Not sure which course you are referring to in particular. The general basics required for machine learning are:
Probability and Statistics - Gets used a lot, especially in classification. A good understanding of conditional probability and Bayes theorem is an absolute necessity.
Linear Algebra - Required more from an implementation standpoint. Most procedures are best implemented as matrix and vector operations instead of loops. You can use a lot of nested for-loops to achieve the same results as matrix operations but that is not computationally optimum.
Optimization - Almost all ML algorithms essentially boil down to a convex optimization problem - be it linear/logistic regression or neural networks or SVMs or tree-based methods. It really helps to have some basic understanding of optimization theory.
Note: Optimization necessarily requires a strong grasp of differential calculus.
Programming skills - You don't need to be an expert developer but basic coding skills are a must. Pick up a commonly used language like Python to get started. Python is easy to learn and has a lot of open source packages for machine learning. It also integrates well with Big data tools like Hadoop and Spark (PySpark). These tools may not be needed for beginners but they will be useful later when you deal with massive datasets.
Andrew Ng uses MATLAB in his Coursera course. It is extremely powerful but very expensive at the same time. The open source free equivalent OCTAVE is simply not as good and somewhat painful to use. It may be useful to know that a majority of the machine learning community uses Python. So you would be recommended learning that. The subsequent development of prototypes into products usually happens in more traditional languages like C++ or Java.
A good, well-maintained computer - Don't underestimate the importance of this. It may not matter in the beginning but lack of raw computation power and RAM can be frustrating while working with bigger datasets and computationally intensive techniques like neural networks. Maintain your computer well. Always ensure that there is no accumulated dust inside the system and its cooling unit. Dust can significantly affect the system's performance and result in longer training times of algorithms as well as overheating of the computer.