Learning Maths for Computer Science (Middle School level)

Question

What is the most efficient method by which I can learn mathematics for computer science (beginning at a high school sophomore level)? Which subjects should I focus on, and which subjects should I omit?

Furthermore, in what order should I approach the subjects.

Lastly, are there any good textbooks you'd recommend?

Thanks for your help.

Answer 1

I would not suggest real analysis as a starting point for CS Math, especially not for high school students. There are certainly folks that need real analysis, for things like Learning Theory, Information Theory, or Computational Complexity of Game Theory (e.g., folks who look at complexity classes like PPAD for which computing Brouwer Fixed Points and Nash Equilibria are complete problems). That's not most folks in CS, or even most folks in CS Theory.

Discrete Math is more foundational in CS. This usually encompasses logic (Boolean logic, first-order statements), basic set theory (set operations, set equality proofs), proof by induction, Big-O and asymptotics, Number Theory, Graph Theory, Combinatorics, and Discrete Probability.

I would also second Linear Algebra as being incredibly important for a lot of areas: graphics, data science, robotics, computational geometry, cryptography, error-correcting codes, quantum computing, hardness of approximation, isomorphism testing, and more.

Answer 2

It really depends on what you want to do in computer science. In German universities you will have a mandatory course in linear algebra and real analysis, numerical analysis (which needs knowledge of both of the former subjects) and statistics (which again needs both). Other subjects include graph theory, computability theory and cryptography (which needs linear algebra and a followup lecture on algebra).

But if you only want to understand say machine learning, then you probably won’t need much numerical analysis, graph theory, computability theory or crypto. Similarly computer graphics won’t need much more than linear algebra and maybe a bit of real analysis.

So I would suggest starting with linear algebra and real analysis and go from there. I don’t have a preference for any books but these are among the most teached subjects, so you will quickly find a good text suitable to you.