# Algebra

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About *Algebra:*

Here is a listing of all the material that is currently available online.

Preliminaries

Integer Exponents - In this section we will start looking at exponents and their properties.

Rational Exponents - We will define rational exponents in this section and extend the properties from the previous section to rational exponents.

Real Exponents - This is a short acknowledgment that the exponent properties form the previous two sections will hold for any exponent.

Radicals - Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals.

Polynomials - We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials.

Factoring Polynomials - This is the most important section of all the preliminaries. Factoring polynomials will appear in pretty much every chapter in this course. Without the ability to factor polynomials you will be unable to complete this course.

Rational Expressions - In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them.

Complex Numbers - Here is a very quick primer on complex numbers and how to manipulate them.

Solving Equations and Inequalities

Solutions and Solution Sets - We introduce some of the basic notation and ideas involved in solving in this section.

Linear Equations - In this section we will solve linear equations, including equations with rational expressions.

Applications of Linear Equations - We will take a quick look at applications of linear equations in this section.

Equations With More Than One Variable - Here we will look at solving equations with more than one variable in them.

Quadratic Equations, Part I - In this section we will start looking at solving quadratic equations. We will look at factoring and the square root property in this section.

Quadratic Equations, Part II - We will finish up solving quadratic equations in this section. We will look at completing the square and quadratic formula in this section.

Quadratic Equations : A Summary - We’ll give a procedure for determining which method to use in solving quadratic equations in this section. We will also take a quick look at the discriminate.

Applications of Quadratic Equations - Here we will revisit some of the applications we saw in the linear application section, only this time they will involve solving a quadratic equation.

Equations Reducible to Quadratic Form - In this section we will solve equations that can be reduced to quadratic in form.

Equations with Radicals - Here we will solve equations with square roots in them.

Linear Inequalities - We will start solving inequalities in this section by looking at linear inequalities.

Polynomial Inequalities - In this section we will look at solving inequalities that contain polynomials.

Rational Inequalities Here we will solve inequalities involving rational expressions.

Absolute Value Equations - We will official define absolute value in this section and solve equation that contain absolute value.

Absolute Value Inequalities - We will solve inequalities that involve absolute value in this section.

Graphing and Functions

Graphing - In this section we will introduce the Cartesian coordinate system and most of the basics of graph equations.

Lines - Here we will review the main ideas from the study of lines including slope and the special forms of the equation of a line.

Circles - We will look at the equation of a circle and graphing circles in this section.

The Definition of a Function - We will discuss the definition of a function in this section. We will also introduce the idea of function evaluation.

Graphing Functions - In this section we will look at the basics of graphing functions. We will also graph some piecewise functions in this section.

Combining functions - Here we will look at basic arithmetic involving functions as well as function composition.

Inverse Functions - We will define and find inverse functions in this section.

Common Graphs

Lines, Circles and Piecewise Functions - This section is here only to acknowledge that we’ve already talked about graphing these in a previous chapter.

Parabolas - We’ll be graphing parabolas in this section.

Ellipses - In this section we will graph ellipses.

Hyperbolas - Here we will be graphing hyperbolas.

Miscellaneous Functions - In this section we will graph a couple of common functions that don’t really take all that much work to so. We’ll be looking at the constant function, square root, absolute value and a simple cubic function.

Transformations - We will be looking at shifts and reflections of graphs in this section. Collectively these are often called transformations.

Symmetry - We will briefly discuss the topic of symmetry in this section.

Rational Functions - In this section we will graph some rational functions. We will also be taking a look at vertical and horizontal asymptotes.

Polynomial Functions

Dividing Polynomials - We’ll review some of the basics of dividing polynomials in this section.

Zeroes/Roots of Polynomials - In this section we’ll define just what zeroes/roots of polynomials are and give some of the more important facts concerning them.

Graphing Polynomials - Here we will give a process that will allow us to get a rough sketch of some polynomials.

Finding Zeroes of Polynomials - We’ll look at a process that will allow us to find some of the zeroes of a polynomial and in special cases all of the zeroes.

Partial Fractions - In this section we will take a look at the process of partial fractions and finding the partial fraction decomposition of a rational expression.

Exponential and Logarithm Functions

Exponential Functions - In this section we will introduce exponential functions. We will be taking a look at some of the properties of exponential functions.

Logarithm Functions - Here we will introduce logarithm functions. We be looking at how to evaluate logarithms as well as the properties of logarithms.

Solving Exponential Equations - We will be solving equations that contain exponentials in this section.

Solving Logarithm Equations - Here we will solve equations that contain logarithms.

Applications - In this section we will look at a couple of applications of exponential functions and an application of logarithms.

Systems of Equations

Linear Systems with Two Variables - In this section we will use systems of two equations and two variables to introduce two of the main methods for solving systems of equations.

Linear Systems with Three Variables - Here we will work a quick example to show how to use the methods to solve systems of three equations with three variables.

Augmented Matrices - We will look at the third main method for solving systems in this section. We will look at systems of two equations and systems of three equations.

More on the Augmented Matrix - In this section we will take a look at some special cases to the solutions to systems and how to identify them using the augmented matrix method.

Nonlinear Systems - We will take a quick look at solving nonlinear systems of equations in this section.

Preliminaries

Integer Exponents - In this section we will start looking at exponents and their properties.

Rational Exponents - We will define rational exponents in this section and extend the properties from the previous section to rational exponents.

Real Exponents - This is a short acknowledgment that the exponent properties form the previous two sections will hold for any exponent.

Radicals - Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals.

Polynomials - We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials.

Factoring Polynomials - This is the most important section of all the preliminaries. Factoring polynomials will appear in pretty much every chapter in this course. Without the ability to factor polynomials you will be unable to complete this course.

Rational Expressions - In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them.

Complex Numbers - Here is a very quick primer on complex numbers and how to manipulate them.

Solving Equations and Inequalities

Solutions and Solution Sets - We introduce some of the basic notation and ideas involved in solving in this section.

Linear Equations - In this section we will solve linear equations, including equations with rational expressions.

Applications of Linear Equations - We will take a quick look at applications of linear equations in this section.

Equations With More Than One Variable - Here we will look at solving equations with more than one variable in them.

Quadratic Equations, Part I - In this section we will start looking at solving quadratic equations. We will look at factoring and the square root property in this section.

Quadratic Equations, Part II - We will finish up solving quadratic equations in this section. We will look at completing the square and quadratic formula in this section.

Quadratic Equations : A Summary - We’ll give a procedure for determining which method to use in solving quadratic equations in this section. We will also take a quick look at the discriminate.

Applications of Quadratic Equations - Here we will revisit some of the applications we saw in the linear application section, only this time they will involve solving a quadratic equation.

Equations Reducible to Quadratic Form - In this section we will solve equations that can be reduced to quadratic in form.

Equations with Radicals - Here we will solve equations with square roots in them.

Linear Inequalities - We will start solving inequalities in this section by looking at linear inequalities.

Polynomial Inequalities - In this section we will look at solving inequalities that contain polynomials.

Rational Inequalities Here we will solve inequalities involving rational expressions.

Absolute Value Equations - We will official define absolute value in this section and solve equation that contain absolute value.

Absolute Value Inequalities - We will solve inequalities that involve absolute value in this section.

Graphing and Functions

Graphing - In this section we will introduce the Cartesian coordinate system and most of the basics of graph equations.

Lines - Here we will review the main ideas from the study of lines including slope and the special forms of the equation of a line.

Circles - We will look at the equation of a circle and graphing circles in this section.

The Definition of a Function - We will discuss the definition of a function in this section. We will also introduce the idea of function evaluation.

Graphing Functions - In this section we will look at the basics of graphing functions. We will also graph some piecewise functions in this section.

Combining functions - Here we will look at basic arithmetic involving functions as well as function composition.

Inverse Functions - We will define and find inverse functions in this section.

Common Graphs

Lines, Circles and Piecewise Functions - This section is here only to acknowledge that we’ve already talked about graphing these in a previous chapter.

Parabolas - We’ll be graphing parabolas in this section.

Ellipses - In this section we will graph ellipses.

Hyperbolas - Here we will be graphing hyperbolas.

Miscellaneous Functions - In this section we will graph a couple of common functions that don’t really take all that much work to so. We’ll be looking at the constant function, square root, absolute value and a simple cubic function.

Transformations - We will be looking at shifts and reflections of graphs in this section. Collectively these are often called transformations.

Symmetry - We will briefly discuss the topic of symmetry in this section.

Rational Functions - In this section we will graph some rational functions. We will also be taking a look at vertical and horizontal asymptotes.

Polynomial Functions

Dividing Polynomials - We’ll review some of the basics of dividing polynomials in this section.

Zeroes/Roots of Polynomials - In this section we’ll define just what zeroes/roots of polynomials are and give some of the more important facts concerning them.

Graphing Polynomials - Here we will give a process that will allow us to get a rough sketch of some polynomials.

Finding Zeroes of Polynomials - We’ll look at a process that will allow us to find some of the zeroes of a polynomial and in special cases all of the zeroes.

Partial Fractions - In this section we will take a look at the process of partial fractions and finding the partial fraction decomposition of a rational expression.

Exponential and Logarithm Functions

Exponential Functions - In this section we will introduce exponential functions. We will be taking a look at some of the properties of exponential functions.

Logarithm Functions - Here we will introduce logarithm functions. We be looking at how to evaluate logarithms as well as the properties of logarithms.

Solving Exponential Equations - We will be solving equations that contain exponentials in this section.

Solving Logarithm Equations - Here we will solve equations that contain logarithms.

Applications - In this section we will look at a couple of applications of exponential functions and an application of logarithms.

Systems of Equations

Linear Systems with Two Variables - In this section we will use systems of two equations and two variables to introduce two of the main methods for solving systems of equations.

Linear Systems with Three Variables - Here we will work a quick example to show how to use the methods to solve systems of three equations with three variables.

Augmented Matrices - We will look at the third main method for solving systems in this section. We will look at systems of two equations and systems of three equations.

More on the Augmented Matrix - In this section we will take a look at some special cases to the solutions to systems and how to identify them using the augmented matrix method.

Nonlinear Systems - We will take a quick look at solving nonlinear systems of equations in this section.