This is not a valid question, because the mathematics you need depends on the fields you may be working in, so very different.
Mathematics is not really calculations. First of all, this is a language. So, there are different aspects of it. What you need to actually implement in your code is one thing. Much wider aspect is how you communicate. This is a very different thing. You might need to find some algorithm which you could easily understand in principle, but you might have trouble reading the actual literature just because of trouble of understanding of mathematical language. You can ask a question on the forum, but it might be misunderstood just because your either use very vague non-mathematical language or misuse terminology which is commonly understood as mathematical.
I'll try to list something which I think is the most important or most likely be a problem. This would be pretty much of a minimal common subset.
- Absolutely critical: elementary school mathematics, especially algebra and geometry. You need to be able to proof theorems and understand the proofs.
- Very important: set theory. Just the basics: main concepts and definitions and basic set operations. You also need to understand relationships between formal logic, sets and bitwise operations (bit sets, etc.).
- Often needed: graph theory. Usually just rudimentary basics, such as basic notions, definitions, even understanding just terminology.
- Very often needed, especially when you works with graphics: analytical geometry, linear algebra. In particular, you need to understand transform matrices and matrix algebra, coordinate systems, coordinate system transform.
- Often needed on advanced mathematical level: the theory of complex numbers and elements of the functions of complex variable. Most often, only the basics.
- Often needed on advanced mathematical level: theory of order (partially ordered sets); relationships, basics of relational algebra (mostly important on the advanced level of relational databases).
- Calculus? Basically, every engineer is supposed to know the basics of it, but in practical computing it is very important is some narrow fields of research and development: solving problems of mathematical modeling, integral/differential equations in the worlds of continual models. Interestingly, in near past most of the software developers in the world were of this kind; but now the number of developers boosted by the developers of… who knows what?… I would say, people shuffling data and graphics back and forth… :-)
- Needed for some special category of developers: elements of discreet mathematics. It is especially important in security, encryption, massive data transfer, archiving, optimization of data flow, etc. By some reason, this is a main domain of so called theoretical computer science. I think, not just because this is the most fundamental part of computing, but mostly because many other fields are much more difficult for pure and strict mathematical approach. For example, the practice of multithreading is being developed many years, but fundamental results on, say, optimization of the throughput of the multithreading algorithms are pretty modest, so most tasks are practically solved on intuitive/experimental level, which is not always satisfactory. Anyway, if you lean mathematical aspects of it, which require very advanced level, you may get a competitive edge in future. Or never had such skills requested in your work… :-(
Well, this is already a long list; I could have forgotten some items; and I might be unfamiliar with some other. Anyway, I hope you can get an idea. I would advise one principle: focus one the most fundamental aspects first, try to go in depth rather then in width; better know less but better; don't focus on learning more facts, focus on deep understanding of the ideas; don't trust your intuition, especially at first; the only reliable way to make sure you understand the topic is only one: implement something non-trivial with your own hands.
Good luck,
—SA
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