One of the challenges of data science in general is that it is a multi-disciplinary field. For any given problem, you may need skills in data extraction, data transformation, data cleaning, math, statistics, software engineering, data visualization, and the domain. And that list likely isn’t inclusive.
One of the first questions when it comes to machine learning in specific, is “how much math do I need to know?”
This is where I would recommend you start, to get the most value for your time:
Matrix Multiplication (Subject: Linear Algebra)
Probability (Subject: Statistics)
Normal Distributions (Subject: Statistics)
Bayes Theorem (Subject: Statistics)
Linear Regression (Subject: Statistics)
Of course you will run across other math needs, but I think the above list represents the foundation.
If you need places to get started with those topics, check out Kahn Academy, Coursera, or your location library.
In order to limit the scope of the talk, I focused on matrices, vectors and basic operations with them. There is a practical example that uses a machine learning algorithm, but it’s just to show how R handles a more involved equation with matrices. The talk is not an attempt to teach machine learning.