Role and need of Mathematics in Data Science
Firstly, I think this question is both broad and opinion-based, however most people don't think so. I'll explain why:

Data Science is a domain which various very much with the industry it is applied in, so very much application-based.

For example: Someone like me in the growth and customer support segment, I use markov models and reinforcement learning, as customers moves can most likely be modeled as a (stochastic) graph. So, when I look out for hiring someone into my team, I look for graph theory skills, linear algebra (obviously) and statistics. 

However, for someone working in the segment where NLP is used, the math needed is different, and so does with every other application of data science.

However, some really very important courses which help someone in the path of a data scientist according to me are:


Linear Algebra
Statistics
Probability theory
Discrete Math
Analytical methodology (Numerical Analysis would be a close to precise name for that)


Some would argue that Information Theory is also very important, however I haven't really used it heavily in my day job, so I don't think it's absolutely necessary.

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