This note covers the following topics: 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 Application.
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 note covers the following topics: Group Theory, Exercises on Group
Theory, Ring Theory, Exercises on Ring Theory, Field Theory, Exercises for Field
Theory, Galois Theory, Exercises on Galois Theory.
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 the following topics:
Groups, Subgroups, Applications to number theory, Linear Combinations, Vector
Spaces and Linear Algebra, Subspaces, Linear Transformations, Kernel and Image,
Eigenvalues and eigenvectors, Error-correcting codes.
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 in such a way as to maintain
maximum flexibility and usability. This textbook will effectively enable
traditional or nontraditional approaches to elementary algebra. Topics covered
includes: Real Numbers and Their Operations, Linear Equations and Inequalities,
Graphing Lines, Solving Linear Systems, Polynomials and Their Operations,
Factoring and Solving by Factoring, Rational Expressions and Equations, Radical
Expressions and Equations, Solving Quadratic Equations and Graphing Parabolas.
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.
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.
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.
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.