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Algebra
Online
15 WeeksQuick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | Pondicherry University |
The Syllabus
- Polar Representation of Complex Numbers
- nth Root of Unity
- De Moivre’s Theorem for Rational Indices
- Equivalence Relation
- Composition of Functions and Invertible Functions
- One-to-one Correspondence and Cardinality of a set
- Division Algorithm
- Divisors and Euclidean Algorithm
- Congruence Relation Between Integers
- Statement of Fundamental Theorem of Arithmetic and Principle of Mathematical Induction
- Systems of Linear Equations, Row Reduction and Echelon Forms
- The Matrix Equation Ax=b and the Solution Set of Linear System
- Application Of Linear System and Linear Independence
- Introduction to linear transformation and matrix of a linear transformation
- The Inverse of a Matrix
- Subspace of ln and Rank of a matrix
- Eigen value and Eigen vector - I
- Eigen value and Eigen vector - II
- Diagonalization of Matrix
- Problems
- Groups Introduction - I
- Groups Introduction - II
- Subgroups
- Elementary Properties of Abelian Groups
- Elementary Properties of Non-Abelian Groups
- The Group of Integer Modulo n
- Complex Roots of Unity
- Cyclic Group
- General Linear Group
- The Group of Symmetries
- Subgroup Generated by a Subset
- Cosets and Index of Subgroups
- Properties of Group Homomorphisms
- Normal Subgroups
- Quotient Groups
- Class Equation
- Direct Product of a Finite Number of Groups
- Fundamental Theorem of Finite Abelian Groups
- Cayley Theorem and Problems in Group Theory
- Ring-Introduction
- Class of Ring
- Rings from Number Systems
- Ring of Real Quaternions and Rings of Continuous Functions
- Rings of Matrices
- Polynomial Rings
- Subrings and Ideals
- Set of Zero Divisors and Group of Units
- Properties of Ring Homomorphisms
- Operations on Ideals
- Integral Domains and Fields
- Maximal Ideals and Prime Ideals
- Euclidian Domains and Principal Ideal Domains
- Unique Factorization Domains
Instructors
Articles
31 Aug'25, 03:44 PM
17 Jun'25, 10:59 AM
28 Feb'24, 08:51 AM
28 Feb'24, 07:16 AM
31 Aug'25, 03:44 PM
17 Jun'25, 10:59 AM
28 Feb'24, 08:51 AM
28 Feb'24, 07:16 AM