Part I Mathematical foundations: Section 1 - Vector and Matrix Geometry, Properties of vector spaces, Dot products and cross products, Homogeneous co-ordinates, Representing planes as 4D vectors, Co-ordinate transformations, Perspective projections; Section 2 - Algebra and Calculus, Root finding, Newton's method, Analytic solution to quadratic, cubic, and quartic equations, Ray intersections with surfaces, Calculating normals and tangents, Contravariant and covariant vectors, Differential equations; Section 3 - Modern Algebra, Introduction to group theory, Rotation groups, Homomorphisms, Complex numbers, Quaternions, Spherical linear interpolation. Part II Rendering: Section 1 - Ray Tracing, Illumination equations, Reflection and refraction, Bump mapping; Section 2 - Rasterization, Conventional rasterization pipeline, Modern per-pixel lighting methods, Environment mapping, Shadow rendering techniques; Section 3 - Polygonal Techniques, Polygon clipping, Portal clipping, T-junction elimination, Decaling and depth offset; SECTION 4 - Visibility Determination, Bounding volumes, View frustum/portal intersect tests, Plane visibility, BSP trees. Part III Physics: Section 1 - Linear motion, Projectile motion, Position functions, Collision detection, Frictional forces, Elastic collisions; Section 2 - Rotational motion, Moment of inertia, Angular momentum and torque, Centrifugal force, Coriolis force.
