Algebra B.Sc. 2nd Year 3rd Sem.Paper 1st(Part-A) Vandana

Contents:

1. Introductory Concepts (Pages 1-15)
   • Provides a solid foundation in basic algebraic concepts essential for understanding more advanced topics.
2. Properties of Integers (Unit-1)
   • Discusses fundamental properties and theorems related to integers.
3. Elementary Theory of Groups (Unit-2)
   • Introduces the concept of groups, a fundamental structure in abstract algebra.
4. Permutation Groups (Unit-3)
   • Explores permutation groups, including their applications and properties.
5. Coset Decomposition and Direct Product (Unit-4)
   • Examines the decomposition of groups into cosets and the direct product of groups.
6. Homomorphism, Isomorphism, and Normal Subgroups
   • Discusses advanced group theory concepts, including homomorphism, isomorphism, and the role of normal subgroups.

Description:

“Algebra” is an essential textbook for B.Sc. 2nd Year, 3rd Semester students, meticulously crafted by a team of distinguished authors: Dr. G.P. Singh, Dr. Bindu Kumari, Dr. Naveen Kumar Shrivastav, Dr. A.K. Ray, and Dr. Suraj Kumar Shukla. Published by Vandana Publication Gorakhpur, this 148-page book is tailored to provide a deep understanding of algebraic principles.

The book is structured into six key sections, each focusing on crucial areas of algebra:

1. Introductory Concepts (Pages 1-15) sets the stage by covering basic algebraic notions.
2. Properties of Integers delves into the essential properties and theorems involving integers.
3. Elementary Theory of Groups introduces group theory, a cornerstone of abstract algebra.
4. Permutation Groups explores the properties and applications of permutation groups.
5. Coset Decomposition and Direct Product discusses how groups can be broken down into cosets and explores the concept of the direct product.
6. Homomorphism, Isomorphism, and Normal Subgroups covers advanced group theory topics crucial for a deeper understanding of algebra.

This book is an invaluable resource for students, providing clear explanations, detailed examples, and practical problem-solving techniques. It is designed to build a robust foundation in algebra, preparing students for more advanced studies and applications in mathematics.