbers. In this section, the answer to root questions will always be a whole number.

  • Grouping Symbols and the Order of Operations
    This section concludes our study of whole numbers and their arithmetic. We name and discuss the use of grouping symbols (parentheses, brackets, etc.), and then describe and illustrate the accepted order of operations.

Chapter 3: Rational Numbers

• • Fractions of Whole Numbers
    This section introduces the concepts of fractions and rational numbers and illustrates how fractions can be modeled with number lines and other representations.

  • Equivalent Fractions, Reducing Fractions to Lowest Terms, and Elevating Fractions to Higher Terms
    In this section, the focus is on equivalent fractions—fractions with the same value but formed from different pairs of whole numbers. This allows us to reduce fractions to lowest terms and elevating them to higher terms.

  • Multiplication of Fractions
    In this section, we introduce the first operation on fractions, multiplication, along with how multiplication is used in applications. Exponentiation (repeated multiplication) and square roots are also mentioned.

  • Division of Fractions
    This section begins with the concept of reciprocal, and then uses that to describe how to divide fractions. Applications involving division are included at the end of the section.

  • Addition and Subtraction of Fractions with Like Denominators
    This section introduces addition and subtraction of fractions. Examples and problems in this section are restricted to the situation in which the fractions have the same denominator.

  • Addition and Subtraction of Fractions with Unlike Denominators
    This section picks up where the previous section left off and considers how to add and subtract fractions with different denominators. Examples also illustrate when addition and subtraction appear in applied problems.

  • Proper Fractions, Improper Fractions, and Mixed Numbers
    This section describes the relationship between proper fractions, improper fractions, and mixed numbers. Multiplication and division with mixed numbers is also included here.

  • Addition and Subtraction of Mixed Numbers
    This section described addition and subtraction of mixed numbers.

  • Comparing Fractions
    In this section, we learn how to determine when one fraction is greater than or smaller than another and how to arrange a list of fractions in order.

  • Complex Fractions
    This section describes "complex fractions" and how to simplify them. A complex fraction is a fraction formed by the ratio of two expressions which can involve fractions and operations on them.

  • Combinations of Operations with Fractions
    This chapter concludes by reviewing order of operations in the context of fractions.

Chapter 4: Decimals (coming soon!)

Chapter 5: Sets and Venn Diagrams

• Introduction
  A brief introduction to the topics that we will examine in this chapter. 

• Basic Set Concepts
  We learn how to frame collections of objects (mathematical or otherwise) as sets, and some of the basics of counting sets, as well as the definition of cardinality.

  • Exercises

• Subsets
  A subset of a given set is also a set, but one that takes all of its members from that given set. We learn to describe and define subsets, discuss the empty set, and count the number of subsets of a given finite set. 

  • Exercises

• Understanding Venn Diagrams
  In this section, we learn to use Venn diagrams to describe and visualize the relationship between sets, their subsets, and other sets with which they may share members. 

  • Exercises

• Set Operations with Two Sets
  We begin to work with set algebra to explore and create more complex sets from various types of sets as building blocks.

  • Exercises 

• Set Operations with Three Sets
  We explore what happens when we look at the overlaps and relationships between three sets. Venn diagrams reach a point of complexity and difficulty beyond three sets.

  • Exercises

• Chapter Summary
  Reviewing key terms and concepts

  • Key Terms

  • Key Concepts

  • Formula Review

  • Chapter Review (exercises)

Chapter 6: Logic and Deductive Reasoning

• Introduction
  Introduction to logic and deductive reasoning

• Statements and Quantifiers
  In this section, we define logical statements, we introduce symbolic ways of thinking about statements, and we explore the meaning of the negation of a statement.

  • Exercises

• Compound Statements
  In this chapter, we learn how to build more complex ("compound") statements using logical connectives: "I love sunshine and I love rainbows," or "You are going to the store or you're grounded," and evaluating the consequences of this compounding on the truth value of the complete statement.

• Constructing Truth Tables
  A truth table is a simple way to keep track of all of the different ways in which a compound statement can be interpreted, depending on the meanings and truth values of the statements that make it up. In this chapter we begin to study truth tables with basic compound statements.

  • Exercises

• Truth Tables for the Conditional and Biconditional
  In this chapter, we explore the truth table concept with more complicated statements, using all of the connectives that we have available to us up to this point.

  • Exercises

• Equivalent Statements
  In this section we use truth tables to explore what it means for two statements to be logically equivalent (have the same truth values) and see how we can use that information to understand sentences in ordinary language a little better. 

  • Exercises

• De Morgan's LawsDe Morgan's Laws provide a special format for equivalent statements, showing how to negate conjunctions and disjunctions without a preamble like, "it is not the case that."

  • Exercises

• Logical Arguments
  In this section we put together all of the ideas in this chapter so far to see how logical statements can be used along with the rules of deductive reasoning to draw valid logical conclusions. 

  • Exercises

• Chapter Summary
  Reviewing key terms and concepts

  • Key Terms

  • Key Concepts

  • Chapter Review (exercises)

Chapter 7: Proportions and Percents

• Ratios and Rates
  A ratio compares two numbers or two quantities that are measured with the same unit. When a ratio is written in fraction form, the fraction should be simplified. To find the ratio of two measurements, we must make sure the quantities have been measured with the same unit. If the measurements are not in the same units, we must first convert them to the same units. A rate compares two quantities of different units. A rate is usually written as a fraction.

• Proportions and their Applications
  A proportion states that two ratios or rates are equal. The proportion is read “a is to b, as c is to d”. If we compare quantities with units, we have to be sure we are comparing them in the right order. For any proportion of the form a/b = c/d, where b ≠ 0, d ≠ 0, its cross products are equal. So, cross products can be used to test whether a proportion is true. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign).

• Understand Percent
  A percent is a ratio whose denominator is 100. Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per 100, so the denominator of the fraction is 100. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal. To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100, it is easy to change that fraction to a percent.

• Solve General Applications of Percent
  We will solve percent equations by using the methods we used to solve equations with fractions or decimals. Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.

• Solve Sales Tax, Commission, and Discount Applications
  Sales tax and commissions are applications of percent in our everyday lives. To solve these applications, we follow the same strategy we used in the section on decimal operations. The sales tax is a percent of the purchase price which is calculated as the product of the tax rate and the purchase price. A commission is a percentage of total sales as determined by the rate of commission. A discount is a percent off the original price while a mark-up is the amount added to the wholesale price.

Chapter 8: Foundations for Algebra

• Numbers and Properties of Operations
  This section introduces number sets and properties that a set of numbers may or may not have, including closure, commutativity, associativity, distributivity, and identity in inverse properties.

• Prime and Composite Numbers
  In this section, we begin with the concept of divisibility and provide some useful rules for determining whether a number is divisible by some common factors. Then we study primes and composites, using the Sieve of Eratosthenes to generate a list of primes. This enables us to find the prime factorization of a number, which is useful tool in determining the greatest common divisor and least common multiple of numbers.

• Signed numbers
  This is a brief section introducing signed numbers. We focus on how sign numbers appear on a number line, the relationship between opposite and the inverse property, and comparing signed numbers with greater than and less than.

• Absolute Value
  This is a brief section introducing signed numbers. We focus on how sign numbers appear on a number line, the relationship between opposite and the inverse property, and comparing signed numbers with greater than and less than.

• Addition and Subtraction of Signed Numbers
  This section discusses addition and subtraction of signed numbers. While most of the examples focus on integers, the principles apply to all real numbers.

• Multiplication and Division of Signed Numbers and Integer Exponents
  This section completes the study of arithmetic with sign numbers, introducing multiplication and division with signed numbers and exponentiation with integer powers. The section concludes with examples of applying the order of operations, to problems with signed numbers.

• Use the Language of Algebra
  One of the reasons why algebra is such a powerful tool is that it allows us to translate information from a wide variety of contexts into the precise and, in many ways, simpler language of algebra. In this section, we begin exploring that language, including the concepts of variables, expressions, and equations. The emphasis is on evaluating algebraic expressions and translating from English language descriptions into algebraic expressions.

• The Distributive Property and Algebra
  In the final section of this chapter, we explore two essential tools for simplifying algebra expressions: combining like terms and distributing over parentheses.

Chapter 9: Sequences

• Introduction to Sequences
  This section introduces the definition of a sequence and basic terminology, such as the general term. It then explains how to use the general term to determine the first few terms or a specific term of a sequence, and vise versa, how to find the general term form a few given terms. The Σ notation is also introduced and applied to evaluate the sum of several terms.

• Arithmetic Sequences and Partial Sums
  This section focuses on a specific type of sequence - Arithmetic sequences. It covers their definition, the formula for the 𝑛 nth term, and the formula for partial sum. You will learn how to determine whether a given sequence is arithmetic, and how to use these formulas to find the 𝑛 nth term and the sum of the first several terms. The section also includes applications of these techniques to solve word problems.

• Geometric Sequences and Partial Sums
  This section focuses on a specific type of sequence - geometric sequences. It covers their definition, the formula for the nth term, and the formula for partial sum. You will learn how to determine whether a given sequence is geometric, and how to use these formulas to find the nth term and the sum of the first several terms. The section also includes applications of these techniques to solve word problems.

Chapter 10: Solving Linear Equations

• Introduction to Solving Linear Equations
  In this chapter, we will solve equations by keeping quantities on both sides of an equal sign in perfect balance.

• Solve Equations Using the Subtraction and Addition Properties of Equality
  The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. We can use the Subtraction and Addition Properties of Equality to solve equations by isolating the variable on one side of the equation. Usually, we will need to simplify one or both sides of an equation before using the Subtraction or Addition Properties of Equality.

• Solve Equations Using the Division and Multiplication Properties of Equality
  We can also use the Division and Multiplication Properties of Equality to solve equations by isolating the variable on one side of the equation. The goal of using the Division and Multiplication Properties of Equality is to "undo" the operation on the variable. Usually, we will need to simplify one or both sides of an equation before using the Division or Multiplication Properties of Equality.

• Solve Equations with Variables and Constants on Both Sides
  You may have noticed that in all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we’ll see how to solve equations where the variable terms and/or constant terms are on both sides of the equation.

• Solve Equations with Fraction or Decimal Coefficients
  The General Strategy for Solving Linear Equations can be used to solve for equations with fraction or decimal coefficients. Clearing the equation of fractions applies the Multiplication Property of Equality by multiplying both sides of the equation by the LCD of all fractions in the equation. The result of this operation will be a new equation, equivalent to the first, but with no fractions. When we have an equation with decimals, we can use the same process we used to clear fractions.

• Using Linear Equations to Work with Repeating Decimals
  In this section, we explore one particular application in detail, learning how to use a linear equation to reconstruct an equivalent fraction from a given repeating decimal expression.

• Linear Equations in One Variable with Applications
  This page provides a detailed exploration of linear equations in one variable, designed to help learners understand how to solve various types of linear equations through examples and exercises. It focuses on using the properties of equality, developing strategies for solving equations, and addressing scenarios with no solutions, infinite solutions, or specific variable solutions within formulas.

• Chapter Review
  This section provides useful resources to help you practice the concepts we've covered: a list of key concepts summarizing all of the techniques we practiced; a list of further exercises; and a practice test that might help you prepare for assessments in your own class.

  • Key Concepts

  • Review Exercises

Chapter 11: Linear Inequalities

• Graphing Inequalities and Interval Notation
  This section explains what an inequality is and ways to express a simple inequality such as graphing an inequality on a number line, using interval notation and set-builder notation.

• Solving Linear Inequalities
  Solving an inequality is similar to solving an equation, because you use the same algebraic steps to isolate the variable, like adding, subtracting, or multiplying/dividing by a positive number. The main difference is that if you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality sign.

• Applications of Linear Inequalities
  In this section, we will focus on how to translate words and phrases such as "exceeds," "no more than," "fewer than," into appropriate inequality signs, so that we can generate an inequality to model and solve story problems.

Chapter 12: Graphs and Functions

• Coordinate System and Graphs
  This section introduces rectangular coordinate system, how to plot points, how to graph lines by plotting points, including two special lines, vertical and horizontal lines.

• Graph Linear Inequalities in Two Variables
  This section focuses on inequalities in two variables. We will learn how to determine whether a given point is a solution to an inequality and how to graph such inequalities. The section also includes applications of these concepts to real-world (word) problems.

• Functions and Notation
  This section introduces definitions of relation and function, domain and range of a relation, and function notation. We will lean how to determine whether a given relation is a function, identify the domain and range, and evaluate function values.

• Graphs of Functions
  This section covers vertical line test, graphs of typical functions such as linear function, quadratic function, cubic function, and absolute value function. We will learn how to test whether a given graph represents a function by vertical line test, how to read information, such as domain and range, function values, from a given graph.

Chapter 13: Exponential and Logarithmic Functions

• Rules of Exponents
  In this section, you will learn rules of exponents and apply them to simplify expressions.

• Evaluate and Graph Exponential Functions
  In this section, you will learn about the properties of exponential functions, how to graph them, and how to solve exponential equations. You will also explore real-world applications that can be modeled by exponential functions, as well as how to solve those application problems.

• Evaluate and Graph Logarithmic Functions
  In this section, you will learn how to convert between exponential and logarithmic forms, explore the characteristics of logarithmic functions and their graphs, and study natural and common logarithmic functions. We’ll also discuss real‑world applications of logarithmic functions.

Chapter 14: Simple and Compound Interest

• Simple Interest
  Borrowing money comes at a cost. The fee paid for the use of money is called interest. The amount of money that is borrowed or loaned is known as the principal or present value. Simple interest is calculated only on the original principal. When money is loaned, the borrower typically pays a fixed interest rate on the principal for the duration of the loan.

• Compound Interest
  Compound interest is calculated not only on the original principal but also on the interest from previous periods. This means that over time, you earn (or pay) interest on the original amount and on the interest that has already been added.

Chapter 15: Counting Techniques

• Inflation
  Inflation is the rate at which the general level of prices for goods and services rises over time, leading to a decrease in the purchasing power of money.

• Solving Inflation Problems
  In this section, you will learn how to compute past, present, and future values while accounting for inflation. You will also gain an understanding of how inflation affects purchasing power over time.

• The Basics of Loans
  This section covers key terms and basic loan concepts, such as amortization and financing costs.

• Credit Cards
  In this section, you will learn how to read credit card statements, calculate the average daily balance, and determine finance charges.

• Interest Rates
  In this section, you will learn how to identify three different types of interest rates and understand the relationships between them.

• Installment Loans
  An installment loan is a loan with a fixed term in which the borrower pays a consistent amount each period until the loan is fully repaid. These periods are almost always monthly. In this section, you will learn how to calculate monthly installment payments and loan payoffs.

• Car Loans
  Obtaining a car can be daunting. The variety of models, features, additional costs, and securing financing are all steps that must be considered. This section will address some of the key issues associated with car ownership.

• Home Ownership
  This section examines the advantages, disadvantages, and costs of homeownership compared to renting. It also explains how to calculate mortgage payments, mortgage payoffs, total mortgage costs, and escrow payments.

Chapter 16: Systems of Measurement

• Systems of Measurement (Part 1)
  In this section we will see how to convert among different types of units, such as feet to miles or kilograms to pounds. The basic idea in all of the unit conversions will be to use a form of 1, the multiplicative identity, to change the units but not the value of a quantity.

• Systems of Measurement (Part 2)
  Performing arithmetic operations on measurements with mixed units of measures in the metric system requires the same care we used in the U.S. system. Many measurements in the United States are made in metric units. We make conversions between the systems just as we do within the systems—by multiplying by unit conversion factors. The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit. The metric system uses degrees Celsius.

• Temperature Measurements
  The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit. The metric system uses degrees Celsius.

Chapter 17: Geometry

• Points, Lines, and Planes
  This first section of the Geometry chapter begins with the fundamental objects of geometry: the point, line, and plane. Fundamental properties of lines, such as parallel and perpendicular lines, as well as intersections and unions of rays and line segments, are discussed.

• Angles
  An angle is formed when two rays meet at a common endpoint. This section provides definitions of important types of angles and terms for describing the relationships between angles. These relationships are useful in being able to deduce the measurements of some angles from others.

• Triangles
  This section on triangles continues the study of angles in the previous section, emphasizing types of triangles and using angle relationships to find unknown angle measures from given ones. The concepts of similarity and congruence, including the Congruence Theorems, are also included.

• Pythagorean Theorem
  The Pythagorean Theorem is one of, if not the, most famous named theorems in mathematics. In this section, the theorem is used to find lengths of triangles in abstract and concrete settings and to derive the distance formula.

• Polygons, Perimeter, and Circumference
  This section begins by defining and classifying polygons. The central topic, though, is perimeter, including circumference and the perimeter of figures involving semicircles. The section concludes with the sums of interior and exterior angles of polygons.

• Area
  This section is focused on the calculation of area for standard shapes, including circles, and some shapes formed by combining the standard ones.

• Volume and Surface Area
  This section moves to three dimensions, exploring the surface area and volume of some common solids, including prisms, cylinders, cones, and spheres.

• Right Angle Trigonometry
  This final section of Geometry begins with 30-60-90 and 45-45-90 triangles and their properties before introducing the trigonometric functions in the context of right triangles.

Chapter 18: Counting Techniques

• The Multiplication Principle
  You can count the number of shoes and belts in your closet, perhaps, but can you feasibly count how many combinations of those shoes and belts you could make? If you have more than a few of each, the answer is likely 'no'! When planning a meal for a group, can you count how many ways there are to combine, say, the toppings on a salad? We will begin by using tree diagrams to visualize large sets like this, and then we’ll see how the multiplication principle can make that process much easier.

• Permutations and Factorials
  How many ways can we place a group of objects in order? How do we deal with situations where simple counting becomes complicated by rules, such as not being allowed to reuse a letter in a password? Permutations and factorials are the main tools we turn to when trying to count circumstances like these, and more.

• Combinations and Applied Problems
  In this section, we discuss the combination formula: counting the number of ways to select a group from a larger set. This concept is the final tool in our counting toolbox, and will be extremely useful in probability! We also tie together all of the elements of this chapter in some more complex applied problems and examples.

Chapter 19: Probability

• Introduction to Probability
  In this section, we will introduce the concept and formal definition of probability and discuss basic calculations for theoretical and empirical probabilities.

• Probability with Permutations and Combinations
  In this section, we learn to calculate probabilities when the sample spaces can be counted using permutations or combinations.

• Odds
  If you've ever participated in or read about any kind of betting, you may be familiar with the concept of "odds"—another way of measuring uncertainty. In this section, we define odds and explain how to convert between odds and conventional probability.

• The Addition Rule for Probability
  In this section, we discuss probabilities for the union of two events—“event A or event B”—when the events are either mutually exclusive or overlapping.

• Conditional Probability and the Multiplication Rule
  What about calculating the likelihood of an intersection between several events—“event A and event B”? The multiplication rule provides a framework for calculating the probability of multiple events occurring in a multi-stage experiment.

• "AND" Probability - Independent Events
  When two events are independent, the outcome of one does not affect the probability of the other. When events are independent, calculating the probability of their intersection becomes a simple multiplication. In this section, we’ll learn how to identify and work with independent events.

• Expected Value
  In the final section of our chapter on probability, we introduce the concept of expected value for experiments with numerical outcomes—the theoretical average result if an experiment were repeated many times. Expected value has wide-ranging applications in fields that involve making or preparing numerical predictions.

Chapter 20: Statistics

• Introduction
  Statistics is the branch of mathematics concerned with collecting, organizing, analyzing, interpreting, and presenting data. In this chapter, you will explore numerical methods for describing data, a field known as descriptive statistics. You’ll learn not only how to calculate these measures, but more importantly, how to interpret them.

• Definitions of Statistics and Key Terms
  The mathematical theory of statistics is easier to learn when you know the language. This section presents important terms that will be used throughout the text.

• Organizing Data
  In this section, we will learn about two types of data and how to organize them using a frequency table.

• Mean, Median, and Mode
  The mean, median, and mode are three common measures of central tendency used to describe the center of a dataset. They help in analyzing and interpreting data.

• Range, Variance, and Standard Deviation
  Range, variance, and standard deviation are measures of variability that describe how spread out the data values are in a dataset. These tools help us understand the consistency or dispersion within a dataset.

Chapter 21: Statistics II

• Visualizing Data - Bar Charts, Pie Charts, and Histograms
  Bar charts and pie charts are used to display categorical data, with bar charts showing frequencies through the heights of bars and pie charts showing proportions as slices of a circle. Histograms, on the other hand, are used for numerical data and group values into intervals (bins) to show how the data are distributed. Together, these charts help readers compare categories, understand proportions, and recognize patterns in quantitative data.

  • Exercises

• Percentiles
  Percentiles divide a data set into 100 equal parts and help describe the relative standing of a value within the group. For example, a score at the 70th percentile means it is higher than 70% of all other scores. Percentiles are especially useful for interpreting test results, growth charts, and any situation where understanding how an individual value compares to the rest of the data is important.

• Quartiles and Box Plots
  The common measures of location are quartiles and percentiles. Quartiles are special percentiles. The first quartile, Q1, is the same as the 25th percentile, and the third quartile, Q3, is the same as the 75th percentile. The median, Q2, is called both the second quartile and the 50th percentile.

• The Normal Distribution
  A normal distribution forms a continuous, bell-shaped curve. In a normal distribution, the mean, median, and mode are all the same, and the data are symmetrically spread so that values farther from the center become increasingly rare. Many real-world measurements—such as heights, test scores, and measurement errors—often follow this pattern. Normal distributions are important in statistics because they allow us to make predictions and estimate probabilities.

• The Standard Normal Distribution
  A z-score is a standardized value. Its distribution is the standard normal distribution. The mean of the z-scores is 0 and the standard deviation is 1. If y is the z-score for a value from the normal distribution with mean m and standard deviation s, then y tells you how many standard deviations x is above (greater than) m or below (less than) m.

• Applications of the Normal Distribution
  This section examines two applications of normal distributions.