Mathematics for Computer Games Development using Unity (

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

Created by: Penny de Byl

Produced in 2022

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.

Quality Score

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Overall Score : 96 / 100

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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.
Who this course is for:
  • Beginner game development students who want to be able to understand the mathematics behind game engines.
  • Skilled programmers keen to move into 2D and 3D game development spaces.
  • Game development enthusiasts who want a deeper understanding of how mathematics is applied in games.
  • Anyone with an appreciation of mathematics who wants to investigate how it is applied in computer game environments.

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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.

Hi, I'm Dr Penny de Byl. I'm a full stack developer of most things computer sciency and academic w



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By Jax Jaxon on a month ago

I wanted to get a better understanding of matrix and linear algebra basics by taking this course. I did have experience on both topics but I wanted to revisit and maybe get some fresh angle on the topics.Even though course is meant for beginners I felt the early chapters (bitwise operations etc) were too basic and simple for my taste. Further the course advanced and got into more complex topics I enjoyed it more.All in all I think this is a very good, albeit just a bit short, introduction to mathematics related in the games programming.

By Philip Raymond Davies on a month ago

Another great tutorial from Penny, I've taken a quite a few of Penny;s courses and each one has been a gem.This course focuses on the mathematical side of coding and gives you a fundamental understanding of what goes on under the hood in Unity.Very clear and concise explanations and walkthroughs.I must admit to getting a bit lost at the latter end of the course when we started Quaternions but I plowed on through and got there in the end. I still have a problem wrapping my head around some of the concepts introduced here so I will go away and come back later when I have a little more understanding of the topics covered, as a lot of the mathematical topics covered here I didn't do in school.I am very keen to learn so the material covered in this course is a very valuable object of reference for me and I thoroughly recommend this course to anyone wishing to advance their knowledge of maths for game development.

By Barbaros S on 2 months ago

It is one of the best designed courses, I have ever bought from Udemy . Penny is a really good instructor. I recommend this course to those who wanna know what's going on behind the scene

By Jason C McKinney on 4 months ago

Turns out, the hardest part of this course for me is finding the words to describe how glad I am to have enrolled in it. If you want to know the math that's running under the hood of game engines, this is the course you want to start with. Penny is a natural born teacher, able to explain otherwise difficult concepts in a fun, engaging way that just make such simple sense, and makes you wish you would have had her for a high-school teacher so long ago. I'm a few seconds away from looking at the rest of the courses she offers and enrolling in some more. I definitely recommend her courses here at Udemy!!!

By Maksim on a month ago

Totally worth it. Great place to start 3D maths journey.It would be amazing to see physics course for Unity3d developers from you.

By Mike Tam on 3 months ago

Game math is one of the essential skills someone has to know to create a qualitative and realistic game. After finishing this course I must say that Penny does an awesome job on explaining nearly anything you need to understand the math behind of game development. Especially the transmission of the theory to the practical part gives you a better overview of each part. The course starts with the math in 2D and goes to 3D as well by creating step by step your own math library which you can use in the future for your own projects. No matter in what language you develop you can transform the C# code to your needs (e.g. I am developing also using OpenGL). Penny has a lot of experience in 3D game math and this one can see how well she explains the concepts. All in one I believe this is the best course to learn game math by multiple examples. I have to mention, that the last part which is of Quaternions, is not quite easy to understand and requires some time and knowledge about complex numbers to understand them. Even for someone with a master degree like me, it is not easy to understand them from the beginning. Great job Penny.

By Rahul Raman on a month ago

Absolutely loved taking this course! I was on the hunt for a good explanation of vector math and matrices, but everything I came across (until now) was difficult or detached from the actual task of game development. This course was well explained, with just the right amount of time spent on theory and the rest dedicated to the application of it. I learned a bit about what goes on under the hood of the math libraries we use on a daily basis, and I wholly enjoyed doing so.

By David Mang on a month ago

She takes her time explaining each concept with plenty of examples, and there are a lot of quizzes to practice your knowledge.

By Leonardo Gasperin on 2 months ago

YEAH!! now I understand so much more about the unity transform(AGLA or in pt-br GAAL for games), and layermask(bitwise) for game THX PENNY U'RE AWESOME!!

By Hugo Lacerda on 3 months ago

Curso que superou qualquer expectativa. Recomendo muito a todos que querem entender como a matemtica funciona dentro do Unity e pretendem desenvolver jogos.

By Donald J. De Los Rios on 3 months ago

The course was challenging, especially once we got into the vectors sections. Then the Quaternions, a real eye opener. I loved the thoroughness of the step by step explanations. I've got a very solid mathematics library to reference now. Thank you Penny.

By Hari Nidamarthy on 2 months ago

Very important course to understand the fundamental mathematics involved in game development. I got a very different picture of what is happening behind the scenes in a game.