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Editorial Reviews. About the Author. One of the world's leading researchers in abstract algebra, Book 1 of 2 in Basic Algebra (2 Book Series). ISBN Chapter 1: Introduction to Basic Algebra Ideas. Introduction: The Ideas of Algebra ; Lesson 0. Translating Words into Math Symbols; Lesson 1. Simple Operations. Looking for books on Basic Algebra? Check our section of free e-books and guides on Basic Algebra now! This page contains list of freely available E-books, .
It allows the formulation of functional relationships. Polynomials Main article: Polynomial A polynomial is an expression that is the sum of a finite number of non-zero terms , each term consisting of the product of a constant and a finite number of variables raised to whole number powers. A polynomial expression is an expression that may be rewritten as a polynomial, by using commutativity, associativity and distributivity of addition and multiplication.
A polynomial function is a function that is defined by a polynomial, or, equivalently, by a polynomial expression. The two preceding examples define the same polynomial function.
Two important and related problems in algebra are the factorization of polynomials , that is, expressing a given polynomial as a product of other polynomials that can not be factored any further, and the computation of polynomial greatest common divisors. A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.
Abstract algebra Main articles: Abstract algebra and Algebraic structure Abstract algebra extends the familiar concepts found in elementary algebra and arithmetic of numbers to more general concepts. Here are listed fundamental concepts in abstract algebra.
Sets : Rather than just considering the different types of numbers , abstract algebra deals with the more general concept of sets: a collection of all objects called elements selected by property specific for the set. All collections of the familiar types of numbers are sets.
Set theory is a branch of logic and not technically a branch of algebra. The notion of binary operation is meaningless without the set on which the operation is defined.
Identity elements : The numbers zero and one are abstracted to give the notion of an identity element for an operation. Zero is the identity element for addition and one is the identity element for multiplication.
Not all sets and operator combinations have an identity element; for example, the set of positive natural numbers 1, 2, 3, Inverse elements : The negative numbers give rise to the concept of inverse elements.
Associativity : Addition of integers has a property called associativity. That is, the grouping of the numbers to be added does not affect the sum.
This property is shared by most binary operations, but not subtraction or division or octonion multiplication. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles.
Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. Lynn Marecek has focused her career on meeting the needs of developmental math students.
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Table of Contents 1. Foundations 2. Solving Linear Equations and Inequalities 3.
Math Models 4.