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Modern Algebra

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Free Online Course: Modern Algebra provided by Swayam is a comprehensive online course, which lasts for 8 weeks long. The course is taught in English and is free of charge. Upon completion of the course, you can receive an e-certificate from Swayam. Modern Algebra is taught by Dr. T. Asir.

IIT Kanpur NPTEL via Swayam
8 weeks long
Finished
Overview

  • Much of Modern Algebra involves properties of sets together with operations. In the course on Modern Algebra, we have discussed about two major concepts namely Groups and Rings. Basically Group is a structure which involves a set with a single operation whereas Ring is a structure which involves a set with two operations.In the course on Modern Algebra we have covered the basic concepts of group theory and ring theory as extensively as possible. This course will serve as a useful tool to any learner who wishes to learn about Algebra, Linear Algebra, Topology and Algebraic Number Theory. Also, this course is essential for all leaners planning for advance degree in mathematics or planning to enter the teaching profession.

Syllabus


  • Week – I
    1. Groups - Introduction2. Subgroups3. Elementary Properties of Abelian Groups4. Elementary Properties of Non Abelian Groups
    Week – II
    5. The group of Integer Modulo n6. Complex Roots of Unity7. Cyclic Group8. General Linear Group
    Week – III
    9. The Group of Symmetries10.Subgroups Generated by a Subset11.Cosets and Index of Subgroups12.Properties of Group Homomorphism and Isomorphism
    Week – IV
    13.Normal Subgroups14.Quotient Groups15.Class Equation16.Direct Product of a Finite Number of Groups
    Week – V
    17.Fundamental Theorem of Finite Abelian Groups18.Cayley's Theorem and Problems in Group Theory19.Rings - Introduction20.Class of Rings
    Week – VI
    21.Rings from Number System22.The Ring of Real Quaternion's and Rings of Continuous Functions23.Ring of Matrices24.Polynomial Rings
    Week – VII
    25.Subrings and Ideals26.Zero - Divisor and Group of Units27.Properties of Ring Homomorphism28.Operations on Ideals
    Week – VIII
    29.Integral Domains and Fields30.Maximal Ideals and Prime Ideals31.Euclidean Domains and Principal Ideal Domain32.Unique Factorization Domains

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