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Displaying sprites in a 2.5D raycasting engine

I'm developing a raycasting engine like the one used in DOOM, Wolfenstein 3D, etc. My engine is capable of correctly displaying walls and textures on walls, but I'm stuck at sprites rendering. Given ...
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What mathematics would I need to know in order to build a 2.5D raycasting engine

I realize this is a fairly common-type question, but I've been studying Maths in my spare time, fairly slowly at that, and I really want to develop a raycasting engine like the original DOOM. I know ...