This course note
focuses on traditional algebra topics that have found greatest application in
science and engineering as well as in mathematics. Major topics covered
includes: Groups, Subgroups, Cosets, Cyclic Groups, Permutation Groups,
Conjugation in Sn, Isomorphisms, Homomorphisms and Kernels, Quotient Groups, The
Isomorphism Theorems, Presentations and Groups of Small Order, Sylow Theorems
and Applications, Rings, Ring Homomorphisms and Ideals, Field of Fractions,
Euclidean Domains, Polynomial Rings.
This PDF Lectures covers the following topics related to Elementary
Algebra : Foundations, Solving Linear Equations and Inequalities, Math Models,
Graphs, Systems of Linear Equations, Polynomials, Factoring, Rational
Expressions and Equations, Roots and Radicals, Quadratic Equations.
Author(s): Lynn Marecek, Santa Ana College, Maryanne Anthony-smith,
Santa Ana College, Andrea Honeycutt Mathis, Northeast Mississippi Community
College
The contents include: Mathematical Notation and Symbols, Indices,
Simplification and Factorisation, Arithmetic of Algebraic Fractions, Formulae
and Transposition.
Author(s): HELM, Mathematics Education Centre, Loughborough
University
The contents
include: Basic Algebraic Structures, The Integers, Other Examples of Rings,
Quotients and Isomorphisms, Finite Groups, Modules, Galois Theory, Commutative
Algebra, Set Theory.
Author(s): Rui L. Fernandes, University of Illinois
at Urbana-Champaign, Manuel Ricou, Instituto Superior Tecnico
This
note covers the following topics: The Laws of Algebra, Coordinates,The Cartesian
Coordinate Plane, Graphs of Equations, Three Interesting Curves, Functions,
Function Notation, Linear and Quadratic Functions, Polynomial Functions,
Rational Functions, Function Composition, Exponential and Logarithmic Functions,
Systems of Equations, Sequences and Series, Complex Numbers and the Fundamental
Theorem of Algebra.
This note describes the
following topics: Functions and Their Graphs, Intercepts, Zeros, and Solutions,
Polynomials and Rational Functions, Systems of Equations and Inequalities,
Matrices and Determinants, Sequences and Probability, Conics and Parametric
Equations.
This is a set of lecture notes on
introductory school algebra written for middle school teachers. Topics covered
includes: Symbolic Expressions, Transcription of Verbal Information into
Symbolic Language, Linear Equations in One Variable, Linear Equations in Two
Variables and Their Graphs, Simultaneous Linear Equations, Functions and Their
Graphs, Linear functions and proportional reasoning, Linear Inequalities and
Their Graphs, Exponents, Quadratic Functions and Their Graphs, The Quadratic
Formula and Applications.
This lecture note
discusses unique factorization and the modern theory of rings and their ideals,
emphasizing Euclidean domains. Other algebraic structures (groups, fields) also
are introduced.
This book covers the following topics: Subnormal
and Normal series, Invariant Series and Chief Series, Commutator Subgroup,
Central series and Field extensions, Field Extensions and constructions,
Algebraic Extension and Transcendental Extensions, Roots Of Polynomials, Simple
Extensions, Construction By Straight Edge and Compass, Symmetric Rational
Functions, Normal Extension, Galois Theory and Finite Fields.
Author(s): Guru Jambheshwar University of
Science and Technology, Hisar
First chapter explains the basic arithmetic and algebraic properties of
the familiar number systems the integers, rational numbers, real numbers, and
the possibly less familiar complex numbers. Second chapter introduces some basic
ideas from Number Theory, the study of properties of the natural numbers and
integers.3rd chapter, describes algebra of polynomials in a variable x with
coefficients in a commutative ring S.
This book covers the following
topics: Multiplication of monomial expressions, Factors found by rearrangement
and grouping of terms, Bemainder Theorem, Discussion of roots of a quadratic
equation, Irrational equations, nationalizing factors, Radix fractions, General
convergent, Reduction of quadratic surds to continued fractions, Theory op
Numbers, Congruences, Multiplication of determinants.
Beginning and Intermediate
Algebra is an open source book written by Tyler Wallace. This book covers the
following topics: Pre-Algebra, Solving Linear Equations, Inequalities, Systems
of Equations, Graphing, Polynomials, Factoring, Quadratics, Rational
Expressions, Functions and Radicals.