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[A Must-Know for Game Developers] Practical Game Mathematics

It's an undeniable fact that mathematics is essential for game developers. Instead of excessively deep traditional math lectures, learn all the mathematical techniques you can use right away!

(4.7) 3 reviews

52 learners

Level Basic

Course period Unlimited

Unity
Unity
game-math
game-math
gemini
gemini
ChatGPT
ChatGPT
Unity6
Unity6
Unity
Unity
game-math
game-math
gemini
gemini
ChatGPT
ChatGPT
Unity6
Unity6

What you will gain after the course

  • Understanding Commonly Used Mathematical Techniques

  • Eliminating aversion to mathematics

  • Using mathematics through original research

banner

Mathematics "On" Game Engine

Why is all game math education always so difficult?

Game math for most game developers who don't need to dig into the engine internals!

  • For those of us working with game engines, I've removed everything unnecessary and included only what's actually used.


  • I support students' understanding and research through unlimited Q&A.


  • I've included a video on "Math Research with AI". Let's go beyond even what we don't know.

  • I focused everything on developing your 'practical game math skills'.
    I hope this course saves you time.

why

Projects where math was the main focus

So why do we need game mathematics?

Can you logically explain 'magic'? Magic in novels or movies is irrational. But magic in games is different. We need to logically implement those irrational phenomena through code.

What's the secret? In the end, it's all 'mathematics.'

  • Red Dead Redemption 2: The natural feel of never colliding when riding alongside NPCs (utilizing asymptotes and multiplication)

  • Mjolnir's Return: The elegant curve of the hammer returning precisely to my hand (Bézier curve)

  • 3D Maneuvering Gear: The physical sensation of rope being pulled taut (tension)

  • Falcon 9 Landing: Simulation of landing at the precise angle (arctangent)

  • Field of View Detection: How to know if an enemy is behind or in front of you (dot/cross product of vectors)

Beyond simple method calls, if you want to design and implement your own theories, game mathematics is essential.

However, many people get intimidated just by hearing the word "math." Even when you muster up the courage to open any game math book in Korea, it's filled with "engine internal logic" or "complex proofs", leaving you at a loss about how to actually apply it to your own game.

That's why I'm going to teach Korea's first practical game math used "on top of" game engines.

Complex engine internal theory? I threw it all out. I only included practical concepts you can actually use in real game development.

Formulas are all over the internet, and Unity does the calculations for us. We don't need to memorize formulas or calculate them ourselves. We focus only on 'how to apply them'.

My Beliefs

pos

UniCoti

I believe that games as a medium have the highest potential and are the most valuable content for delivering stories. That's why I have a firm goal of someday creating an ideal game that will deeply move humanity.


Even if I don't achieve that dream myself, I created this course with the desire to leave a legacy and help other developers realize this dream.
I hope you will join me on this great journey where games receive the true recognition they deserve.

Though I still have much to learn, I want to make a positive impact on society,
and unlike existing textbooks/courses that cover engine internals and math you'll never use, I aim to help with a course that focuses on utilizing the engine.

What will you gain after taking this course?

You'll be able to research the mathematical theories behind the algorithms you want.

You'll be able to implement many magical situations that need to happen within games.
I hope this course becomes a turning point in your life.

It's designed so that through AI, you'll learn to tackle even mathematical fields you don't know, enabling you to attempt techniques you haven't learned. Of course, you'll still need to study, but through AI, you'll be able to save a lot of time and understanding.

Unlike other courses, I've excluded all the math knowledge that's only used inside engines and unnecessary for the majority of engine users—such as polygons, projections, matrices, meshes, frustums, and quaternion calculations—and explained only the necessary knowledge, to the necessary extent.



  • The math knowledge you've learned before, of course you can forget it and calculations? Of course you can make mistakes. This isn't a college entrance exam. You have the internet and a computer. I've captured the essence.

I'll show you practical examples for each technique!

image 127

Player Movement Example

Vector(2-2), Vector Magnitude(3-2)

image 128

Using Mathf

System.Math, Mathf(3-1)

image 129

Bullet Firing Example

Vector Normalization [Theory/Practice](3-3), B-A Dir(3-4)

image 130

Vector Similarity Example

Vector Similarity (3-6), (4-3)

Trigonometric Functions Application Example

Trigonometric Functions(4-1)

Normal Vector Application Example

Normal Vector(4-4)

Object tracking example

Application of Asymptotes[Theory/Practice](3-5), Inverse Functions(4-2),

Interpolation[Lerp](4-5)

Front-Back Field of View Detection Example

Vector Dot Product - Field of View Detection [Advanced](5-1)

Left-right field of view determination example

Vector Cross Product (5-2)

Examples implemented in code

Euler angles and quaternions concepts(5-3), Bézier curves(5-4), calculus(5-5), Taylor series(5-6), numerical solutions(5-7)

I show you examples for every mathematical concept directly, so it's easy to understand when and where to use them!

****** Important! If you want to learn game development but need help ******

If you want to learn game development but have difficulty purchasing the course, please reach out to me in any way to share your situation, and I will help you. Email, Instagram DM, Inflearn Q&A, blog, YouTube comments, etc..

Learning Content

  • Introduction to Overall Learning Content by Section


OT and Prerequisites/Basic Concepts

  • Before entering this course, you'll learn about Unity basics and environment setup, as well as essential foundational math concepts!

  • Normally this would be paid content, but... I've brought you the video.


Beginner Skills

  1. System.Math, Mathf


  2. The magnitude of a vector

  3. Vector Normalization [Theory]

  4. Vector Normalization [Practical]

  5. Direction to destination, B-A Direction

  6. Asymptote Application [Theory]

  7. Application of Asymptotes [Practical]

  8. Vector Similarity

In the beginner techniques organized by the above table of contents, you will mainly learn techniques with low difficulty but high importance, cost-effective techniques. It will be the beginning of being able to apply them.


Intermediate Techniques

  1. Trigonometric Functions

  2. Inverse Functions [Theory]

  3. Inverse Functions[Practice]

  4. Vector Dot Product [Theory]

  5. Vector Dot Product [Practical]

  6. Normal

  7. Interpolation [Lerp]

In the intermediate techniques section organized by the above table of contents, you will learn mathematics that is frequently used as main-level techniques with moderate difficulty. You will learn more powerful mathematical concepts and enter the stage of expanding your knowledge.

Advanced Techniques + AI Research

  1. Vector Dot Product - Field of View Detection [Advanced]

  2. Vector Cross Product

  3. Euler Angles and Quaternion Concepts

  4. Bezier Curve

  5. Calculus

  6. Taylor series

  7. Numerical Solution [Newton-Raphson Method]

  8. Mathematical Research with AI

In the advanced techniques composed of the above table of contents, you will learn quite difficult, main-level/research-level techniques. Based on the information you know, you will learn to transform equations, find meaning, and truly research mathematics through AI for what you don't know.

radian

Importance and Difficulty

Importance and Difficulty Level

When starting a lecture, I mention the importance and difficulty level of the concept before beginning! Since math can be somewhat challenging and academic in nature, I included this to help reduce the burden.

Well... I shouldn't say this, but if the importance is low but the difficulty is high and it's stressing you out, just give up on it! You can always come back and learn it later!

Notes Before Taking the Course

  • If you want to make a game on your own, it's important to fully understand each lecture before moving on. (Questions👍)

  • If there's anything you don't understand or have additional questions about, please feel free to ask. (I will reply directly)

Practice Environment

  • Operating System and Version (OS): Windows (No additional explanation for Mac)

  • Tools used: Unity, Visual Studio.

  • PC Specs: Refer to Unity6 recommended specifications.

  • Version : 6000.0.55f1

  • AI: Gemini, ChatGPT

Learning Materials

  • The completed version is available at the GitHub link, so please refer to it if you encounter errors or want to try the demo.

Prerequisites and Important Notes

  • It's good to have basic coding knowledge, but if you don't, you can make up for it by reviewing well.

  • If there's something you don't know, use AI, Google searches, questions, etc.!


Recommended for
these people

Who is this course right for?

  • Game developer (aspiring) unfamiliar with math

  • A game developer who learned the theory but has never actually used math

  • A student who wants to learn the most fun way to use mathematics

  • A student who is interested in mathematics itself

Need to know before starting?

  • Basic knowledge of Unity is required, but videos are included to prepare for that

Hello
This is UniCoti

4,129

Learners

134

Reviews

24

Answers

4.9

Rating

2

Courses

I am a game developer currently active as an affiliate after receiving an offer from Unity.

I am actively working across various platforms, including my blog, Instagram, and YouTube.

I have loved making things since I was young, and the fact that I could create something using nothing but a computer without any physical materials

I got into coding starting with the advantage of being able to create things using nothing but a computer.

Inspired by the game The Legend of Zelda, I believe games are a medium for storytelling that

I believe it has the highest potential, and my life's dream is to create the ideal game.

I created this course so that everyone can develop games more easily and efficiently!

Completed project materials: github.com/UniCoti/inflearn

Game Development Blog: https://inf.run/bHXtb

Currently enrolled in the Department of Computer Science and AI at Dongguk University

More

Curriculum

All

32 lectures ∙ (3hr 55min)

Course Materials:

Published: 
Last updated: 

Reviews

All

3 reviews

4.7

3 reviews

  • tennisman7072858님의 프로필 이미지
    tennisman7072858

    Reviews 3

    ∙

    Average Rating 5.0

    5

    55% enrolled

    I took this course because I wanted to understand traditional game mathematics through examples. Since the lectures are provided with examples, I feel like I'm learning much faster. + I am applying because I want to study this alongside the Unity Secret Book!! Email: khj008300@gmail.com

    • unicoti
      Instructor

      Thank you for your trust and purchase. As I am receiving some feedback now, please share any questions or suggestions for improvement, and I will sincerely supplement my answers. I will also send the book to you right away.

  • rhdqngkwk님의 프로필 이미지
    rhdqngkwk

    Reviews 5

    ∙

    Average Rating 4.6

    4

    100% enrolled

    I completed the course and am leaving a review. The lectures were short and summarized only the key points, so I was able to finish quickly. With other lectures or books, you can sometimes learn several mathematical applications, which broadens your perspective, you know? I had those expectations for this course as well. However, looking at just the curriculum, it seemed difficult to expect anything special, so I hesitated a lot before purchasing. From the preview, it seemed like the teaching style would assume basic knowledge, and all my predictions were correct. So this course might be difficult to complete for those who aren't confident in math. That said, it doesn't cover difficult content, and although I'm not good at math either, I was able to understand all the formulas and solutions presented in the lectures. What's disappointing is the question of whether the course is relevant enough to include some Unity engine lectures - I don't see why Unity lectures need to be in this course. The examples are already well-known content like textbook material, and if anything, the content has been significantly reduced in this course. Unity itself isn't even needed in the latter half of the course. It seems the instructor wanted to provide a foundation so that if you have the knowledge introduced here, you can use math for problem-solving, but I think the curriculum might be flawed. The direction of the course was confusing to me. Excluding the occasional talking to himself, the lectures were clear and the intentions seemed good, so I gave it 4 stars.

    • unicoti
      Instructor

      Thank you for your thoughtful review. To be honest, even though I completed the course, I've been constantly cautious that it might not be perfect, as game mathematics is a field that inherently has dilemmatic aspects when it comes to teaching. In the case of my first course, which focused intensively on Unity, I received many comments saying the explanations for beginners were good, which may have given me a bit too much confidence. I apologize for making you feel the course was incomplete. I will use this as an opportunity to grow further.

  • 7410panda4295님의 프로필 이미지
    7410panda4295

    Reviews 4

    ∙

    Average Rating 5.0

    5

    100% enrolled

    A disappointing lecture in many ways. There are no issues with the curriculum itself, but the way the lecture is delivered is somewhat unfriendly. First, there is little effort to help students understand mathematical notation or to explain things in simpler terms. After a brief, simple introduction, the instructor immediately proceeds with the content using that notation as if it's common knowledge. It feels as though several years of middle and high school mathematics have been compressed into just a few sentences. Because of this, I had to spend a significant amount of time searching externally or using AI to understand things whenever I got stuck. I could somehow accept and move past this by telling myself it was due to my own lack of mathematical knowledge. However, there is something even more disappointing. When you pay for a lecture, it is only natural to expect the lecture materials to be properly displayed on the screen. It is difficult to understand why the instructor occasionally shows their Instagram or lecture materials that were not provided in advance. Watching the instructor scroll through their own e-book or blog while reading explanations was the height of frustration. At one point in the lecture, the instructor says: 'If you look at the book, I've defined the function below.' Naturally, the students do not have the instructor's Instagram handle or their e-book. Why should I have to pause the video and read through these things one by one? The lecture flows so roughly that it feels more like the information is being scattered rather than taught. While the direction of the knowledge they intended to convey was good, I believe the lecture was poorly prepared.

    • unicoti
      Instructor

      I assumed that materials like Instagram or blog posts could be found through searching, and I had assumed the e-book was delivered based on my mention during the orientation that it would be sent upon request via email. I thought that by providing example projects through GitHub, everything shown in the videos—except for the notes—would be accessible, but I realize now that the process might have been too complicated. I am sorry for these shortcomings. Nevertheless, thank you for leaving such a positive review. I will make sure to improve upon this in future projects.

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