Game Mathematics Foundations: Vectors, Matrices, and Physics

Every great game mechanic—from jumping and shooting to camera movement and collision detection—relies on solid mathematical foundations. If you have ever wanted to build games but felt held back by formulas, this guide bridges the gap by explaining complex concepts in plain, accessible language. You will transition from guessing how to position objects to confidently calculating angles, distances, and trajectories. What you'll learn: - Understand coordinate systems and how to position and move objects in 2D and 3D space. - Apply vector arithmetic, including addition, subtraction, normalization, dot products, and cross products. - Utilize basic trigonometry to calculate angles, rotations, and smooth wave-based movements. - Master matrix transformations to scale, rotate, and translate game objects efficiently. - Explore foundational physics concepts like velocity, acceleration, and basic collision detection math. - Compare Euler angles and quaternions to understand how modern game engines handle 3D rotations. This text-based course starts with key terminology and foundational definitions before moving step-by-step into vector geometry, trigonometry, and transformation matrices. You will read clear explanations alongside practical pseudocode examples that apply directly to modern game engines. This course is designed specifically for aspiring game developers, programmers, and designers who want to build a strong mathematical foundation, with no prior advanced math experience required. Start reading today and unlock the mathematical tools needed to bring your game worlds to life.