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Modern Algebra

Modern Algebra. Instructor: Prof. Manindra Agrawal, Department of Computer Science and Engineering, IIT Kanpur. This course discusses topics in abstract algebra, the study of algebraic structures such as Groups, Rings and Fields. The course will focus on teaching the definitions and basic properties of these algebraic structures. And the course will see applications of the algebraic structures in mathematics and computer science. (from nptel.ac.in)

Lecture 07 - Introduction

This lecture covers the following topics: 1. Ring definition and examples. 2. Unique factorization in rings.

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Groups

Lecture 01 - Introduction to Abstraction

Lecture 02 - Subgroups and Homomorphism

Lecture 03 - Isomorphism

Lecture 04 - Quotienting

Lecture 05 - Structure Theorem

Lecture 06 - Applications

Rings

Lecture 07 - Introduction

Lecture 08 - Failure of Unique Factorization

Lecture 09 - Birth of Ideals

Lecture 10 - Ideal Arithmetic

Lecture 11 - Special Ideals

Lecture 12 - Dedekind Domains

Lecture 13 - Quotient Rings

Fields

Lecture 14 - Fields

Lecture 15 - Cauchy Sequences and Real Numbers

Lecture 16 - Properties of Fields

Lecture 17 - Finite Fields

Lecture 18 - Application of Fields