The course structure and material follow Harvard course on Abstract Algebra:

http://wayback.archive-it.org/3671/20150528171650/https://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

COURSE CONTENT:

Chapter-1-Matrices

- Row reduction, row echelon matrix and theorems, Inverse matrix, Determinants and theorems, Permutation, Symmetric group, Cyclic notation , transposition, permutation matrix, sign of permutation, Other formulas for determinants, Co-factor matrix.

Chapter-2-Groups

- Law of Composition, Groups and Sub-groups, Abelian Group, General Linear Group, Order of group, Infinite abelian group, cancellation law, permutation group, General Linear group, symmetric group, subgroup, Special linear group, Proper subgroup, Subgroup of the additive group of , gcd and Euclidean algorithm [upto 18];

Here, you will find the content from “Contemporary Abstract Algebra” by J.A. Gallian (7th Edition).

Page for this Book. (Include Prerequisites, Chapters and its contents links, Solutions to Exercises links )

Chapter-5- Permutation Groups

Solutions of Problems in the book.

Order of subgroup generated by two cyclic subgroups in S_6$.

Chapter-6- Isomorphisms

Solutions to the problems in the book.

Chapter-10- Group Homomorphisms

Exercise Solution: [7]

Chapter-12- Introduction to Rings

Exercise Solutions [1-13]

Chapter-14- Ideal and Factor Rings

Chapter-15- Ring Homomorphisms

Notes

Exercise Solutions [1-10+] [12]

Chapter-16- Polynomial Rings

Exercise Solutions [1-18]

Chapter-17- Factorization of Polynomials

Notes and Solutions

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