Euclidean geometry, Euclidean space, inner product, distance, and angle. Isometries. Vectors in planes and spaces. Lines and planes and surfaces in 3-dimensional space. Linear transformations, projections, orientations and determinants, isomorphisms, and general linear groups. Symmetries and regular polyhedrons. Affine geometry. Affine spaces and affine transformations. Brief discussion on the development of various geometries such as Euclidean and non-Euclidean ones.

CILO-1: Compute the inner product, and length of abstract vectors. [PO: a] CILO-2: Represent Transformations in various objects in various types of Geometry. CILO-3: Connect the geometry concepts and the ones in linear algebra.