What do I need to study for machine learning? Starting from last year, I have been studying various subjects in order to understand some of the most important thesis of machine learning like


  S. Hochreiter, &amp; J. Schmidhuber. (1997). Long short-term memory. Neural Computation, 9(8), 1735-1780. 


However, due to the fact that I don't have any mathematical backgrounds, I started to learn subjects like


Calculus
Multivariate Calculus
Mathematical Anaylsis
Linear Algebra
Differential Equations
Real Anaylsis (Measure theory)
Elementary Probability and Statistics
Mathematical Statistics


Right now, I can't say I have done studying those subjects rigorously, but I know what the subjects above want to deal with. The thing is that I don't know what I have to do at this point. There are many subjects that machine learning uses to solve many problems out there and I don't know how to utilize them correctly. 

For example, reinforcement learning is now one of the most popular topic that hundreds of thousands of researchers are now doing their research to make a breakthrough of curse of dimensionality. But, as a future employee who's gonna work in IT companies, the task on the desk wouldn't be something I expected to do. 

Is it important to have my own expertise to work in the fields? If so, what kinds of subjects do I have to study right now?

For your convenience, I want to know more about Markov process and Markov decision process.
As a master's degree student in Artificial Intelligence, I strongly advise you to study some basics in Machine Learning.

To do that, you can get a good book (Machine Learning, Tom Mitchell, McGraw Hill, 1997) for the theory and practice by yourself trying some Kaggle competitions.

I suggested the book of Mitchell because he is an expert in the field, and lot of Machine Learning courses uses his book. You can also follow his videolectures online 

On Kaggle, you can find many useful tutorials (named as Notebooks) to get started working with the available datasets.
Some tutorials about Titanic Challenge here