Excellent collection of guides/resources for Algebra  - online and e-book (download)*4**4**1*PRELIMINARIES*2*Integer Exponents - In this section we will start looking at exponents and their properties.*4*Rational Exponents - We will define rational exponents in this section and extend the properties from the previous section to rational exponents.*4*Real Exponents - This is a short acknowledgment that the exponent properties from the previous two sections will hold for any real exponent.*4*Radicals - Here we will define radical notation and relate radicals to rational exponents.  We will also give the properties of radicals.*4*Polynomials - We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials.*4*Factoring Polynomials  -This is the most important section of all the preliminaries.*4*Rational Expressions - In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them.*4*Complex Numbers - Here is a very quick primer on complex numbers and how to manipulate them.*1*SOLVING EQUATIONS AND INEQUALITIES*2*Solutions and Solution Sets - We introduce some of the basic notation and ideas involved in solving in this section.*4*Linear Equations - In this section we will solve linear equations, including equations with rational expressions.*4*Applications of Linear Equations - We will take a quick look at applications of linear equations in this section.*4*Equations With More Than One Variable - Here we will look at solving equations with more than one variable in them.*4**4*Quadratic Equations, Part I - In this section we will start looking at solving quadratic equations.*4*We will look at factoring and the square root property in this section.*4**4*Quadratic Equations, Part II - We will finish up solving quadratic equations in this section. *4* We will look at completing the square and quadratic formula in this section.*4**4*Quadratic Equations : A Summary - We*apos*ll give a procedure for determining which method to use in solving quadratic equations in this section.*4*We will also take a quick look at the discriminant.*4**4*Applications of Quadratic Equations - Here we will revisit some of the applications we saw in the linear application section*4*only this time they will involve solving a quadratic equation.*4**4*Equations Reducible to Quadratic Form - In this section we will solve equations that can be reduced to quadratic in form.*4*Equations with Radicals - Here we will solve equations with square roots in them.*4**4*Linear Inequalities - We will start solving inequalities in this section by looking at linear inequalities.*4*Polynomial Inequalities - In this section we will look at solving inequalities that contain polynomials.*4*Rational Inequalities - Here we will solve inequalities involving rational expressions.*4*Absolute Value Equations - We will officially define absolute value in this section and solve equations that contain absolute value.*4*Absolute Value Inequalities - We will solve inequalities that involve absolute value in this section.*1*GRAPHING AND FUNCTIONS*2*Graphing - In this section we will introduce the Cartesian coordinate system and most of the basics of graphing equations.*4*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.*4*Circles - We will look at the equation of a circle and graphing circles in this section.*4**4*The Definition of a Function - We will discuss the definition of a function in this section.*4*We will also introduce the idea of function evaluation.*4**4*Graphing Functions - In this section we will look at the basics of graphing functions.*4*We will also graph some piecewise functions in this section.*4**4*Combining functions - Here we will look at basic arithmetic involving functions as well as function composition.*4*Inverse Functions - We will define and find inverse functions in this section.*1*COMMON GRAPHS*2*Lines, Circles and Piecewise Functions.*4*Parabolas - We*apos*ll be graphing parabolas in this section.*4*Ellipses - In this section we will graph ellipses.*4*Hyperbolas - Here we will be graphing hyperbolas.*4**4*Miscellaneous Functions - In this section we will graph a couple of common functions that don*apos*t really take all that much work to so.*4*We*apos*ll be looking at the constant function, square root, absolute value and a simple cubic function.*4**4*Transformations - We will be looking at shifts and reflections of graphs in this section.*4*Collectively these are often called transformations.*4**4*Symmetry - We will briefly discuss the topic of symmetry in this section.*4*Rational Functions - In this section we will graph some rational functions.  We will also be taking a look at vertical and horizontal asymptotes.*1*POLYNOMIAL FUNCTIONS*2*Dividing Polynomials - We*apos*ll review some of the basics of dividing polynomials in this section.*4*Zeroes/Roots of Polynomials - In this section we*apos*ll define just what zeroes/roots of polynomials are and give some of the more important facts concerning them.*4*Graphing Polynomials - Here we will give a process that will allow us to get a rough sketch of some polynomials.*4*Finding Zeroes of Polynomials - We*apos*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.*4*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.*1*EXPONENTIAL AND LOGARITHM FUNCTIONS*2*Exponential Functions - In this section we will introduce exponential functions.*4*We will be taking a look at some of the properties of exponential functions.*4**4*Logarithm Functions - Here we will introduce logarithm functions.*4*We be looking at how to evaluate logarithms as well as the properties of logarithms.*4**4*Solving Exponential Equations - We will be solving equations that contain exponentials in this section.*4*Solving Logarithm Equations - Here we will solve equations that contain logarithms.*4*Applications - In this section we will look at a couple of applications of exponential functions and an application of logarithms.*1*SYSTEMS OF EQUATIONS*2*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.*4*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.*4**4*Augmented Matrices - We will look at the third main method for solving systems in this section.*4*We will look at systems of two equations and systems of three equations.*4**4*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.*4*Nonlinear Systems - We will take a quick look at solving nonlinear systems of equations in this section.*4**4**4* Extremely useful for teachers of Maths/Mathematics working through College Algebra (Math 1314).