Mathematics for Game Development – Unity 6 Compatible by Penny de Byl

This course is for anyone who’s ever felt that math is a black box in game development. Instead of just using Unity’s built-in functions, you’ll build your own C# math library from the ground up. You’ll learn how vectors, matrices, and quaternions actually work by coding them yourself, then see them in action inside real game projects. It’s practical, hands-on, and designed to make the abstract concrete.

🎯 What you’ll learn

• Use bitwise operations to optimize game processing and memory storage.
• Master vector mathematics for 2D and 3D navigation.
• Implement collision detection with lines, line segments, and ray casting.
• Understand affine transformations for moving and rotating game objects.
• Grasp what a quaternion is and how to use it for rotations.
• Build a complete mathematics library in C# from scratch.

✅ Requirements

• Skills: Familiarity with the Unity Game Engine, confidence in programming with C#, and high school-level mathematics (basic trigonometry and algebra).
• Tools: A computer capable of running Unity 6.
• Hardware: [REQUIRES UPDATE]

📝 Description

This isn’t a dry math textbook. It’s a workshop where you’ll build a C# mathematics library that replicates core Unity functions like Vector2, Vector3, and Matrix4x4. You’ll start with the absolute basics—bits and bytes—and work your way up to quaternions and affine transformations.

The teaching method is hands-on. You’ll write code, build mini-projects, and even play a game that tests your understanding of points and vectors. The goal is to make you comfortable with the math that’s running under the hood of every game engine. You’ll learn how to optimize with bitboards, calculate intersections, and rotate objects without ever hitting a gimbal lock.

Dr. Penny de Byl brings over 25 years of experience in teaching and game development. Her style is clear, direct, and focused on practical application. You won’t just learn what a dot product is—you’ll write the code for it and use it to solve a real game problem.

🧑‍🎓 Who this course is for

• Beginner game developers who want to understand the math behind their engine.
• Skilled programmers moving into 2D and 3D game development.
• Game dev enthusiasts who want a deeper, practical understanding of applied math.
• Anyone with a love for math who wants to see it in action inside a game.

🧑‍🏫 About the Author

Penny de Byl is a full-time professor and game developer with over 25 years of experience in teaching, research, and industry work in games and computer graphics. She is known for her holistic teaching style that breaks down complex topics into digestible, practical lessons. She has authored multiple best-selling courses on Udemy and runs the H3D learning community.

🏁 Final Result

• A complete, custom C# mathematics library that you built yourself.
• A working game project that uses your math library for movement and puzzle-solving.
• A deep, practical understanding of vectors, matrices, and quaternions in a game context.