Mathematics for Game Development

  1. Linear Algebra: Vectors
    1. Introduction to Vectors
      1. Vectors vs Scalars
        1. Definitions
          1. Physical Examples
            1. Mathematical Notation
            2. Vector Representations
              1. Geometric Representation
                1. Coordinate Representation
                  1. Component Form
                  2. Types of Vectors
                    1. Position Vectors
                      1. Direction Vectors
                        1. Displacement Vectors
                          1. Zero Vector
                            1. Unit Vectors
                          2. 2D Vector Operations
                            1. Vector Addition
                              1. Geometric Method
                                1. Component Method
                                  1. Properties of Addition
                                  2. Vector Subtraction
                                    1. Geometric Method
                                      1. Component Method
                                        1. Vector Difference
                                        2. Scalar Multiplication
                                          1. Scaling Vectors
                                            1. Direction Changes
                                            2. Vector Magnitude
                                              1. Length Calculation
                                                1. Distance Formula
                                                2. Vector Normalization
                                                  1. Unit Vector Creation
                                                    1. Normalization Process
                                                    2. Special 2D Vector Relationships
                                                      1. Parallel Vectors
                                                        1. Perpendicular Vectors
                                                          1. Opposite Vectors
                                                        2. 3D Vector Operations
                                                          1. Extension to 3D Space
                                                            1. Three-Component Vectors
                                                              1. 3D Coordinate Systems
                                                              2. 3D Vector Addition and Subtraction
                                                                1. 3D Scalar Multiplication
                                                                  1. 3D Vector Magnitude
                                                                    1. 3D Vector Normalization
                                                                      1. 3D Vector Relationships
                                                                        1. Parallel Vectors in 3D
                                                                          1. Perpendicular Vectors in 3D
                                                                            1. Coplanar Vectors
                                                                          2. The Dot Product
                                                                            1. Dot Product Definition
                                                                              1. Formula in 2D
                                                                                1. Formula in 3D
                                                                                  1. Algebraic Properties
                                                                                  2. Geometric Interpretation
                                                                                    1. Angle Between Vectors
                                                                                      1. Projection of Vectors
                                                                                        1. Orthogonality Testing
                                                                                        2. Dot Product Applications
                                                                                          1. Lighting Calculations
                                                                                            1. Field of View Determination
                                                                                              1. Surface Orientation
                                                                                                1. Work and Energy
                                                                                              2. The Cross Product
                                                                                                1. Cross Product Definition
                                                                                                  1. Formula in 3D
                                                                                                    1. Determinant Method
                                                                                                    2. Geometric Interpretation
                                                                                                      1. Perpendicular Vector Generation
                                                                                                        1. Right-Hand Rule
                                                                                                          1. Area of Parallelogram
                                                                                                            1. Volume of Parallelepiped
                                                                                                            2. Cross Product Applications
                                                                                                              1. Surface Normal Calculation
                                                                                                                1. Torque Calculation
                                                                                                                  1. Orientation Determination
                                                                                                                    1. Plane Equations

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                                                                                                                1. Foundational Mathematical Concepts

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                                                                                                                3. Linear Algebra: Matrices