This book aims
to give an introduction to using GAP with material appropriate for an
undergraduate abstract algebra course. It does not even attempt to give an
introduction to abstract algebra, there are many excellent books which do this.
Topics covered includes: The GGAP user interface, Rings, Groups, Linear Algebra,
Fields and Galois Theory, Number Theory.
This text is
intended for a one- or two-semester undergraduate course in abstract algebra.
Topics covered includes: The Integers, Groups, Cyclic Groups, Permutation
Groups, Cosets and Lagrange’s Theorem, Algebraic Coding Theory, Isomorphisms,
Normal Subgroups and Factor Groups, Matrix Groups and Symmetry, The Sylow
Theorems , Rings, Polynomials, Integral Domains, Vector Spaces, Finite Fields.
book covers the following topics: Group Theory, Basic Properties of
Groups, Ring Theory, Set Theory, Lagrange's Theorem, The Symmetric Group Redux,
Kernels of Homomorphisms and Quotient Groups and Normal Subgroups.
book explains the following topics: Group Theory, Subgroups, Cyclic
Groups, Cosets and Lagrange's Theorem, Simple Groups, Solvable Groups, Rings and
Polynomials, Galois Theory, The Galois Group of a Field Extension, Quartic
This note explains the following
topics: Linear Transformations, Algebra Of Linear Transformations,
Characteristic Roots, Characteristic Vectors, Matrix Of Transformation,
Canonical Form, Nilpotent Transformation, Simple Modules, Simi-simple Modules,
Free Modules, Noetherian And Artinian Modules, Noetherian And Artinian Rings,
Smith Normal Form, Finitely Generated Abelian Groups.
This book covers the following topics related to Abstract Algebra:
The Integers, Foundations, Groups, Group homomorphisms and isomorphisms, Algebraic structures, Error correcting codes,
Roots of polynomials, Moduli for polynomials and Nonsolvability by radicals.
topics: Preliminaries, Integers, Groups, Cyclic Groups, Permutation Groups,
Cosets and Lagrange's Theorem, Introduction to Cryptography, Algebraic Coding
Theory, Isomorphisms, Homomorphisms, Matrix Groups and Symmetry, The Structure of Groups, Group
Actions, The Sylow Theorems, Rings, Polynomials, Integral Domains, Lattices and
Boolean Algebras, Vector Spaces, Fields and Galois Theory
Author(s): Thomas W. Judson, Stephen F. Austin State University
This is a foundational textbook on abstract algebra with emphasis on
linear algebra. Covered topics are: Background and Fundamentals of Mathematics,
Groups, Rings, Matrices and Matrix Rings and Linear Algebra.
book covers the following topics: Binary Operations, Introduction to Groups, The Symmetric Groups, Subgroups, The
Group of Units of Zn, Direct Products of Groups, Isomorphism of Groups, Cosets
and Lagrange s Theorem, Introduction to Ring Theory, Axiomatic Treatment of R N
Z Q and C, The Quaternions, The Circle Group.
Edwin Clark, Department of Mathematics, University of South Florida
This note covers the following topics: Basic Algebra of Polynomials,
Induction and the Well ordering Principle, Sets, Some counting principles, The
Integers, Unique factorization into primes, Prime Numbers, Sun Ze's Theorem,
Good algorithm for exponentiation, Fermat's Little Theorem, Euler's Theorem,
Primitive Roots, Exponents, Roots, Vectors and matrices, Motions in two and
three dimensions, Permutations and Symmetric Groups, Groups: Lagrange's Theorem,
Euler's Theorem, Rings and Fields, Cyclotomic polynomials, Primitive roots,
Group Homomorphisms, Cyclic Groups, Carmichael numbers and witnesses, More on
groups, Finite fields, Linear Congruences, Systems of Linear Congruences,
Abstract Sun Ze Theorem and Hamiltonian Quaternions.
This note covers the following topics: Natural Numbers, Principles of
Counting, Integers and Abelian groups, Divisibility, Congruences, Linear
Diophantine equations, Subgroups of Abelian groups, Commutative Rings, A little
Boolean Algebra, Fields, Polynomials over a Field, Quotients of Abelian groups,
Orders of Abelian groups, Linear Algebra over, Nonabelian groups, Groups of
Symmetries of Platonic Solids, Counting Problems involving Symmetry, Proofs of
theorems about group actions, Homomorphisms between groups, The Braid Group, The
Chinese remainder theorem, Quotients of polynomial rings, The finite Fourier
This study guide now contains over 600 problems, and more than half
have detailed solutions, while about a fifth have either an answer or a hint. The ideal way to
use the study guide is to work on a solved problem, and if you get stuck, just
peek at the solution long enough to get started again.
This book focuses on
the study of the noncommutative aspects of rings and modules, and the style will
make it accessible to anyone with a background in basic abstract algebra.
Covered topics are: Rings, Modules, Structure Of Noncommutative Rings,
Representations Of Finite Groups.
The book, Algebra: Abstract and Concrete provides a thorough introduction to
algebra at a level suitable for upper level
undergraduates and beginning graduate students. The book addresses the
conventional topics: groups, rings, fields, and linear algebra, with symmetry as
a unifying theme.