**Course: **Algebra-II

**Content:** **>>** Introduction of Group Theory : Definition and examples taken from various branches (example from number system, roots of Unity, 2 ×2 real matrices, non singular real matrices of a fixed order). Elementary properties using definition of Group. Definition and examples of sub- group – Statement of necessary and sufficient condition and its applications. **>>** Definitions and examples of (i) Ring, (ii) Field, (iii) Sub-ring, (iv) Sub- field. **>>** Concept of Vector space over a Field : Examples, Concepts of Linear combinations, Linear dependence and independence of a finite number of vectors, Sub- space, Concepts of generators and basis of a finitedimensional vector space. Problems on formation of basis of a vector space (No proof required). **>>** Real Quadratic Form involving not more than three variables (problems only). **>>** Characteristic equation of square matrix of order not more than three determination of Eigen Values and Eigen Vectors (problems only). Statement and illustration of Cayley-Hamilton Theorem.

**Syllabus:** B.Sc. Mathematics General courses

**University:** All Indian Universities

**Learning Objective:>>** Introduce students to Group Theory , Ring & Field.

**>>**Learn to find and use eigenvalues and eigenvectors of a matrix.

**>>**Learn about and work with vector spaces and subspaces.

**Learning Methods :** See here

**How to buy a course and join PALMATHS**** :** See here

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