Math Primer
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Level: |
Beginner |
Instructor(s): |
Frank Luna |
Time Blocks: |
2 weeks |
Availability: |
This Primer is included with Game Mathematics |
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Why should I take this primer?
This primer course reviews the fundamental mathematics necessary to get you started with game development. Essentially it is a quick review of all the key math topics that you studied in you high school level mathematics classes. The purpose here is to quickly prepare you for the more advanced mathematics you will study in the 3D Game Engine Programming series and ultimately in the Game Mathematics course (both of which assume this prior knowledge).
This primer combines key elements from the fields of algebra, geometry, and trigonometry in a way that makes sure that if you are a little rusty in these areas, you will feel comfortable before moving on with your other studies.
Who should take the primer?
Unless you are a very skilled mathematician, you should probably take this seminar at some point during your studies (certainly before taking Game Mathematics). It is an excellent way to clear out the cobwebs and get back to basics as this is where many students find themselves struggling when they start tackling the mathematics of 3D games.
Since this seminar provides a fun and unique way to brush up on basic mathematics, it would also be a great choice if you who wish to augment your studies in school.
What will I learn if I take this primer?
We begin the seminar by (re)introducing you to the real numbers. This will include discussion of integers, rational numbers, and irrational numbers. We will look at how real numbers are used and the types of operations you can perform on them. We'll also examine number lines and basic interval notation so that you can be sure that we are all using the same “language”. This will naturally lead to a discussion of equations and their properties (reflexive, symmetric, transitive, substitution) and you'll see how the real numbers are used to create them. Then we will have a discussion about fractions and exponents as these are generally the trickiest of the real number issues that students have to learn about.
From there you will review the principles of high school level algebra. You'll begin with the concept of variables and look at how they are used to form equations. The next step is to cover the fundamental algebraic rules for solving equations. This will include discussion of both single-variable equations and multi-variable equations. At first, you'll deal primarily with linear equations, but then you will advance to looking at solving non-linear equations, such as quadratics. Our focus will mostly be on methods for simplifying and rearranging equations. Your lesson will conclude with an introduction to some of the common functions you will deal with in game development and you'll find out how they can be used to solve equations. This will include discussion of domain, range, and sets, inverse functions, square roots, exponentials, and logarithms.
Next you'll move on to the basics of analytic geometry, starting with the Cartesian coordinate system and an introduction to graphing points. Then we will talk about lines, planes and spheres and their equations in 2D and 3D. This will set the stage for the most important topic: finding the intersections of these shapes. This will give you a chance to use all of the algebraic methods you learned in the last lesson.
Finally we will wrap things up with the core primitive of most modern 3D game engines: triangles. It is vital that you have a firm grasp of the properties of triangles, and right triangles in particular, so you will get a quick review of some of the core elements of trigonometry. We will talk about the properties of triangles and look at the relationships that exist between their internal angles and the lengths of their sides. This will lead to discussion of the most commonly used trigonometric functions that relate triangle properties to unit circles, including the sine, cosine and tangent functions.
This will set the stage nicely for you if you intend to move on with your 3D Engine Programming training or your mathematics training (see the Game Mathematics course).
What are the prerequisites to understanding the material?
Knowledge of basic arithmetic is required. Since we are essentially going to be moving quickly through the basics of high school math as it pertains to game development, it would be helpful to have taken some high school level math classes as well. If you have not taken high school level mathematics, you should still be able to get through this seminar, but you will likely find it a bit more challenging than would otherwise be the case.
What materials are necessary to complete the primer?
No software is needed to complete this course. However, a good scientific calculator is recommended since you should make an effort to review some of the material on your own and work out the examples on paper.
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