Notes on Abstract Algebra

Abstract Algebra by Paul Garrett

This note on Abstract Algebra by Paul Garrett covers the topics like The integers, Groups, The players: rings, fields , Commutative rings , Linear Algebra :Dimension, Fields, Some Irreducible Polynomials, Cyclotomic polynomials, Finite fields, Modules over PIDs, Finitely generated modules, Polynomials over UFDs, Symmetric groups, Naive Set Theory, Symmetric polynomials, Eisenstein criterion, Vandermonde determinant, Cyclotomic polynomials, Roots of unity, Cyclotomic, Primes in arithmetic progressions, Galois theory, Solving equations by radicals, Eigen vectors, Spectral Theorems, Duals, naturality, bilinear forms, Determinants, Tensor products and Exterior powers.

Author(s): Paul Garrett

412 Pages

Abstract Algebra Theory and Applications

This PDF covers the following topics related to Abstract Algebra : The Integers, Groups, Cyclic Groups, Permutation Groups, Cosets and Lagrange’s Theorem, Matrix Groups and Symmetry, Isomorphisms, Homomorphisms, The Structure of Groups, Group Actions, Vector Spaces.

Author(s): Thomas W. Judson

442 Pages

Abstract Algebra by Santiago Canez

This PDF covers the following topics related to Abstract Algebra : Introduction to Groups, Integers mod n , Dihedral Groups, Symmetric Groups, Homomorphisms, Group Actions, Some Subgroups, Cyclic Groups, Generating Sets, Zorn’s Lemma, Normal Subgroups, Cosets and Quotients, Lagrange’s Theorem, First Isomorphism Theorem, More Isomorphism Theorems, Simple and Solvable Groups, Alternating Groups, Orbit-Stabilizer Theorem, More on Permutations, Class Equation, Conjugacy in Sn, Simplicity of An, Sylow Theorems, More on Sylow, Applications of Sylow, Semidirect Products, Classifying Groups, More Classifications, Finitely Generated Abelian, Back to Free Groups.

Author(s): Santiago Canez, Northwestern University

103 Pages

Abstract Algebra by Ulrich Meierfrankenfeld

This PDF covers the following topics related to Abstract Algebra : Groups, Sets, Functions and Relations, Definition and Examples, Basic Properties of Groups, Subgroups, Homomorphisms, Lagrange’s Theorem, Normal Subgroups, The Isomorphism Theorems, Group Actions and Sylow’s Theorem, Group Action, Sylow’s Theorem, Field Extensions, Vector Spaces, Simple Field Extensions, Splitting Fields, Separable Extension, Galois Theory, Sets, Equivalence Relations, Bijections, Cardinalities, List of Theorems, Definitions, etc, List of Theorems, Propositions and Lemmas, Definitions from the Lecture Notes, Definitions from the Homework.

Author(s): Ulrich Meierfrankenfeld, Department of Mathematics, Michigan State University

149 Pages

Advanced Abstract Algebra by Manonmaniam Sundaranar University

This book covers the following topics: Group, Normal subgroups and Quotient groups, homomorphism, isomorphism, Cayleys theorem, permutation groups, Sylow’s Theorems, Rings,Polynomial rings, Vector spaces, Extension field.

Author(s): Manonmaniam Sundaranar University

109 Pages

Notes on Abstract Algebra by John Perry

This note covers the following topics: Integers, monomials, and monoids, Direct Products and Isomorphism, Groups, Subgroups, Groups of permutations, Number theory, Rings, Ideals, Rings and polynomial factorization, Grobner bases.

Author(s): John Perry

314 Pages

Honors Abstract Algebra

This note describes the following topics: Peanos axioms, Rational numbers, Non-rigorous proof of the fundamental theorem of algebra, polynomial equations, matrix theory, Groups, rings, and fields, Vector spaces, Linear maps and the dual space, Wedge products and some differential geometry, Polarization of a polynomial, Philosophy of the Lefschetz theorem, Hodge star operator, Chinese remainder theorem, Jordan normal form,Galois theory.

Author(s): Yum-Tong Siu

102 Pages

Introduction to Abstract Algebra by Alexander Paulin

This note explains the following topics: Sets and Functions, Factorization and the Fundamental Theorem of Arithmetic, Groups, Permutation Groups and Group Actions, Rings and Fields, Field Extensions and Galois Theory, Galois Theory.

Author(s): Alexander Paulin

83 Pages

Lecture Notes for Abstract Algebra I

This note covers the following topics: Group Theory, classification of cyclic subgroups, cyclic groups, Structure of Groups, orbit stabilizer theorem and conjugacy, Rings and Fields, homomorphism and isomorphism, ring homomorphism, polynomials in an indeterminant.

Author(s): James S. Cook

177 Pages

Abstract Algebra Lecture Notes

This 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 Polynomials.

Author(s): Dr. David R. Wilkins

NA Pages

Advance Abstract Algebra

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.

Author(s): Dr. Pankaj Kumar

84 Pages

Abstract Algebra Theory and Applications (PDF 442P)

Covered 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

442 Pages

Elements of Abstract and Linear Algebra

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.

Author(s): Edwin H. Connell

NA Pages

Elementary Abstract Algebra

This 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.

Author(s): W Edwin Clark, Department of Mathematics, University of South Florida

105 Pages

Intro Abstract Algebra

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.

Author(s): Paul Garrett

200 Pages

Algebra Abstract and Concrete

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.

Author(s): Frederick M. Goodman

NA Pages