How is Math used in Video Game designing and programming?
Math is an absolute fundamental foundation to successful game development and game design.
Math is everything when it comes to games. From having the ability to calculate the trajectory of an Angry Bird flying through the sky, to ensuring that a character can jump and come back down to the ground without the help of mathematics, games simply wouldn't work.
A character wouldn't be able to walk up a slope, slide down a slide, fire a bullet from a gun, or even jump without the help of the mathematics. The most basic of games use some form of math to the most complex of games. Math is essential to the production of games. It is the flour to the cake that game developers are trying to bake. Without it, the cake wouldn't rise.
Math is used in every aspect of game development, including art. Maya is a math based program that plots out the vertices and normals in mathematical form while the artist just uses a tool that allows them to create stunning 3D graphics without worrying about math. Simply put, you could model Godzilla in notepad and push it into Maya, if you knew were to plot the points in numerical form (which is extremely difficult).
However, a lot of the math is computed at runtime and handled by the game engines that render back face culling, and the other nitty gritty things that would be too cumbersome to do without the use of using an engine to alleviate the math calculation portion at runtime.
A lot of math in gameplay scripting is fairly simple, but math used in game engine architecture is far more complex and a lot more taxing mentally. Math in game development is simulated either by the developer or handled by the engine at runtime by running computations to calculate the operation that is needed.