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Algebra - I | Mathematics for B.Sc. Students | Semester II (Core IV) | NEP 2020 Odisha

Algebra - I | Mathematics for B.Sc. Students | Semester II (Core IV) | NEP 2020 Odisha

Author : H K Dass, Rajnish Verma & Rama Verma

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  • ISBN : 9789364689212
  • Pages : 296
  • Binding : Paperback
  • Language : English
  • Imprint : S Chand Publishing
  • © year : 2025
  • Size : 6.50*9.25

Price : 325.00 260.00

This textbook has been designed to meet the needs of B.Sc. Second Semester (Core IV) students of Mathematics as per the Common Minimum Syllabus prescribed for Odisha University and other Universities and Colleges under the recommended National Education Policy 2020 in Odisha.

The book provides a structured and comprehensive exploration of fundamental algebraic concepts, including Permutation Groups, Isomorphisms, Normal Subgroups, Rings, Fields, and Polynomial Factorization. Each chapter is carefully crafted with clear explanations, step-by-step proofs, illustrative examples, and practical applications to enhance conceptual understanding. The content progresses from foundational principles to advanced topics, ensuring a seamless learning experience.

A dedicated section on the Evolution of Algebra enriches students' appreciation of the subject. Additionally, the book features real-world examples, such as Cosets and the Rubik's Cube, as well as applications of Polynomial Factorization, making abstract concepts more tangible and engaging.

  • Very lucid and logical presentation of concepts, for easy and quick understanding.
  • Close to 200 examples for easy understanding of concepts
  • More than 1000 exercise questions strengthen the well-explained theoretical concepts.
  • A section on Multiple Choice Questions (MCQs) to enhance understanding and exam readiness.

The book is a must-have resource for mastering algebra and building a strong foundation for future mathematical pursuits.

Historical Developments in Algebra
Expansion of "Galois Theory" or "Representation Theory"

Unit-I

1. Permutation Groups and Notations
2. Isomorphism and Automorphisms
3. Cosets, Lagrange's Theorem and Consequences

Unit-II

4. External and Internal Direct Products
5. Normal Subgroups and Factor Groups
6. Homomorphism and Isomorphism

Unit-III

7. Ring and Field

Unit-IV

8. Factorization of Polynomials
9. Unique Factorization in Z[x]
10. Divisibility in Integral Domains

Examination Paper

This textbook has been designed to meet the needs of B.Sc. Second Semester (Core IV) students of Mathematics as per Common Minimum Syllabus prescribed for Odisha University and other Universities and Colleges under the recommended National Education Policy 2020 in Odisha.

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