Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
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
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 Scott M. LaLonde
This note explains the following topics: What is Abstract Algebra, The integers mod n, Group Theory, Subgroups, The Symmetric and Dihedral Groups, Lagrange’s Theorem, Homomorphisms, Ring Theory, Set Theory, Techniques for Proof Writing.
Author(s): Scott M. LaLonde
151 Pages
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
Abstract Algebra by Romyar Sharif
This note covers the following topics: Set theory, Group theory, Ring theory, Isomorphism theorems, Burnsides formula, Field theory and Galois theory, Module theory, Commutative algebra, Linear algebra via module theory, Homological algebra, Representation theory.
Author(s): Romyar Sharif
328 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 Theory and Applications
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.
Author(s): Thomas W. Judson
444 Pages
This 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.
Author(s): Scott M. LaLonde
151 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
Introduction to Abstract Algebra by Samir Siksek
This book covers the following topics: Algebraic Reorientation, Matrices, Groups, First Theorems, Orders and Lagrange’s Theorem, Subgroups, Cyclic Groups and Cyclic Subgroups, Isomorphisms, Cosets, Quotient Groups, Symmetric Groups, Rings and Fields.
Author(s): Samir Siksek
139 Pages
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 With Applications
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.
Author(s): Irwin Kra
187 Pages
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
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
This note covers the following topics related to Abstract Algebra: Topics in Group Theory, Rings and Polynomials, Introduction to Galois Theory, Commutative Algebra and Algebraic Geometry.
Author(s): Dr. David R. Wilkins
NA Pages
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
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