Intermediate Algebra: Art of Problem Solving

How to Use This Book
Acknowledgments
Contents
1 Basic Techniques for Solving Equations
	1.1 Isolation
	1.2 Substitution
	1.3 Elimination
	1.4 Larger Systems of Linear Equations
	1.5 Summary
2 Functions Review
	2.1 Function Basics
	2.2 Graphing Functions
	2.3 Composition
	2.4 Inverse Functions
	2.5 Summary
3 Complex Numbers
	3.1 Arithmetic of Complex Numbers
	3.2 The Complex Plane
	3.3 Real and Imaginary Parts
	3.4 Graphing in the Complex Plane
	3.5 Summary
4 Quadratics
	4.1 Factoring Quadratics
	4.2 Relating Roots and Coefficients
	4.3 Completing the Square
	4.4 The Discriminant
	4.5 Quadratic Inequalities
	4.6 Summary
5 Conics
	5.1 Parabolas
	5.2 Problem Solving With Parabolas
	5.3 Maxima and Minima of Quadratics
	5.4 Circles
	5.5 Ellipses
	5.6 Hyperbolas
	5.7 Summary
6 Polynomial Division
	6.1 Polynomial Review
	6.2 Introduction to Polynomial Division
	6.3 Synthetic Division
	6.4 The Remainder Theorem
	6.5 Summary
7 Polynomial Roots Part I
	7.1 The Factor Theorem
	7.2 Integer Roots
	7.3 Rational Roots
	7.4 Bounds
	7.5 Graphing and the Fundamental Theorem of Algebra
	7.6 Algebraic Applications of the Fundamental Theorem
	7.7 Summary
8 Polynomial Roots Part II
	8.1 Irrational Roots
	8.2 Nonreal Roots
	8.3 Vieta's Formulas
	8.4 Using Roots to Make Equations
	8.5 Summary
9 Factoring Multivariable Polynomials
	9.1 Grouping
	9.2 Sums and Differences of Powers
	9.3 The Factor Theorem for Multivariable Polynomials
	9.4 Summary
10 Sequences and Series
	10.1 Arithmetic Sequences
	10.2 Arithmetic Series
	10.3 Geometric Sequences
	10.4 Geometric Series
	10.5 Sequence, Summation, and Product Notation
	10.6 Nested Sums and Products
	10.7 Summary
11 Identities, Manipulations, and Induction
	11.1 Brute Force
	11.2 Ratios
	11.3 Induction
	11.4 Binomial Theorem
	11.5 Summary
12 Inequalities
	12.1 Manipulating Inequalities
	12.2 The Trivial Inequality
	12.3 AM-GM Inequality with Two Variables
	12.4 AM-GM with More Variables
	12.5 The Cauchy-Schwarz Inequality
	12.6 Maxima and Minima
	12.7 Summary
13 Exponents and Logarithms
	13.1 Exponential Function Basics
	13.2 Introduction to Logarithms
	13.3 Logarithmic Identities
	13.4 Using Logarithm Identities
	13.5 Switching Between Logs and Exponents
	13.6 Natural Logarithms and Exponential Decay
	13.7 Summary
14 Radicals
	14.1 Raising Radicals to Powers
	14.2 Evaluating Expressions With Radicals
	14.3 Radical Conjugates
	14.4 Summary
15 Special Classes of Functions
	15.1 Rational Functions and Their Graphs
	15.2 Rational Function Equations and Inequalities
	15.3 Even and Odd Functions
	15.4 Monotonic Functions
	15.5 Summary
16 Piecewise Defined Functions
	16.1 Introduction to Piecewise Defined Functions
	16.2 Absolute Value
	16.3 Graphing Absolute Value
	16.4 Floor and Ceiling
	16.5 Problem Solving with the Floor Function
	16.6 Summary
17 More Sequences and Series
	17.1 Algebra of Recursive Sequences
	17.2 Telescoping
	17.3 Sums of Polynomial Series
	17.4 Arithmetico-Geometric Series
	17.5 Finite Differences
	17.6 Summary
18 More Inequalities
	18.1 Mean Inequality Chain
	18.2 The Rearrangement Inequality
	18.3 When Formulas Fail
	18.4 Summary
19 Functional Equations
	19.1 Finding Values
	19.2 Finding Functions with Substitution
	19.3 Separation
	19.4 Cyclic Functions
	19.5 Summary
20 Some Advanced Strategies
	20.1 Symmetry
	20.2 Substitution for Simplification
	20.3 Method of Undetermined Coefficients
	20.4 Constructing Polynomials From Roots
	20.5 Common Divisors of Polynomials
	20.6 Symmetric Sums Revisited
	20.7 Summary
References
Hints to Selected Problems
Index