Wale Akinfaderin, a research scientist intern at IBM Research, has written an article on the mathematical background required to fully understand machine learning.
He includes a list of educational resources for those who wish to brush up in certain areas.
Wale correctly stresses that you don’t need this level of knowledge to start making use of machine learning. There are many packaged solutions. However, if you wish to master the topic, some mathematical prowess is inescapable.