TITLE: What are the prerequisites for stochastic calculus?
QUESTION [31 upvotes]: I am not a math student, and only kind of picking up something whenever I need it. After emerged in the field of machine learning, probability, measure theory and functional analysis seem to be quite intriguing. I am considering learning stochastic calculus myself, but do not quite know what kind of prerequisites should I have. Anyone got some suggestions about the things I need to check before I challenge myself in stochastic calculus?

REPLY [15 votes]: To gain a working knowledge of stochastic calculus, you don't need all that functional analysis/ measure theory. What you need is a good foundation in probability, an understanding of stochastic processes (basic ones [markov chains, queues, renewals], what they are, what they look like, applications, markov properties), calculus 2-3 (Taylor expansions are the key) and basic differential equations.
Some people here are trying to scare you away. It is certainly possible to apply stochastic calculus and gain an intuitive understanding of what's going on without knowing the details of a mean square limit or how to prove a function is square integrable in Lp space. 
After all, it is a tool that first came into being for thermodynamic processes. Many of the Physicists who use it don't concern themselves with martingales and measure theory and all that in their applications. 
Don't get me wrong, Functional analysis/ pdes/ measure theory are all interesting topics, but they are not necessary.
I'd recommend the book: "Paul Wilmott Introduces Quantitative Finance"