Module-1(10 hours): General and special linear groups, bilinear forms
Module-2(20 hours): Symplectic groups, symmetric forms, quadratic forms, Orthogonal geometry, orthogonal groups
Module-3(18 hours): Clifford algebras, Hermitian forms, Unitary spaces, Unitary groups.

To give an introduction to different types of finite classical groups

To study the simplicity of Sympletic, Orthogonal and Unitary groups

To study some applications in Finite Geometry

This course will help students to learn certain matrix groups over finite fields and their simplicity. This will help to do research in finite geometry, representation theory and related areas.

L. C. Grove, Classical Groups and Geometric Algebra, Graduate Studies in Mathematics 39, American Mathematical Society, 2002

E. Artin, Geometric Algebra, John Wiley & sons, 1988

L. M. Batten, Combinatorics of Finite Geometries, Cambridge University Press, 1997

G. E. Moorhouse, Incidence Geometry, 2007, available online from http://www.uwyo.edu/moorhouse/handouts/incidence geometry.pdf