>>52525539 Pure computer science is study of how programs and machine logic work. This is basically discrete math, formal logic (e.g. type theory), boolean algebra, etc. Algorithm analysis (like proving how some part of a program scales as its input set grows larger) tends to delve into calculus.
If you're planning to apply that knowledge to programming you'll probably also want to understand the math relevant to the program's subject. Some random examples off the top of my head: Calculus and linear algebra show up a lot in graphics and computational physics, but also applications like navigation systems. Computers can only approximate real numbers so everything is discrete math in some way. If you need to study some larger phenomena probability and statistics may turn out to be very useful --- even web analytics are basically this. Signal processing, image and audio compression often involve complex numbers, Fourier transforms, etc.
>>52525539 its not exactly used in any way. You simply have to grasp the concept of variables to be able to write programs. You have to treat everything in your program as a variable made up of other variables.
Then it depends on what you want to write. You have to be fond of solving problems on your own since programming is 1% Idea and 99% figuring out how to get there. Anyone can write code , its figuring out how everything should work together thats the hard (fun) part.
Personally I've always been into procedural generation , so I started learning about noise functions , at first I was making simple 1D terrains using the basic random class , then I moved on to simple 2D terrains using perlin noise , then I learned about using fractals to make the terrain look more realistic.
You work your way up and learn as you go. There is no learning everything there is to know about programming. Thats not how it works.
Computer science is incredibly broad, and pretty deep in places.
For absolute minimum "general" get a degree and get out as a corporate programmer job: High school algebra, Calc 1 All relevant trig, graph theory, set theory and introductory number theory are covered in the CS courses.
For graphics work, add in trig Calc through multivariate Linear algebra Linear programming
Cryptography add in Statistics Number theory And a dedicated graph theory
Many people would include all of those in their CS degree.
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