CS 172 - Game Mathematics II

1. Define a vector and describe and utilize common vector operations including addition, subtraction, and dot products.
2. Define a matrix and common matrix properties and operations including the identity and transpose matrix determinant, matrix addition, subtraction, and multiplication.
3. Solve systems of linear equations using matrix operations and gaussian elimination.
4. Interpret common vector operations from both an analytic and geometric viewpoint.
5. Define a linear transformation recognize linear transformations from both algebraic and geometric representations.
6. Write common transformation matrices used in game programming, including scaling, skewing, translation, rotation, and projection matrices.
7. Define imaginary and complex numbers and their common properties and operations such as power, multiplication, division, addition, subtraction, conjugate, and magnitude.
8. Define hypercomplex numbers and quaternions, and describe how they and their common operations represent a generalization of complex numbers.
9. Apply quaternion operations to common game programming tasks such as 2D collision, 3D reflection, polygon penetration, and lighting and shadow casting in 3D games.
10. Apply the principles of game mathematics to represent scene generation in a 3D game including motion, lighting and texturing.
11. Clearly communicate problem and solution descriptions to peers, and work with peers to jointly solve mathematical problems.