Essential Maths For Beginner Gamedevs - Which Math is Useful? - monstrousmath.com

Essential Maths For Beginner Gamedevs – Which Math is Useful?

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Like: 4348
There’s plenty of tutorials on learning maths for gamedev, but why and where is this maths actually useful? Here, I try to give examples of how and when different types of mathematics pop-up, and how they are actually used when making a game. I have added links throughout the video and below if you want to learn these topics in more detail, but hopefully this will make you aware of the different areas of maths used in gamedev!
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Tutorials and Learning Resources for each topic covered (I have tried to include one video, one blog and one interactive thing to account for different types of learners!):

Numbers
+, -, x and ÷ are used frequently! The good thing here is that even if you aren’t the best at doing sums quickly, the computer is! As long as you recognise when you should be using each operation, you’ll be fine (e.g. subtract some health when your player takes damage).

Brush up on BODMAS! It’s important to know what order more complicated calculations will calculate in – while remembering that you can use brackets to specifically order the way a sum will resolve:

Discrete Maths
An umbrella term for lots of maths. Wikipedia splits it into 17 sub-topics (which are all individually still very broad):
You will almost definitely do a discrete maths course at university, if you do CompSci or a related degree. You could learn about any of these sub-topics for years.

Logic
Video tutorial on boolean logic (its for GMS2, but the logic and concepts apply universally):

Coordinate Systems
Most 2D games use an x and y-axis – 3D games will use the z-axis too. Here’s what I mean when some are inverted:
Video on non-Euclidean games:
Blog on non-Euclidian games:

Trigonometry
Tutorial on angles (also vectors and some other topics too):
An interactive visualisation of trig:

Pythagoras Theorem
Video tutorial:
Article/guide:

Vectors
Video:
Professor Dave’s intro to vectors:
Blog/guide:

Vector Normalisation
Khan Academy blog with interactive example at the bottom:
Video tutorial on normalisation:

Dot Product
Dot product video tutorial:
Codeer’s Video:
Interactive dot product visualisation:

Video explanation of the cross product by Professor Dave:
Article/guide on cross product from Maths is Fun:
Visualisation:

Blog:
Video Tutorial:

Graph Theory
This is a broad topic. Wikipedia gives some good insight into the variety of uses:
Tutorial series on finite state machines by MATLAB:
Interactive Path Finding:

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Timestamps
0:00 – Intro
0:30 – The Problem
1:15 – The Solution
1:52 – Calculus Not Needed for Making Games
2:19 – Numbers
3:38 – Discrete Maths
4:44 – Logic
6:40 – Coordinate Systems
8:09 – Trigonometry
10:17 – Pythagoras Theorem
10:58 – Vectors
12:51 – Vector Normalisation
14:31 – Dot Product
16:01 – Cross Product
16:51 – Quaternions
18:26 – Graph Theory
19:42 – Recap
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#math #gamedev #mathingames #indiedev #gamedevmath

1. YuMi GaNdA says:

thanks BRo

2. Titik Sasanti says:

that was exactly what I needed , thank you so much

3. Facundo Blasco says:

ty cuz ive been having a hard ti getting started.

4. falcon says:

I am good at games

5. Proton Orbit says:

Your channel is severely underrated mate. Fantastic stuff here!

7. Slubmeister says:

Kind of upsetting that you've stopped uploading, just found your channel and I'm kind of astonished of how you have such good content but such little recognition

8. Purplox says:

Did you just spend three minutes of your video stating that you need to do basic arithmetic, hut not really because its automated for you?

… I hate to be rude mate, and I hope I dont come off that way, but you know the field of computer graphics and the field of artificial intelligence are both extremely calculus and linear algebra heavy, right? That starts with basic aritmetic, and oftentimes extends to abstract algebra. It's not "nice to know but not necessary".

9. Dorago says:

Hey there! Could you please recommend which degree would be worth choosing for game development, Software Engineering or Computer Science

10. John Tryl says:

This was surprisingly refreshing. It often feels like there's too many disjointed tutorials, with no roadmap or motivation. You did a good job with this one. Glad I found this vid. Calc is more useful in controls and electrical engineering; if you want write software for airplanes and helicopter and you get the idea, that's where you'll use calculus, otherwise, study your linear algebra if you wan to make games. Basically exactly what you said. Nice work.

11. zambonni says:

I am a High School MATH teacher. This is the most AMAZING video I've ever seen to explain WHY and HOW we use math in video games. Kids love video games so this appeals to them! SUPER AMAZING AWESOME JOB. Thank you for making this. I hope this gets a million views!

12. Kwauhn says:

It's weird to me that you mentioned quaternions but not matrices. I feel like when discussing game maths I'd bring up things in this order: vectors > matrices > quaternions. Especially how vectors and quaternions can both be represented as matrices, it feels like a natural bridge to the quasi-4d weirdness of quaternions.

13. Scott Warner says:

Just popping in to say that if you go into discrete math without first having at least done pre-calculus, you're going to have a bad time.

14. Teal Comet says:

I learn math on my own because I knew it was somehow useful in game development, but recently I was starting to lose motivation, asking myself when/why would I ever use this super complicated formula or that property. Thanks to this video, I understand better, and I'm ready to keep increasing my math knowledge and skills ! This is an excellent video 😀 !

15. SomeDude says:

Shouldn't one know thier mathematical use, before using them in programming?

16. Vinicius H. says:

i had my journey of learning unity and going through my education alongside one another. As i progressed in maths, i became a better gamedev, and vice versa. I think it's fundamental to learn math in order to be a good gamedev

17. myerpheus says:

Great video. Well done on telling my why and how. So important!

18. k goblin says:

Quick commentary on programmers

19. Joe Vaghn says:

School is a lot of theory without much practical experience

20. orestesdd says:

What language do you use? Is it C++ or some other computer language? Thank you. 🤔

21. I’m a smoothie says:

When I get to level 999 it’s over for you h035

22. Robert Mock says:

Is there a good book to show me the maths I need and teach me step by step? I’m looking to get into game development myself like work for a game studio like naughty dog

23. caspar valentine says:

quaternions are an affront to god

24. AnonTen says:

You missed that a game is basically a big Euler method integrator at its core. When you do things like "pos += velocity * dt" it's literally integration using Euler method.

25. Luke skywalker says:

I personally don't use quaternions, because for me it is easier to use matrices (theoretically e.g. coordinates are stored in x,y,z variables so they are not technically matrices but spiritually…)

26. Tejas with me says:

Oh man… I'm shocked! For past 3 weeks or so I've been learning Godot from Heartbeast's old platformers video & i remember that he used Vector normalizers & finding that it's the same concept as he told just refreshed my memory!!!
Thanks for this amazing video Sir ❤
Love from India 🇮🇳

27. Darren New says:

I will say I studied calculus for three years before I got to a physics class advanced enough that I needed it. Then I went "Oh! That makes so much more sense." It took another 20+ years to figure out why I read Great Expectations and Macbeth in high school. As for "numbers," you need to learn the limitations of floating point too.

28. temul says:

i start the video and hear "calculus is not very useful" excuse me
i need calculus every time i make a movement system lmao it's the only reason i want to learn some calc (otherwise i don't really like it)
(pinned comment is pretty good though)

29. Aloo.mp4 says:

Basic Integral and differential calculus can be quite useful

30. notecolt2 says:

Dude just summed up my high school maths and my first 2 years at uni

31. Frank Rivera says:

Math is singular!

32. Electric Trojan says:

Get a physics degree

33. 4115 Steve says:

mentioning vector normalization reminded me of James Bond Golden Eye on n64. I think you would move faster if you moved side ways.

34. Alejo Fossati says:

Math or Maths

35. Jacob ophoven says:

When I have to do math I just keep trying random things until its what I want

36. Game Dev Artisan says:

Great video! I really liked the attention given to Vectors, as that seems to be where many people spend time spinning their wheels, so it's nice to see such detail given in consumable portions. Nice work!

37. Nguyễn Thanh Phong says:

38. Pirate Skeleton says:

With regards to Calculus, have to slightly disagree. While I don't find too much use for the limit or integration, the derivative is quite useful, especially given that it can be used to understand how to calculate stuff like velocity. My educational background is electrical engineering, specifically control system engineering. For my game project I end up applying quite a lot of concepts used in both control and signal processing systems. Stuff such as lag filters can be used to create smooth camera movement and eliminate high frequency noise. Concepts such as negative feedback loops, that have roots in differential equations, can be quite useful for making simulated automated systems that are meant to behave within your games physics environment. That being, said, I do agree with your other mathematical suggestions. I use trig in combination with vectors quite a lot.

39. loszhor says:

Thank you for the information.

40. Squidlord77 says:

Oh, so you're familiar with Metacognition? Lol. I've been to school for 6 years….. Gonna go back for 4 more? Woah! Lol 🤣

41. GoldDeniel says:

Brrruuuh you just explained a bug that I made years ago.. I never knew why my character was moving faster sideways… I thought the normalization was kind of automatic I guess…

42. DoomERA says:

would this also aplly to someone who has forgot everything from school?

43. Vincenzo Sacco says:

I think that also physics and rigid body related stuffs need an honourable mansion, especially for 3D games, maybe you can make a variant of this video for physics

BTW sorry for my bad English, I'm Italian.

44. Nilaier says:

Nah, ChatGPT will deal with it

45. aik21899 says:

Which game is played at 3:31?

46. Ray Ray says:

"Until next time, good bye!"

I don't think he's coming back guys.

47. Kayote says:

This is so amazing! As a software engineer, I dont need Math daily, however, I have always felt the need to learn it to get deeper into the field. This is a great starting point!

48. shaheer ahmed says:

BRO THANKS FOR MAKING THIS VIDEOO❤❤❤❤

49. Angry Crafters says:

14:13 Neither does Goldeneye 64 for the Nintendo 64!

50. Django says:

Matrix maths can be hand in game dev.