Probability's Connection to Calculus If it is the case that I wish to concentrate my efforts in learning Probability, Statistics and Game Theory, then is it also the case that I must become proficient in calculus?
Is calculus a foundation for all mathematical learning... or are there other foundations that would better pertain to Probability, Statistics or Game Theory.
I ask this because
-When reading books such as "Introduction to Probability" "Introduction to Statistics" or "Introduction to Game Theory" I always end up encountering terminology or notation that I cannot understand and therefore cannot progress through the rest of the book.  I am unfamiliar with the terminology/notation and my immediate reaction is that these terminology/notation are related to calculus in some way ---> am I mistaken in this assumption?  Are there mathematical foundations outside of calculus?
 A: You're asking several related questions here, and some of them I'm not sure you're asking, but here's one I'm pretty sure you're asking: no, calculus is not the only foundational thing you need to learn in mathematics. Even very applied mathematicians should learn lots of linear algebra as it is quite ubiquitous, and it is always a good idea to know a little analysis (roughly, rigorous calculus) and topology. Depending on what you're interested in, it's also a good idea to learn some abstract algebra, maybe a little number theory, and some more analysis and topology. And depending on what kind of probability you're interested in, it would be a good idea to learn some combinatorics as well. 
This is not a complete list, exactly, but it's a start. There's a lot of mathematics out there. 
A: Well, calculus is not a tool for intuition, it's name says it : it's meant to calculate. I believe the purpose for calculus is that when our intuition fails to explain things, we rely on theorems and then use calculus to confirm our intuition. We don't use calculus as a fundamental : it's a tool. The fundamentals lie behind the ideas of those theories. For instance, probability without calculus is just a bunch of nice ideas, because there's always series in there, integrals, and such, so you need to calculate stuff if you want to be able to say something interesting...
EDIT : As an example, so that downvote can be removed...
Guessing the expectation of a continuous random variable can be a pain if the variable has a non-trivial expression, and probabilistic theorems might not make it easier to solve it : using calculus to compute the integral might make it work. Here, calculus helped where probabilistic intuition couldn't ; that doesn't mean there is no intuition in calculus. That is what I meant by "Calculus is not a tool to develop intuition. It's a tool for computing."
All this was said in a probabilistic context. Calculus lovers, I am not offending you : calculus is amazing on its own, too.
Hope that helps,
