Church Turing thesis

shounakbhatta

Hello,

I an new to this subject. I was going over Church Turing thesis.

There are certain concepts which I am unable to understand. If somebody can help me understand:

The thesis states:'every effective calculable function is a computable function'.

Now, here what does a function means? Is it the same as we know in mathematics as y=f(x)?

The three ways of computability, the lambda calculus, Turing machine and recursive function define the same class of function. What is meant by that?

Can anybody please help me?

What is

(a) primitive recursive function?
(b) general recursive function

Thanks

-- Shounak