>> 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
>> 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.