Abstract Algebra – CSIR-NET June 2026
Starting From: 25 May 2026
By Sunil Bansal

Class Time- 6-8:30pm

Course Description

Build a strong foundation in Abstract Algebra through a systematic approach designed specifically for CSIR-NET Mathematical Sciences. The course moves from basic concepts to advanced theorem-based problem solving with complete syllabus coverage, conceptual understanding, and exam-oriented practice.

Topics Covered

Module 1: Foundations

• Sets, Functions and Relations
• Equivalence Relations
• Partitions and Classes
• Binary Operations

Module 2: Group Theory

• Definition and Examples of Groups
• Subgroups and Cyclic Groups
• Permutation Groups
• Cosets and Lagrange's Theorem
• Normal Subgroups
• Quotient Groups
• Group Homomorphism and Isomorphism
• Kernel and Image
• Cayley's Theorem
• Direct Product of Groups
• Fundamental Theorem of Homomorphism
• Sylow Theorems and Applications

Module 3: Ring Theory

• Definition and Examples of Rings
• Integral Domains and Fields
• Ring Homomorphism
• Ideals and Quotient Rings
• Prime and Maximal Ideals
• Principal Ideal Domains (PID)
• Euclidean Domains
• Unique Factorization Domains (UFD)
• Polynomial Rings

Additional Features

• Basic to Advanced Level Teaching
• Previous Year Question Discussions
• DPP and Practice Sheets
• Live Doubt Sessions
• Strategy Sessions for CSIR-NET June 2026