Cover -- Table of Contents -- Part I: Essential Topics in Mathematics -- Chapter 1 Numbers -- Overview -- Numbers as Written -- How Computers Represent Numbers -- Exercises -- Summary -- You Should Now Know -- Chapter 2 Arithmetic -- Overview -- Fractions -- Proportions, Ratios, and Percentages -- Exponentials -- Logarithms -- Exercises -- Summary -- You Should Now Know -- Chapter 3 Algebra -- Overview -- Basic Algebra -- Working with Equations -- Factoring and Solving Quadratic Equations -- Functions and Graphs -- Exercises -- Summary -- You Should Now Know -- Chapter 4 Geometry and Trigonometry -- Overview -- Angles -- Triangles -- Calculations with Triangles -- Rotations and Reflections -- Exercises -- Summary -- You Should Now Know -- Chapter 5 Vectors -- Overview -- Getting from Here to There -- Vector Motion -- Vector Calculations -- Matrices -- Exercises -- Summary -- You Should Now Know -- Chapter 6 Calculus -- Overview -- Differentiation and Integration -- Differential Equations -- Approximation Methods -- Exercises -- Summary -- You Should Now Know -- Part II: Essential Topics in Physics -- Chapter 7 Acceleration, Mass, and Energy -- Overview -- Ballistics -- Mass and Momentum -- Energy -- Exercises -- Summary -- You Should Now Know -- Chapter 8 Detecting Collisions Between Simple Shapes -- Overview -- Ground Rules -- When Circles Collide -- When Squares Collide -- When Ellipses Collide -- When Things Collide -- Exercises -- Summary -- You Should Now Know -- Chapter 9 Collision Resolution -- Overview -- Resolving a Single Collision -- Multiple Collisions -- Exercises -- Summary -- You Should Now Know -- Chapter 10 Detecting Collisions Between Complex Shapes -- Overview -- Problems with Complex Shapes -- Some Reasonable Problems -- Built-In Solutions -- Exercises -- Summary -- You Should Now Know -- Chapter 11 A Simple Pool Game.

Overview -- Primary Elements of a Simulation -- Taking a Shot -- Exercises -- Summary -- You Should Now Know -- Part III: Complex Motion -- Chapter 12 Force and Newton's Laws -- Overview -- Force -- Gravity -- Rockets and Satellites -- Exercise -- Summary -- You Should Now Know -- Chapter 13 Angular Motion -- Overview -- The Physics of a Lever -- Spin -- Spinning Collisions -- Spin Applied to the Pool Game -- Exercises -- Summary -- You Should Now Know -- Chapter 14 Friction -- Overview -- How Friction Works -- Friction and Angular Motion -- Exercise -- Summary -- You Should Now Know -- Chapter 15 Strings, Pulleys, and Conveyor Belts -- Overview -- Pulling Things Around -- Continuous Momentum -- Exercise -- Summary -- You Should Now Know -- Chapter 16 Oscillations -- Overview -- Springs -- Simple Harmonic Motion -- Damped Harmonic Motion -- Complications of Springs -- Calculating Spring Motion -- Waves -- Exercise -- Summary -- You Should Now Know -- Part IV: 3-D Mathematics -- Chapter 17 3-D Geometry -- Overview -- 3-D Vectors -- Rendering -- Casting a Ray -- Exercise -- Summary -- You Should Now Know -- Chapter 18 Transforms -- Overview -- Describing Locations in Space -- Applying Transforms -- Exercise -- Summary -- You Should Now Know -- Chapter 19 3-D Collision Detection -- Overview -- Colliding Worlds -- Colliding Footballs -- Colliding Boxes -- Colliding Cans -- Varieties of Collisions -- Resolving Collisions in Three Dimensions -- Exercise -- Summary -- You Should Now Know -- Chapter 20 Lighting and Textures -- Overview -- Light -- Materials -- Shading -- Exercises -- Summary -- You Should Now Know -- Chapter 21 Modeling Techniques -- Overview -- Mathematical 3-D Modeling -- Animated Surfaces -- Bone Animations -- Exercises -- Summary -- You Should Now Know -- Part V: Game Algorithms -- Chapter 22 Speeding Things Up -- Overview.

Cheap and Expensive Calculations -- Pseudo-Physics -- Culling -- Exercises -- Summary -- You Should Now Know -- Chapter 23 Tile-Based Games -- Overview -- Generating a Game from Bits -- Advanced Tiling -- Exercises -- Summary -- You Should Now Know -- Chapter 24 Mazes -- Overview -- Classifying Mazes -- Creating Mazes -- Navigating Within Mazes -- Exercises -- Summary -- You Should Now Know -- Chapter 25 Game Theory and Artificial Intelligence -- Overview -- Introduction to Game Theory -- Tactical AI -- Top-Down AI -- Bottom-Up AI -- Exercises -- Summary -- You Should Now Know -- Chapter 26 Search Techniques -- Overview -- Problem Solving -- Case Study -- Genetic Algorithms -- Exercises -- Summary -- You Should Now Know -- Appendix A: Glossary of Mathematical Terms -- Appendix B: Code References -- Appendix C: The Greek Alphabet -- Appendix D: Learning Resources -- Appendix E: Answers to Exercises -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.