Lecture Notes on Abstract Algebra by Aditya Sengupta

Lecture Notes on Abstract Algebra by Aditya Sengupta

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.

Author(s): Aditya Sengupta

86 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

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

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