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Mathematics for Game Development - Unity 6 Compatible (Udemy.com)

A Beginner's Guide to Essential Mathematics, Data Structures and Algorithms used in Game Programming applied in Unity

Created by: Penny de Byl

Last updated March 2026

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What you will learn

  • How to use bitwise operations to optimise processing and storage in games.
  • Everything there is to know about vector mathematics and how to navigate in 2D and 3D space.
  • The principles and practice behind collision detection with lines, line segments and ray casting.
  • The beauty of affine transformations and the fundamentals in transforming game objects.
  • What a quaternion is and how it is used to rotate game objects.
  • How to build a mathematics library in C# from scratch.

How it compares

Against the other 183 rated Udemy courses in Unity on CourseDuck:

  • Rating4.5 out of 5higher than 48% of them
  • Reviews1,850#23 of 184 by number of reviews
  • Length15.3 hourslonger than 71% of them
  • Last updatedMarch 2026more recently than 93% of them

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Course Description

Did you know computer games use mathematics to perform every single task, from rendering to animation and physics to AI?  Mathematics is everywhere.  A fundamental understanding of mathematics is critical in every occupation and nowhere is it more important than in games development. It underpins all primary operations performed by a game engine.  You can't even move a character across the screen without it.  Keen to learn more and build up your knowledge in mathematics to improve your game development skills?  Then this course is for you.

In this course you will build your own C# classes to work with the geometrical constructs of 2D and 3D space that will develop your understanding of positioning and moving game objects. In short you will build your own maths library to replicate some of Unity's Vector2, Vector3, Matrix4x4 and some Mathf methods.  Throughout, we will be using the Unity Game Engine to help emphasise the mathematics concepts.

Join Dr Penny de Byl as she introduces game development mathematics using her internationally acclaimed holistic teaching style and expertise from over 25 years of teaching, research and work in games and computer graphics. Through-out the course you will follow along with hands-on workshops designed to teach you the vital mathematical techniques used in programming computer game mechanics and visuals.

During the course we will be building a game that not only uses the code we've written to move 2D and 3D objects around on the screen, but to play the game you will have to use your knowledge of points and vectors to solve puzzles that will reinforce your learning.  You will also build numerous mini projects to apply mathematical concepts and see how they work in games environments.

Learn how to program and work with:

  • Bitwise Operations, Bit Packing and Bitboards

  • 2D and 3D Space

  • Points

  • Vectors

  • Matrices

  • Mapping from one coordinate system to another

  • Positioning Objects

  • Navigation

  • Angles

  • Interpolation

  • Quaternions

What students are saying about this course:

  • Brilliant course. Might be the most helpful course I've found on Udemy so far. Penny is an amazing instructor. Even by the end of the first section learned super valuable information that I can apply to my games.

  • Early in the program but already learned enough to make the purchase price worthwhile.

  • As always, the professor delivers a great, clear course on a badly needed subject to learn. She is so knowledgeable and can impart her knowledge to her students. I recommend all her courses and her YouTube channel.

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Instructor Details

Penny de Byl

Hi, I'm Dr Penny de Byl.  I'm a full stack developer of most things computer sciency and academic with a true passion for teaching.  I've been teaching others about games development, programming, computer graphics, animation and web design for over 25 years in universities in Australia and Europe at the full professor level. I've also consulted for Unity, SAE, the Australian Institute of Entertainment and Wikitude. My best selling textbooks including Holistic Game Development with Unity are used in over 100 institutions world-wide.  My graduates work at companies like Apple, Ubisoft, LinkedIn and Deloitte Digital.

I have an honours degree in computer graphics and a Ph.D. in artificial intelligence for games characters.  Over the course of my career I've won numerous awards for teaching excellence at the state, national and international levels including the Australian Learning and Teaching Council's Excellence in Teaching Award and the Unity Mobile Game Curriculum Competition. My approach to teaching computer science and related fields is project-based giving you hands-on workshops you can immediately get your teeth into.

I want you to leave my virtual classroom fully armed with a toolkit of skills for life-long learning.  I'm excited to now be focussing my efforts full-time on Udemy to bring my years of knowledge and experience to those eager to learn about technology.


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Reviews

4.5

1,850 ratings on Udemy

Select a bar to show only those reviews.Select the bar again to show every rating.

By Batucan Sülün on 5/20/2026

Some sections are explained very well. However, since some parts require knowledge of linear algebra, they can sometimes be a bit unclear. Aside from that, the challenges in the course are a great addition and very educational. It helped clarify a few topics I was struggling with. I can’t wait to build a game using bitboards.

By Zachary Pugh on 10/31/2025

Overall very informative. I think the best parts are the coverage of bitwise operations and the explanations of dot products and cross products. For much of the course, you develop mathematical operations for repositioning and rotating objects, and you build your own library of methods from scratch. This is useful for background knowledge, but Unity already has very useful libraries for vector mathematics and quaternion rotations, and they are hardly explored in the course. It is a bit like taking and driver's ed course, and then instead of learning how to drive you learn how to build a drive train and wheel assembly. I wish the course went more into detail about built-in methods like Quaternion.AngleAxis and then give practice problems where they might be implemented. The second issue is a minor thing, but having to create a new Unity project every chapter creates a lot of storage bloat and down-time as I am waiting for the project to build. I try to keep instructional projects as a reference material in the future. I think it would be more helpful to frame the scripts and assets so they are consolidated into a single project.

By Rene Rodriguez Clavijo on 9/30/2024

really complete an amazed of what I've been capable of do with this knowledge, I think the house example at the end was kind of complicated but it's clearer once you start experimenting yourself. Thanks

By Abdulwahhab Ayoob on 10/1/2022

I Lerand How Much the Math is useful , with Dr.Pennys Help I looked deepley to Math behined Unitys Transform Class

By Sylvia Esteves on 5/20/2021

Learned so much. Great course! Even if you are a beginner like me, Penny will guide you through the world math so that you can understand each concept with ease.

By Juan Hernandez on 12/27/2020

something i think she need to explain more, but overall is good

By Alicia S on 12/13/2020

This course is good for Unity3D beginner.

By Aliozer on 11/14/2020

Amazing.

By David Etter on 10/25/2020

The instructor is engaging, using pertinent examples, and keeps the class interesting from beginning to end.

By Ryan Pinheiro on 10/11/2020

Otima aula !!! bem explicado

By Olivier Raveneau on 10/9/2020

Ce cours vous fera dcouvrir une partie des mathmatiques derrires les moteurs 3D. Il en dcoulera une meilleur comprhension et donc une meilleur utilisation de ces moteurs.

By Marscel Ray on 10/2/2020

Nice job

Showing 12 of 325 reviews

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Overall Score : 90 / 100