Rusczyk R. Introduction to algebra

Alpine: AoPS, 2007. — 658 p. — ISBN: 9781934124017, 193412401X.Learn the basics of algebra from former USA Mathematical Olympiad winner and Art of Problem Solving founder Richard Rusczyk. Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!How to Use This Book
Acknowledgements
Follow the Rules
Numbers
Order of Operations
When Does Order Matter?
Distribution and Factoring
EquationsX Marks the Spot
Expressions
Arithmetic with Expressions
Distribution, Subtraction, and Factoring
FractionsOne-Variable Linear Equations
Solving Linear Equations I
Solving Linear Equations II
Word Problems
Linear Equations in DisguiseMore Variables
Evaluating Multi-Variable Expressions
Still More Arithmetic
Distribution and Factoring
Fractions
EquationsMulti-Variable Linear Equations
Introduction to Two-Variable Linear Equations
Substitution
Elimination
Word Problems
More Linear Equations in Disguise
More VariablesRatios and Percents
Basic Ratio Problems
More Challenging Ratio Problems
Conversion Factors
Percent
Percentage ProblemsProportion
Direct Proportion
Inverse Proportion
Joint Proportion
Rate ProblemsGraphing Lines
The Number Line and the Cartesian Plane
Introduction to Graphing Linear Equations
Using Slope in Problems
Find the Equation
Slope and Intercepts
Comparing LinesIntroduction to Inequalities
The Basics
Which Is Greater?
Linear Inequalities
Graphing Inequalities
OptimizationQuadratic Equations - Part 1
Getting Started With Quadratics
Factoring Quadratics I
Factoring Quadratics II
Sums and Products of Roots of a Quadratic
Extensions and ApplicationsSpecial Factorizations
Squares of Binomials
Difference of Squares
Sum and Difference of Cubes
Rationalizing Denominators
Simon's Favorite Factoring TrickComplex Numbers
Numbers, Numbers, and More Numbers!
Imaginary Numbers
Complex NumbersQuadratic Equations - Part 2
Squares of Binomials Revisited
Completing the Square
The Quadratic Formula
Applications and ExtensionsGraphing Quadratics
Parabolas
CirclesMore Inequalities
Quadratic Inequalitie
Beyond Quadratics
The Trivial Inequality
Quadratic OptimizationFunctions
The Machine
Combining Functions
Composition
Inverse Functions
Problem Solving with Functions
OperationsGraphing Functions
Basics
Transformations
Inverse Functions RevisitedPolynomials
Addition and Subtraction
MultiplicationExponents and Logarithms
Exponential Functions
Show Me the Money
Interesting Problems
What is a Logarithm?Special Functions
Radicals
Absolute Value
Floor and Ceiling
Rational Functions
Piecewise Defined FunctionsSequences & Series
Arithmetic Sequences
Arithmetic Series
Geometric Sequences
Geometric Series
TelescopingSpecial Manipulations
Raising Equations to Powers
Self-similarity
SymmetryHints to Selected Problems