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Learn MoreMath For Video Games: The Fastest Way To Get Smarter At Math
Rating: 4.7 out of 54.7(2,036 ratings)
22,855 students
Math For Video Games: The Fastest Way To Get Smarter At Math
Learn Math for Video Game Design & Coding through Solving fun Video Game Problems
Created byGameDev.tv Team, Ben Tristem, Gary Pettie
Last updated 3/2025
English
What you'll learn
- Fundamental math concepts
- Number base manipulation including binary, decimal and hex
- Addition, subtraction, multiplication and division in multiple bases
- IEEE754 floating point and why it matters
- Deeply understand vector space in 2D, 3D and higher!
- Trigonometry calculations such as sin, cos and tan
- More advanced vector math such as dot and cross products
- Projectile motion mathematics
- Combinatorics and probability theory and where to use it
Explore related topics
Course content
7 sections • 122 lectures • 13h 22m total length
- Welcome To The Course1:00
In this video (objectives)…
Ask lots of questions
Immediately practice every concept
Learn to love the beauty of math
Challenge each other
Give feedback.
After watching (learning outcomes)…
Be ready to start the course.
- Addition & Subtraction4:36
In this video (objectives)…
Explain addition in terms of numberline.
Demonstrate subtraction.
Show Unity integer overload.
After watching (learning outcomes)…
Have a basic understanding of the integer number line.
- Rounding6:20
In this video (objectives)…
Round numbers using traditional rounding, floor, and ceiling Link Text
- Multiplication & Number Blocks7:18
In this video (objectives)…
Multiplication on the number line.
Visualising multiplication with blocks.
After watching (learning outcomes)…
Have a very basic grasp of multiplication.
- Division9:30
In this video (objectives)…
Division of integers.
How the sign quadrant applies.
After watching (learning outcomes)…
Know how to divide whole numbers, and what sign of answer to expect.
- Remainders8:28
In this video (objectives)…
Understand the concept of remainders left from division and how these can be used to organize data and make decisions.
- BODMAS3:39
In this video (objectives)…
How brackets work.
The order of operations.
After watching (learning outcomes)…
Know the basic order of operations most computers use.
- Quiz
- Squaring, Cubing & Powers9:31
In this video (objectives)…
Powers or exponents as a shortcut for repeated multiplication.
Squaring and square roots as they relate to area.
Cubing and cube roots as they relate to volume.
After watching (learning outcomes)…
Have a better basic understanding of exponents.
- Sideways Calculators6:09
In this video (objectives)…
Turning your calculator sideways may make it scientific!
How the top row of buttons work.
About raising to any power.
A preview of reversing powers.
After watching (learning outcomes)…
Feel more confident with the top two rows of your scientific calculator.
- Squaring Decimals4:23
In this video (objectives)…
Square 2.5.
Square 3.5.
After watching (learning outcomes)…
Understand how to raise a decimal number to a power.
- Reversing Powers7:40
In this video (objectives)…
Look at what reversing a cube means.
See a general rule for combining powers.
After watching (learning outcomes)…
Understand how to reverse a powers.
- Quiz
- Charts & Graphs 1018:46
After watching (learning outcomes)…
How to label your graph axis properly with units. Interpreting the slope of a graph in math.
- Area Under Chart 1016:20
After watching (learning outcomes)…
Approximate the area under a curve with rectangles
- Gradient Of A Line6:10
After watching (learning outcomes)…
Calculate the gradient of a straight line.
Estimate the gradient at a point on a curve - Distance, Speed & Time6:33
In this video (objectives)…
Ben looks at a speed vs time chart, and explores how the area underneath relates to distance covered. We also start looking at what slope or gradient means on a graph.
- Quiz
- Rates Of Change8:19
In this video (objectives)…
Plot 2^T chart by hand.
Measure slope at two points.
Plot 3^T by hand, and compare slopes
After watching (learning outcomes)…
Know how to measure slope of a chart.
- The Magic of e7:07
In this video (objectives)…
Look at acceleration curves.
Note how 2^x has a slope less than it's value.
Note how 3^x has a slope greater than it's value.
Discover e^x (about 2.718...) has a slope equal to it's value!
After watching (learning outcomes)…
Have some understanding of the natural number e.
- Logarithms 1019:14
In this video (objectives)…
Recall how roots reversed powers.
How do we answer a^b=c if we don't know b?
Logarithms answer this sort of question.
In plain English, how many times did b multiply by it's self?
After watching (learning outcomes)…
Understand how to use base 10 and base e logs.
- Logarithms - Changing Base4:55
In this video (objectives)…
Learn the formula behind changing logarithmic bases and use this to calculate logs to any base using a calculator
- Factorials & Permutations6:16
In this video (objectives)…
Understand wow factorials are calculated, and how they relate to permutations. What's a practical application for factorials in math?
- Number Bases7:06
In this video (objectives)…
Understand the concepts behind different number bases and gain the skills to be able to convert and interpret binary and hexadecimal numbers.
- Scientific Notation11:31
In this video (objectives)…
Learn to write very large and very small numbers concisely using scientific notation.
- How To Pass Your First Math Checkpoint0:48
In this video (objectives)…
Where to get instant help via Discord
Recognise an integer overflow
Add and subtract integers (inc -ve)
Draw and label the 4 sign quadrants.
Multiply -ve and +ve integers
Divide +ve and -ve integers
Expand BODMAS or PEMDAS acronyms
Evaluate A Maths Statement Containing Brackets
Raise one number to the power of another
Access a scientific calculator
Use a computer to square a decimal number
Take square roots and cube roots of whole numbers.
Interpret a simple line chart
Approximate the area under a curve with rectangles
Calculate the gradient of a straight line
Interpret the meaning of the gradient of a graph
Use the Speed, Distance, Time magic triangle
Estimate the gradient at a point on a curve
Correctly identify the definition of the natural number e
Recognise situations in which a base 2 logarithm
Perform base 2 logarithms on a scientific calculator
Calculate a factorial manually & on a calculator
Use a factorial for simple permutation calculations
Apply all basic math skills to a new situation
After watching (learning outcomes)…
Celebrate how much you've learned this section.
- Quiz
- What Now?0:10
- Introduction: Algebra & Equations0:59
In this video (objectives)…
We discuss what to expect from the "algebra and equations" section of the course.
- Algebra 1018:07
In this video (objectives)…
Understand some of the fundamental principles behind algebra. Including working with variables and manipulating equations.
- Inequalities8:28
In this video (objectives)…
Manipulate inequalities to isolate terms
Understand the connection between inequalities and if-statements
- Plotting Graphs5:43
In this video (objectives)…
Start graphing linear equations and see how changing variables can affect the plotted lines.
- Gradient and Intercept6:28
In this video (objectives)…
Use Cartesian co-ordinates to specify points on your graph and use these to find the gradient, or slope, of the line. We also look at the intercept points, where the line crosses the x- and y- axes.
- Linear Equations9:19
In this video (objectives)…
Learn to recognise linear equations without having to draw them.
- Quiz
- Graphing Simultaneous Equations7:15
In this video (objectives)…
Learn how to recognise problems that can be converted to simultaneous equations and solve them graphically by drawing the lines, to seeing where they intersect.
- Simultaneous Equations (Substitution)5:23
In this video (objectives)…
Solve our simultaneous equation using the substitution method.
- Simultaneous Equations (Elimination)6:53
In this video (objectives)…
Solve our simultaneous equation using the elimination method.
- Parallel Lines7:21
In this video (objectives)…
Sometimes our two lines don't have a single point of intersection. Learn how to recognise parallel lines from their equations.
- Quiz
- Parabolas4:47
In this video (objectives)…
The parabola is one of the most common curves you'll encounter, so it's time to learn all the jargon that helps us to describe them.
- The Quadratic Equation3:53
In this video (objectives)…
Now we know about the parabola, it's time to look at how each term of the quadratic equation affects is shape and position on a graph.
- Intercept Form7:52
In this video (objectives)…
Learn to write a quadratic equation in intercept, or factored, form and learn how to identify the roots of the parabola without having to do any solving.
- The FOIL Method4:28
In this video (objectives)…
Learn to use the FOIL method for multiplying two binomials, which allows use to convert our quadratics from intercept and vertex form back into standard form.
- Vertex Form7:48
In this video (objectives)…
Vertex form is the third and final way of writing our quadratic equations and it allows us to quickly identify the vertex of our curve.
- Quiz
- Completing The Square Part 15:27
In this video (objectives)…
Learn a simple way to convert quadratic equations from standard form to vertex form by thinking about the problem geometrically.
- Completing The Square Part 27:02
In this video (objectives)…
In part 2 we look at how to complete the square with more complex examples, where the coefficient of x^2 isn't 1.
- Factoring Quadratics8:48
In this video (objectives)…
Learn a quick and easy way to convert quadratic equations from standard form to intercept form.
- Less than Two Roots5:31
In this video (objectives)…
Identify quadratics with less than two roots
- Quiz
- Section Wrap-Up1:13
In this video (objectives)…
Congratulations on making it to the end of the section. Here's what we learnt!
- Introduction: Angles and Circles1:10
In this video (objectives)…
We discuss what to expect from the "Angles and Circles" section of the course.
- The Circle3:50
In this video (objectives)…
Let's cover some of the terminology relating to circles that we're going to need going forward.
- What is Pi?5:38
In this video (objectives)…
Learn what Pi is and where it comes from. Then use that knowledge to calculate the circumference of a circle.
- Degrees and Radians10:17
In this video (objectives)…
Understand how to measure angles in both degrees and radians, and learn how to convert between the two.
- Triangles7:13
In this video (objectives)…
Discover the 4 types of triangle, along with some of the properties that define them.
- Quiz
- Pythagorean Theorem7:50
In this video (objectives)…
Learn to find the hypotenuse of a triangle using the Pythagorean theorem and understand why a^2 + b^2 = c^2
- Sine, Cosine, and Tangent Part 17:56
In this video (objectives)…
We introduce you to the three main trigonometric functions; sine, cosine, and tangent, and look to understand the relationships they share.
- Sine, Cosine, and Tangent Part 210:53
In this video (objectives)…
We investigate some more common angles and look at the ASTC quadrants.
- SOH CAH TOA11:13
In this video (objectives)…
Learn to find unknown angles in a right triangle using the relationships of SOH CAH TOA.
- Quiz
- The Sine Rule11:00
In this video (objectives)…
We start looking at how to solve triangles that don't include a right angle. Using the sine rule we learn how to solve AAS, SSA, and ASA type triangle.
- The Cosine Rule7:32
In this video (objectives)…
Solve the final SAS and SSS type triangles using the cosine rule.
- The Sine & Cosine Rules Explained11:25
In this video (objectives)…
Investigate how the sine and cosine rules are constructed using our knowledge of the Pythagorean theorem and SOH CAH TOA.
- Solving Any Triangle3:48
In this video (objectives)…
Recap everything we've learnt about the Pythagorean theorem, SOH CAH TOA, the sine rule, and the cosine rule.
Breaking everything down into a handy decision tree, we now have a way to quickly identify the right formula for the triangle problem we're trying to solve.
- Quiz
- Graphing Sine, Cosine, and Tangent4:16
In this video (objectives)…
Graph the sine, cosine, and tangent functions on a graph and get an understanding of periodic motion.
- Manipulating Sine Waves8:51
In this video (objectives)…
Understand how altering the; amplitude, magnitude, wavelength, frequency, and position of our waves can help us animate objects.
- Combining Waves5:16
In this video (objectives)…
Start combining waves to construct more complex patterns and behaviors using constructive and destructive interference.
- Quiz
- Section Wrap-up1:01
In this video (objectives)…
Congratulations on making it to the end of the section. Here's what we learnt!
- Introduction: Vectors and Matrices1:12
- Reading and Writing Vectors9:54
In this video (objectives)…
Find out what a vector is and learn the many ways in which they can be written down.
- Magnitude vs Squared Magnitude12:46
In this video (objectives)…
Find out how to calculate the magnitude of a vector using what we already know about the Pythagorean theorem, and learn about some of the benefits of using the squared magnitude.
- Coordinate Systems4:46
In this video (objectives)…
We discuss the idea of chirality and the difference between left- and right-handed coordinate systems.
- Vector Addition9:48
In this video (objectives)…
Learn to add and subtract multiple vectors and see who this can be used to add forces to an object or make a camera follow the player.
- Scalar Multiplication6:35
In this video (objectives)…
Learn how a scalar can be used to increase the magnitude of a vector using scalar multiplication.
- Quiz
- Normalizing Vectors5:12
In this video (objectives)…
Now that we've started changing the size of our vectors we need a way to convert them back into unit vectors, and we do this via a process called normalizing the vector.
- Zero Vectors2:29
In this video (objectives)…
In this lecture we look at zero vectors and what it means for a vector has a no magnitude.
- Dot Product13:05
In this video (objectives)…
The dot product is a way of multiplying two vectors together and is useful for comparing vectors and finding the angle between them. It is also known as the scalar product.
- Cross Product10:26
In this video (objectives)…
The cross product is the second way to multiply to vectors, also known as the vector product. We use the cross product of two vectors to find the normal vector between them.
- Reflection9:23
In this video (objectives)…
Discover the math that allows you to bounce an object off a surface in 3D, using everything we've learnt about vectors so far.
- Project on a Plane8:50
In this video (objectives)…
Learn how to project a vector onto a plane, which will allow your player to slide along walls without getting stuck.
- Quiz
- What is a Matrix6:07
In this video (objectives)…
Discover what a matrix is and learn how to define them and write them down.
- Addition and Scalar Multiplication5:29
In this video (objectives)…
Expand on what we know about the addition and scalar multiplication of vectors and apply similar techniques to a matrix.
- Adjacency Matrix6:14
In this video (objectives)…
Learn some basics of graph theory as we look at how we might represent a graph using an adjacency matrix.
- Matrix Multiplication7:44
In this video (objectives)…
Learn how to multiply two matrices together and find out some useful information about the graph that is being represented by our adjacency matrix.
- Quiz
- Identity Matrix5:14
In this video (objectives)…
We know that multiplying by the scalar 1 will leave a matrix unchanged but but we can also achieve the same effect using multiplying by an identity matrix. This knowledge will be helpful when it comes to finding the matrix inverse in a later lecture.
- Determinant6:38
In this video (objectives)…
The determinant of a matrix can then tell us whether a matrix is invertible and helps us find the matrix inverse. But how do we calculate it?
- Matrix Inverse9:30
In this video (objectives)…
It's finally time to look at how we find the matrix inverse. The method we use along the way involves the step-by-step process of calculating; a matrix or minors, a matrix of cofactors, and an adjugate matrix.
- Quiz
- Section Wrap-Up1:13
- Introduction: Rotation and Interpolation1:12
In this video (objectives)…
In this section of the course, we'll be looking at rotations, including; 2D, Euler rotation, and Quaterions. We'll also be learning how to use interpolation to help smooth out the movement and rotations of objects.
- Vector Direction7:58
In this video (objectives)…
We've used the vector direction in previous lectures, but now let's look at how to express this direction as an angle between two points. Starting in 2D and using a single angle, we can then extend this into 3D and show the direction as a product of either two or three angles.
- Imaginary Numbers8:07
In this video (objectives)…
The square root of negative numbers do no have a home on our real number line, so let's find them a new one by introducing imaginary numbers!
- Complex Numbers4:03
In this video (objectives)…
Now we have an understanding of imaginary numbers, let's expand things to include the complex numbers. We'll learn how to write these down and also how to add and subtract them, which shares a strong resemblance to how we add and subtract vectors.
- Complex Multiplication8:08
In this video (objectives)…
Find out how to multiply complex numbers and see how this can tie into rotations in two dimensions.
- Quiz
- Polar Coordinates7:18
In this video (objectives)…
Discover another way to express complex numbers using polar form and learn how to multiply and divide complex numbers in this form.
- Rotation Matrix6:59
In this video (objectives)…
Learn how the rotation matrix can be derived and then used to rotate objects in 2D space.
- Euler Rotation9:36
In this video (objectives)…
Let's expand on what we know about the 2D rotation matrix and look at the 3 rotation matrices used to perform euler rotations in 3D.
- Gimbal Lock3:19
In this video (objectives)…
Euler rotations have a big problem and that is gimbal lock, so let's look at what that is and how we might try to avoid it.
- Quiz
- What are Quaternions?4:33
In this video (objectives)…
Quaternions are incredibly useful for rotating objects but what are they and how do the work? Let's start by just treating quaternions as a new type of data structure.
- Quaternion Multiplication Part 111:25
In this video (objectives)…
Learn the rules that govern quaternion multiplication and use polynomial expansion to multiply two quaternions together.
- Quaternion Multiplication Part 27:07
In this video (objectives)…
In this lecture we look at how to simplify our quaternion multiplication and in the process we'll discover the origins of the dot and cross product!
- Quaternion Rotation Part 16:53
In this video (objectives)…
Multiplying quaternions allows us to rotate objects in 3D space. In this lecture we lay the groundwork to help us understand why this is the case.
- Quaternion Rotation Part 27:33
In this video (objectives)…
It's finally time to look at how the quaternion rotation formula converts 4D rotation into 3D.
- Quiz
- LERP7:35
In this video (objectives)…
Find out how linear interpolation (or LERP for short) can help us estimate values between two points, and see how this can help up smooth out the movement of game objects.
- SLERP11:34
In this video (objectives)…
Instead of interpolating along a line, we can also interpolate along the arc of a circle by using Spherical Linear Interpolation, which is primarily used for smoothing out quaternion rotations.
- Easing Functions5:30
In this video (objectives)…
Linear interpolation often feels robotic when applied to the movement of objects. However, we can fix this by applying easing functions to our interpolation.
- Quiz
- Section Wrap-Up1:04
In this video (objectives)…
Congratulations on making it to the end of the section. Let's look at what we learnt!
- Introduction: Probability and Statistics1:05
In this video (objectives)…
We discuss what to expect from the "Probability and Statistics" section of the course.
- Exploring Data5:20
In this video (objectives)…
We begin this section by looking at how to organize and visualize our data.
- Percentages10:23
In this video (objectives)…
Percentages are commonly used for tracking progress towards a given goal and are also useful for comparing values against one another, so let's look at how they work and learn how to convert values into percentages.
- Sigma Notation7:09
In this video (objectives)…
Let's take a look at sigma notation, which gives us a simple and concise way to write long sums.
- Averages7:51
In this video (objectives)…
The mean average is often used to find the central value in a dataset, but did you know there are actually three different approaches to finding the "middle" of our data? So, let’s explore the; mean, median, and mode.
- Outliers4:53
In this video (objectives)…
Whenever we're dealing with sets of data, there's a good chance that we'll have some values that don't quite fit. So, let's look at how identify and handle these outliers.
- Quiz
- Skewness4:49
In this video (objectives)…
Data can fall into a normal distribution, but may also be skewed to either the left or right. So let's investigate the skewness of our data.
- Interquartile Range8:08
In this video (objectives)…
Learn how the range and interquartile range can be used to analyze the variability in our data.
- Standard Deviation9:45
In this video (objectives)…
Find out how to calculate the variance and standard deviation of your data.
- Correlation8:36
In this video (objectives)…
Learn how to calculate the r-value, or coefficient of correlation, which is used to show how strongly correlated our data is. We also look at how to add a line of best fit to our graphs.
- Causation3:08
In this video (objectives)…
You've probably heard the mantra that "correlation does not imply causation", so in this lecture we look at what this actually means.
- Normalizing Data8:53
In this video (objectives)…
Find out how to normalize your datasets or rescale them to any range you need.
- Quiz
- Probability 1018:12
In this video (objectives)…
Probability is all about looking at the chance that some event either will or will not occur. We begin our exploration of probability by looking at "mutually exclusive" events.
- Consecutive Events9:55
In this video (objectives)…
Learn how to calculate the probability for consecutive events, which may be either dependent or independent of each other.
- Complement Rule2:25
In this video (objectives)…
Learn how the complement rule can make calculating certain probabilities much easier.
- Theoretical vs Experimental4:36
In this video (objectives)…
It's not always practical to calculate the theoretical probability. Sometimes it can be quicker and easier to use the theoretical probability instead.
- Quiz
- The Law of Averages8:06
In this video (objectives)…
When dealing with probability, players will often attribute meaning to short-term patterns and outcomes. So let's dig into this misunderstanding of probability and look at the law of averages.
- Bayes' Theorem12:24
In this video (objectives)…
Understand the basics of Bayes' Theorem.
- Cumulative Distribution Function6:07
In this video (objectives)…
In this lecture we look at the cumulative distribution function, which allows us to find the probability that a variable is less than or equal to a given value.
- Elo Rating System11:50
In this video (objectives)…
Learn the math behind the Elo rating system, which is one of the most famous systems for ranking players in tournament games
- Quiz
- Section Wrap-Up1:14
In this video (objectives)…
Congratulations on making it to the end of the section. Let's look at what we learnt!
- That's All Folks1:15
- BONUS Lecture0:28
Requirements
- Pen & paper or digital equivalent
- Internet access for quizzes and reference
- NO math skills required
Description
Maths and video games go hand-in-hand. Video games are a practical, challenging, and fun way to sharpen your math skills. What's more, video games are like living math. From graphics and physics, to AI and movement, games are full of math.
Learn foundational math concepts relevant to game development. In the course we break it down and build it back up, block by block. For each skill you will start from an interesting real-world problem. You'll always understand why you're learning a concept, and feel motivated to solve the problem in hand. In the course you will learn:
How to write and solve equations relevant to game development.
Basic trigonometry the fun way, triangles, circles & stuff.
Enough vector math to make 2D and 3D games.
About imaginary & complex numbers, angles & quaternions.
The concepts learnt will help you create interesting scoring mechanics, have one object smoothly follow another, calculate the path of a projectile, target enemies using triangles and understand how random item drops work.
This course is the result of a successful Kickstarter, and consistent demand from our community of hundreds of thousands of students worldwide. There is a real need to improve math skills, not just for games, but for many areas of life. You'll be amazed how much more colourful the world looks as your math improves.
All the math you learn will be reinforced with quizzes. You'll write your own handwritten notes as you go, to help you remember your skills. We'll translate some of the math to pseudocode so you can see how it applies to C#, C++, Python and any other modern language.
Get plugged into our communities of amazing developers on Facebook (nearly 20k), in our own TA-curated Community (17k views/day), and our student chat group (10k live at any one time).
You will get full lifetime access for a single one-off fee. The creators are qualified and experienced coders and avid gamers, so are able to explain complex concepts clearly, as well as entertain along the way.
Join us on this exciting journey now, you won't be disappointed!
Who this course is for:
- Game developers of any level who want strong math foundations
- Non game-developers who want to learn math the fun way
- Those competent in math who want to hone their skills