Credits: 4 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 360 Linear Algebra II for undergraduates, MAT 660 Linear Algebra for graduate students
Overview: This course provides a bridge to modern geometry. It provides a unified axiomatic approach leading to a coherent overview of the classical geometries (affine, projective, hyperbolic, spherical), culminating in a treatment of surfaces that sets the stage for future study of differential geometry.
- Affine geometry – finite planes, planes over fields, affine transformations, collineations, affine coordinates, triangles and parallelograms, classical theorems of Menelaus and others.
- Projective geometry – finite planes, projective completion of affine planes, homogeneous coordinates, projective transformations, collineations, projective line, poles and polars.
- Conics – affine and projective classifications, group actions.
- Euclidean geometry – isometries, triangles, parallelograms, length minimizing curves, geometry of plane curves.
- Hyperbolic geometry – Poincare upper half plane, Poincare metric, distance function, triangles and area, two-point homogeneity.
- Spherical geometry – Sphere, tangent space, great circles, triangles and area, two-point homogeneity
- Surfaces – Level surfaces, parametrized surfaces, curvature, Gauss theorem, introduction to manifolds.
- An Expedition to Geometry by S Kumaresan and G Santhanam. Hindustan Book Agency, 2005.
- Geometry by M. Audin. Springer International Edition, Indian reprint, 2004.
- Geometry by David A. Brannan, Matthew F. Esplen and Jeremy J. Gray. Cambridge University Press, 2nd edition, 2012.
- Geometry by Roger A Fenn, Springer International Edition, 2005.