How Much Mathematics Does an IT Engineer Need to Learn to Get Into Data Science?

First, the disclaimer, I am not an IT engineer:-) I work in the field of semiconductors, specifically high-power semiconductors, as a technology development engineer, whose day job consists of dealing primarily with semiconductor physics, finite-element simulation of silicon fabrication process, or electronic circuit theory. There are, of course, some mathematics in this endeavor, but for better of worse, I don't need to dabble in the kind of mathematics that will be necessary for a data scientist. However, I have many friends in IT industry and observed a great many traditional IT engineers enthusiastic about learning/contributing to the exciting field of data science and machine learning/artificial intelligence. I am dabbling myself in this field to learn some tricks of the trade which I can apply to the domain of semiconductor device or process design. But when I started diving deep into these exciting subjects (by self-study), I discovered quickly that I don't know/only have a rudimentary idea about/ forgot mostly what I studied in my undergraduate study some essential mathematics. Now, I have a Ph.D. in Electrical Engineering from a reputed US University and still I felt incomplete in my preparation for having solid grasp over machine learning or data science techniques without having a refresher in some essential mathematics.