This PDF Lectures covers
the following topics related to Basic Concepts of Algebra : The Real-Number
System, Integer Exponents, Scientific Notation, and Order of Operations,
Addition, Subtraction, and Multiplication of Polynomials, Factoring, Rational
Expressions, Radical Notation and Rational Exponents, The Basics of Equation
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
The contents include:
Preliminaries About the Integers, Polynomials, and Matrices, Vector Spaces Over
Q, R, and C, Inner-product Spaces, Groups and Group Actions, Theory of a Single
Linear Transformation , Multilinear Algebra, Advanced Group Theory, .
Commutative Rings and Their Modules, Fields and Galois Theory, Modules Over
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
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 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 book is designed specifically as a College
Algebra course for prospective STEM students. Topics covered includes: Review of Beginning/Intermediate
Algebra, Functions and Related Topics, Polynomial Functions, Rational Functions,
Exponential and Logarithmic Functions.
This book is written for pupils in the upper grades of grammar
schools and the lower grades of high schools. The introduction of the simple
elements of Algebra into these grades will, it is thought, so stimulate the
mental activity of the pupils, that they will make considerable progress in
Algebra without detriment to their progress in Arithmetic, even if no more time
is allowed for the two studies than is usually given to Arithmetic alone.
This note covers the following topics:
From Arithmetic To Algebra, The Making of Algebras, Simultaneous Problems,
Partial Solution: Elements of Complexity, Mathematical Certainty, The First
Hebrew Algebra, The Limits of the Teacherís Function, The Use of Sewing Cards,
The Story of a Working Hypothesis, Macbethís Mistake, Jacobís Ladder.