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%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/Algebra">}
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\section{Algebra\label{algebra}\qquad}

\label{Algebra, etymology}The word \emph{algebra} comes from the ninth
century Arabic book \emph{His\^{a}b al-Jabr w'al-Muqabala}, written by
al-Khowarizmi. The title refers to transposing and combining terms, two
processes used in solving equations. In Latin translations, the title was
shortened to \emph{Aljabr}, from which we get the word \emph{algebra}. The
author's name itself made its way into the English language in the form of
our word \emph{algorithm}.

\subsection{Contents}

\subsubsection{Basic Algebra}

\hyperref{+ Real Numbers}{}{}{al01_02.tex}

\hyperref{+ Exponents and Radicals}{}{}{al01_03.tex}

\hyperref{+ Algebraic Expressions}{}{}{al01_04.tex}

\hyperref{+ Fractional Expressions}{}{}{al01_05.tex}

\subsubsection{Equations and Inequalities}

\hyperref{+ Equations and Inequalities - Introduction}{}{}{al02_00.tex}

\hyperref{+ Linear Equations}{}{}{al02_01.tex}

\hyperref{+ Problems Solving with Linear Equations}{}{}{al02_02.tex}

\hyperref{+ Quadratic Equations}{}{}{al02_03.tex}

\hyperref{+ Complex Numbers}{}{}{al02_04.tex}

\hyperref{+ Other Equations}{}{}{al02_05.tex}

\hyperref{+ Linear Inequalities}{}{}{al02_06.tex}

\hyperref{+ Nonlinear Inequalities}{}{}{al02_07.tex}

\hyperref{+ Absolute Value}{}{}{al02_08.tex}

\subsubsection{Functions and Graphs}

\hyperref{+ The Coordinate Plane}{}{}{al03_01.tex}

\hyperref{+ Graphs of Equations}{}{}{al03_02.tex}

\hyperref{+ Lines}{}{}{al03_04.tex}

\hyperref{+ What Is a Function?}{}{}{al03_05.tex}

\hyperref{+ Graphs of Functions}{}{}{al03_06.tex}

\hyperref{+ Applied Functions}{}{}{al03_07.tex}

\hyperref{+ Transformations of Functions}{}{}{al03_08.tex}

\hyperref{+ Extreme Values of Functions}{}{}{al03_09.tex}

\hyperref{+ Combining Functions}{}{}{al03_10.tex}

\hyperref{+ One-to-One Functions and Their Inverses}{}{}{al03_11.tex}

\subsubsection{Polynomials and Rational Functions}

\hyperref{+ Polynomial Functions and Their Graphs}{}{}{al04_01.tex}

\hyperref{+ Dividing Polynomials}{}{}{al04_03.tex}

\hyperref{+ Real Zeros of Polynomials}{}{}{al04_04.tex}

\hyperref{+ Complex Roots and the Fundamental Theorem of Algebra}{}{}{%
al04_07.tex}

\hyperref{+ Rational Functions}{}{}{al04_08.tex}

\subsubsection{Exponential and Logarithmic Functions}

\hyperref{+ Exponential Functions}{}{}{al05_01.tex}

\hyperref{+ The Natural Exponential Function}{}{}{al05_02.tex}

\hyperref{+ Logarithmic Functions}{}{}{al05_03.tex}

\hyperref{+ Laws of Logarithms}{}{}{al05_04.tex}

\hyperref{+ Exponential and Logarithmic Equations}{}{}{al05_05.tex}

\hyperref{+ Applications of Exponential and Logarithmic Functions}{}{}{%
al05_06.tex}

\subsubsection{Systems of Equations and Inequalities}

\hyperref{+ Pairs of Lines}{}{}{al06_01.tex}

\hyperref{+ Systems of Linear Equations}{}{}{al06_02.tex}

\hyperref{+ Inconsistent and Dependent Systems}{}{}{al06_03.tex}

\hyperref{+ The Algebra of Matrices}{}{}{al06_04.tex}

\hyperref{+ Inverses of Matrices and Matrix Equations}{}{}{al06_05.tex}

\hyperref{+ Determinants and Cramer's Rule}{}{}{al06_06.tex}

\hyperref{+ Application: Partial Fractions}{}{}{al06_10.tex}

\subsubsection{Conic Sections}

\hyperref{+ Parabolas}{}{}{al07_01.tex}

\hyperref{+ Ellipses}{}{}{al07_02.tex}

\hyperref{+ Hyperbolas}{}{}{al07_03.tex}

\hyperref{+ Shifted Conics}{}{}{al07_04.tex}

\subsubsection{Counting and Probability}

\hyperref{+ Counting Principles}{}{}{al08_01.tex}

\hyperref{+ Permutations}{}{}{al08_02.tex}

\hyperref{+ Combinations}{}{}{al08_03.tex}

\hyperref{+ Problem Solving with Permutations and Combinations}{}{}{%
al08_04.tex}

\hyperref{+ Probability}{}{}{al08_05.tex}

\hyperref{+ The Union of Events}{}{}{al08_06.tex}

\hyperref{+ The Intersection of Events}{}{}{al08_07.tex}

\hyperref{+ Expected Value}{}{}{al08_08.tex}

\subsubsection{Sequences and Series}

\hyperref{+ Sequences}{}{}{al09_01.tex}

\hyperref{+ Arithmetic and Geometric Sequences}{}{}{al09_02.tex}

\hyperref{+ Series}{}{}{al09_03.tex}

\hyperref{+ Arithmetic and Geometric Series}{}{}{al09_04.tex}

\hyperref{+ Annuities and Installment Buying}{}{}{al09_05.tex}

\hyperref{+ Infinite Geometric Series}{}{}{al09_06.tex}

\hyperref{+ Mathmatical Induction}{}{}{al09_07.tex}

\hyperref{+ The Binomial Theorem}{}{}{al09_08.tex}

\subsection{\ Related Reference Topics}

{\small \hyperref{Algebraic Equations}{}{}{TAB_alg_equations.tex}}

{\small \hyperref{Matrix Algebra}{}{}{MA_contents.tex}}

\subsection{\ Related Scientific Notebook Topics}

{\small \hyperref{Integers and Fractions}{}{}{../../Help/DM2-1.tex#Numbers}}

{\small \hyperref{Elementary Number Theory}{}{}{../../Help/DM2-2.tex#Prime
factorization}}

{\small \hyperref{Real Numbers}{}{}{../../Help/DM2-3.tex#Basic operations}}

{\small \hyperref{Complex Numbers}{}{}{../../Help/DM2-5.tex#Complex numbers}}

{\small \hyperref{Polynomials and Rational Expressions}{}{}{%
../../Help/DM3-1.tex#Polynomials}}

{\small \hyperref{Solving Polynomial Equations}{}{}{%
../../Help/DM3-3.tex#Exact solutions}}

{\small \hyperref{Exponents and Logarithms}{}{}{%
../../Help/DM3-5.tex#Exponential function}}

{\small \hyperref{Matrix Algebra}{}{}{../../Help/DM8-1.tex#Matrix Algebra}}

{\small \hyperref{Applied Modern Algebra}{}{}{../../Help/DM12.tex}}

\rule{0.67in}{0.01in}

\quad {\small Math Index entries: \hyperref{Addition}{}{}{%
../../Help/DMIndex.tex#Addition}, \hyperref{Average}{}{}{%
../../Help/DMIndex.tex#Average}, \hyperref{Binomial}{}{}{%
../../Help/DMIndex.tex#Binomial distribution}, \hyperref{Complex numbers}{}{%
}{../../Help/DMIndex.tex#Complex numbers}, \hyperref{Determinant}{}{}{%
../../Help/DMIndex.tex#Determinant}, \hyperref{Discriminant}{}{}{%
../../Help/DMIndex.tex#Discriminant}, \hyperref{Division}{}{}{%
../../Help/DMIndex.tex#Division}, \hyperref{Exponent}{}{}{%
../../Help/DMIndex.tex#Exponent}, \hyperref{Factor}{}{}{%
../../Help/DMIndex.tex#Factor}, \hyperref{Factorial}{}{}{%
../../Help/DMIndex.tex#Factorial}, \hyperref{Fraction}{}{}{%
../../Help/DMIndex.tex#Fractions}, \hyperref{Geometric mean}{}{}{%
../../Help/DMIndex.tex#Geometric mean}, \hyperref{Greatest common divisor}{}{%
}{../../Help/DMIndex.tex#Greatest common divisor}, \hyperref{Harmonic mean}{%
}{}{../../Help/DMIndex.tex#Harmonic mean}, \hyperref{Integers}{}{}{%
../../Help/DMIndex.tex#Integers}, \hyperref{Long division}{}{}{%
../../Help/DMIndex.tex#Long division}, \hyperref{Number theory}{}{}{%
../../Help/DMIndex.tex#Number theory}, \hyperref{Partial fractions}{}{}{%
../../Help/DMIndex.tex#Partial fractions}, \hyperref{Polynomials}{}{}{%
../../Help/DMIndex.tex#Polynomials}, \hyperref{Quadratic equations}{}{}{%
../../Help/DMIndex.tex#Quadratic equations}, \hyperref{Radians}{}{}{%
../../Help/DMIndex.tex#Radians}, \hyperref{Radicals}{}{}{%
../../Help/DMIndex.tex#Radicals}, \hyperref{Rational expressions}{}{}{%
../../Help/DMIndex.tex#Rational expressions}, \hyperref{Real numbers}{}{}{%
../../Help/DMIndex.tex#Real numbers}, \hyperref{Subtraction}{}{}{%
../../Help/DMIndex.tex#Subtraction}, \hyperref{Summation notation}{}{}{%
../../Help/DMIndex.tex#Summation notation}}

\noindent \hrulefill

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\noindent \hrulefill

\CustomNote[Acknowledgements]{Margin Hint}{%
Much of the data in the algebra reference materials is an adaptation, with
permission, of information in 
\[
\begin{tabular}{l}
{\Large College Algebra }Second Edition \\ 
{\Large James Stewart }McMaster Universitiy \\ 
{\Large Lothar Redlin} Pennsylvania State University \\ 
{\Large Saleem Watson} California State University, Long Beach \\ 
Copyright 1996, ISBN 0 534-33983-2 \\ 
Brooks/Cole Publishing Company \\ 
An International Thomson Publishing Company
\end{tabular}
\]
}

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