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 note covers some
algebra, Algebraic sets, More algebra, Halbert’s nullstellensatz, Topology of
affine algebraic sets, A brief detour into plane curves, Quasiprojective
varieties, Plane projective curves and bezouts theorems.
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:
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
Noncommutative Rings.
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 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 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.
The book is written in a very clear and
pleasing style. This old textbook truly depicts Leonhard Euler's genius. Too bad
Euler's Identity was not mentioned in here.
Author(s): Leonhard Euler, John Hewlett, Francis Horner, Jean
Bernoulli, Joseph Louis Lagrange
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.
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 Teacher’s Function, The Use of Sewing Cards,
The Story of a Working Hypothesis, Macbeth’s Mistake, Jacob’s Ladder.