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
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.
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
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.
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.
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.
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 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.
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.
This book is
a gentle introduction to abstract algebra. It is ideal as a text for a one
semester course designed to provide a rst exposure of the subject to students in
mathematics, science, or engineering. Covered topics are: Divisibility in the
Integers, Rings and Fields, Vector Spaces, Spaces, Groups, Sets, Functions, and
Relations.
This
book covers the following topics: Ruler and compass constructions, Introduction to rings, The integers, Quotients
of the ring of integers, Some Ring Theory, Polynomials, Field Extensions.
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
transform.
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.
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.