Abstract Algebra
by Dr. H.K. Pathak
₹430
Useful for
About this book
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, 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.
Units I and II (Group Theory with isomorphism theorems, Rings, Fields, Eisenstein Criterion, UFD) form approximately 20-25% of CSIR NET Pure Mathematics. Units III and IV (Vector Spaces, Linear Transformations, Rank-Nullity, Dual space) are equally significant across CSIR NET, GATE MA and IIT JAM. Published by Shree Shiksha Sahitya Prakashan, Meerut.
Syllabus coverage
Unit 1 · Isomorphism Theorems, Cyclic & Permutation Groups
Group homomorphism and isomorphism; First, Second and Third isomorphism theorems; Cyclic groups; Permutation group; Cayley's theorem
Unit 2 · Ring, Field, Integral Domain & Ideals
Rings, Integral domain, Ring Homomorphism, Ideals, Quotient Rings; Field of Quotients; Euclidean Rings; Eisenstein Criterion; Unique Factorization Domain (UFD)
Unit 3 · Vector Spaces
Definition and examples; Subspaces, Linear span; Linear dependence and independence; Basis, Finite dimensional vector spaces; Dimension theorem; Quotient space
Unit 4 · Linear Transformation
Representation as matrices; Algebra of linear transformations; Rank Nullity theorem; Change of basis; Dual space, Bi-dual space; Adjoint of a linear transformation
