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
This note explains basic concepts like sets and relations and progressing
to advanced topics such as group theory, rings, and fields also it covers
fundamental theorems like Lagranges theorem and explores key concepts like
permutations and quotient groups.
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.
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
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.
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.