Abstract Algebra | B.A./B.Sc. 4th Semester DSC | All Chhattisgarh State Universities | NEP 2020 | Useful for CSIR NET, GATE MA & IIT JAM | Dr. H.K. Pathak

Abstract Algebra — Group Theory, Ring Theory, Vector Spaces, Linear Transformations — is the subject that separates students who clear CSIR NET, GATE MA, and IIT JAM from those who don't. This 500-page book covers all four areas completely, in one volume, with previous year papers and MCQs for every topic.  Written by Dr. H.K. Pathak, Ex-Professor and Former Head, School of Studies in Mathematics, Pt. Ravishankar Shukla University (PRSU) Raipur, with 3,400+ Google Scholar citations, this book follows the exact NEP 2020 syllabus for B.A./B.Sc. 4th Semester Discipline Specific Compulsory (DSC) at all Chhattisgarh State Universities.  WHAT THIS BOOK COVERS (All 4 Units as per CG NEP 2020 DSC Syllabus): Unit I — Isomorphism Theorems, Cyclic and Permutation Groups: Group homomorphism and isomorphism; First, Second and Third isomorphism theorems; Cyclic groups, Classification of subgroups; Permutation group, Even and odd permutations; Cayley's theorem Unit II — Ring, Field and Integral Domain, Ideals: Rings, Subrings, Integral domain, Characteristic; Ring Homomorphism, Ideals, Quotient Rings; Field of Quotients; Euclidean Rings, Polynomial Rings; Eisenstein Criterion; Polynomial rings over commutative rings; Unique Factorization Domain (UFD) Unit III — Vector Spaces: Definition and examples; Subspaces, Linear span; Linear dependence and independence; Basis, Finite dimensional vector spaces; Existence theorem for bases; Dimension theorem; Quotient space Unit IV — Linear Transformation: Representation as matrices; Algebra of linear transformations; Rank Nullity theorem; Change of basis; Dual space, Bi-dual space; Natural isomorphism; Adjoint of a linear transformation  CSIR NET, GATE MA & IIT JAM: Units I and II (Group Theory with isomorphism theorems, Rings, Fields, Eisenstein Criterion, UFD) form approximately 20-25% of CSIR NET Pure Mathematics and are major topics in GATE MA and IIT JAM. Units III and IV (Vector Spaces, Linear Transformations, Rank-Nullity, Dual space) are equally significant across all three exams. This single book covers all these exam-critical topics completely.  Published by Shree Shiksha Sahitya Prakashan, Meerut. Includes: Previous Year Solved Papers, Solved Examples, MCQs, Objective Questions, HOTS Questions.