
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.
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.
In this video (objectives)…
Round numbers using traditional rounding, floor, and ceiling Link Text
In this video (objectives)…
Multiplication on the number line.
Visualising multiplication with blocks.
After watching (learning outcomes)…
Have a very basic grasp of multiplication.
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.
In this video (objectives)…
Understand the concept of remainders left from division and how these can be used to organize data and make decisions.
In this video (objectives)…
How brackets work.
The order of operations.
After watching (learning outcomes)…
Know the basic order of operations most computers use.
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.
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.
In this video (objectives)…
Square 2.5.
Square 3.5.
After watching (learning outcomes)…
Understand how to raise a decimal number to a power.
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.
After watching (learning outcomes)…
How to label your graph axis properly with units. Interpreting the slope of a graph in math.
After watching (learning outcomes)…
Approximate the area under a curve with rectangles
After watching (learning outcomes)…
Calculate the gradient of a straight line.
Estimate the gradient at a point on a curve
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.
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.
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.
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.
In this video (objectives)…
Learn the formula behind changing logarithmic bases and use this to calculate logs to any base using a calculator
In this video (objectives)…
Understand wow factorials are calculated, and how they relate to permutations. What's a practical application for factorials in math?
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.
In this video (objectives)…
Learn to write very large and very small numbers concisely using scientific notation.
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.
In this video (objectives)…
We discuss what to expect from the "algebra and equations" section of the course.
In this video (objectives)…
Understand some of the fundamental principles behind algebra. Including working with variables and manipulating equations.
In this video (objectives)…
Manipulate inequalities to isolate terms
Understand the connection between inequalities and if-statements
In this video (objectives)…
Start graphing linear equations and see how changing variables can affect the plotted lines.
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.
In this video (objectives)…
Learn to recognise linear equations without having to draw them.
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.
In this video (objectives)…
Solve our simultaneous equation using the substitution method.
In this video (objectives)…
Solve our simultaneous equation using the elimination method.
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.
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.
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.
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.
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.
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.
In this video (objectives)…
Learn a simple way to convert quadratic equations from standard form to vertex form by thinking about the problem geometrically.
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.
In this video (objectives)…
Learn a quick and easy way to convert quadratic equations from standard form to intercept form.
In this video (objectives)…
Identify quadratics with less than two roots
In this video (objectives)…
Congratulations on making it to the end of the section. Here's what we learnt!
In this video (objectives)…
We discuss what to expect from the "Angles and Circles" section of the course.
In this video (objectives)…
Let's cover some of the terminology relating to circles that we're going to need going forward.
In this video (objectives)…
Learn what Pi is and where it comes from. Then use that knowledge to calculate the circumference of a circle.
In this video (objectives)…
Understand how to measure angles in both degrees and radians, and learn how to convert between the two.
In this video (objectives)…
Discover the 4 types of triangle, along with some of the properties that define them.
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
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.
In this video (objectives)…
We investigate some more common angles and look at the ASTC quadrants.
In this video (objectives)…
Learn to find unknown angles in a right triangle using the relationships of SOH CAH TOA.
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.
In this video (objectives)…
Solve the final SAS and SSS type triangles using the cosine rule.
In this video (objectives)…
Investigate how the sine and cosine rules are constructed using our knowledge of the Pythagorean theorem and SOH CAH TOA.
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.
In this video (objectives)…
Graph the sine, cosine, and tangent functions on a graph and get an understanding of periodic motion.
In this video (objectives)…
Understand how altering the; amplitude, magnitude, wavelength, frequency, and position of our waves can help us animate objects.
In this video (objectives)…
Start combining waves to construct more complex patterns and behaviors using constructive and destructive interference.
In this video (objectives)…
Congratulations on making it to the end of the section. Here's what we learnt!
In this video (objectives)…
Find out what a vector is and learn the many ways in which they can be written down.
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.
In this video (objectives)…
We discuss the idea of chirality and the difference between left- and right-handed coordinate systems.
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.
In this video (objectives)…
Learn how a scalar can be used to increase the magnitude of a vector using scalar multiplication.
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.
In this video (objectives)…
In this lecture we look at zero vectors and what it means for a vector has a no magnitude.
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.
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.
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.
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.
In this video (objectives)…
Discover what a matrix is and learn how to define them and write them down.
In this video (objectives)…
Expand on what we know about the addition and scalar multiplication of vectors and apply similar techniques to a matrix.
In this video (objectives)…
Learn some basics of graph theory as we look at how we might represent a graph using an adjacency matrix.
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.
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.
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?
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.
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.
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.
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!
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.
In this video (objectives)…
Find out how to multiply complex numbers and see how this can tie into rotations in two dimensions.
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.
In this video (objectives)…
Learn how the rotation matrix can be derived and then used to rotate objects in 2D space.
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.
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.
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.
In this video (objectives)…
Learn the rules that govern quaternion multiplication and use polynomial expansion to multiply two quaternions together.
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!
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.
In this video (objectives)…
It's finally time to look at how the quaternion rotation formula converts 4D rotation into 3D.
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.
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.
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.
In this video (objectives)…
Congratulations on making it to the end of the section. Let's look at what we learnt!
In this video (objectives)…
We discuss what to expect from the "Probability and Statistics" section of the course.
In this video (objectives)…
We begin this section by looking at how to organize and visualize our data.
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.
In this video (objectives)…
Let's take a look at sigma notation, which gives us a simple and concise way to write long sums.
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.
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.
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.
In this video (objectives)…
Learn how the range and interquartile range can be used to analyze the variability in our data.
In this video (objectives)…
Find out how to calculate the variance and standard deviation of your data.
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.
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.
In this video (objectives)…
Find out how to normalize your datasets or rescale them to any range you need.
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.
In this video (objectives)…
Learn how to calculate the probability for consecutive events, which may be either dependent or independent of each other.
In this video (objectives)…
Learn how the complement rule can make calculating certain probabilities much easier.
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.
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.
In this video (objectives)…
Understand the basics of Bayes' Theorem.
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.
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
In this video (objectives)…
Congratulations on making it to the end of the section. Let's look at what we learnt!
게임 디자인과 개발을 더 잘 하도록 도와주는 국내 유일 게임 수학 강의
실제 비디오 게임 속 문제 상황을 해결하며 재미있게 학습해보는 게임 개발 핵심 수학 이론
퀴즈를 통한 학습 및 C#, C++, Python 언어로 코드화 하면서 게임 수학 기초 이론 완벽 마스터
—
[수학과 게임 개발에 무슨 관계가 있는건가요?]
게임에서 점수를 집계하는 흥미로운 메커니즘, 한 물체가 다른 물체를 부드럽게 따라가도록 하는 방법, 발사체의 경로를 계산하는 방법, 삼각형의 특성을 이용해 적을 정확하게 겨냥하는 방법, 무작위로 아이템을 드롭하게 하는 방법 등.
완성도 있는 게임 속에는 수학이 살아 움직입니다. 수학과 게임은 절대로 뗄 수 없는 관계입니다.
본 강의에서는 게임 개발과 관련 있는 기초 수학 개념을 배웁니다. 흥미로운 실제 문제를 통해 게임을 더 재밌고 완성도 있게 하는 수학 개념을 여러분의 것으로 만들 수 있습니다.
[게임 수학을 마스터하기 위한 최적의 학습 내용 & 방법]
본 강의에서는 아래와 같은 내용을 배웁니다.
게임 개발과 관련된 방정식을 작성하고 풀어내는 방법
삼각형과 원, 기타 도형을 이용해 삼각법의 기초 내용을 재미있게 학습
2D 및 3D 게임을 충분히 개발할 수 있을 만큼 벡터 연산 학습
허수와 복소수, 각과 사원수에 관해 학습
위 내용을 보다 재밌게 학습하기 위해, 실제 비디오 게임 기획과 개발 과정에서 발생하는 문제상황을 해결해가는 방식으로 수학 개념을 학습합니다. 이를 통해 수학적 개념 뿐만 아니라, 왜 이런 수학적 개념이 필요한지 목적도 이해할 수 있습니다.
학습한 내용을 완벽하게 이해하기 위해 다양한 퀴즈와 함께, 연산 내용을 직접 코드화 해봅니다. 추상적인 개념 수준으로 학습을 끝내지 않고, 강의에서 학습한 수학적 내용을 실제 게임에 적용할 수 있게 됩니다.
[130만 수강생의 게임개발 학습을 도운 Ben & Gray 강사의 한 마디]
GameDevtv Team의 Ben, Gray 입니다. 저희의 <게임 수학 : 게임 개발자가 꼭 알아야 할 핵심 수학 이론> 코스에 오신 것을 환영합니다!
이 코스는 킥스타터에서 성공적으로 펀딩을 완료한 결과물이며, 우리 커뮤니티에 모인 전 세계 수십만 회원들의 한결같은 요구에 답하기 위해 제작되었습니다. 여러분의 손으로 직접 필기 노트를 작성하고, C#, C++, 파이썬 등 최신 프로그래밍 언어로 일부 연산 내용을 코드화 해보면서 여러분의 수학 기초는 더 단단해질 것입니다.
우리는 게임만을 위해서가 아니라 삶의 여러 분야에 적용하기 위해서도 수학을 배워야만 합니다. 여러분의 수학 실력이 향상되는 만큼, 여러분의 세상은 더욱더 다채로워질 것입니다.
지금 바로 더 다채로운 세상의 문을 열기 위한 수학 강의를 저희와 함께하시죠. 분명히 만족하실 겁니다!
강의에서 뵙겠습니다.
- Ben & Gary