Does anyone know what bridges the gap between intuitive calculus and real anaylsis?

I've survived no longer than two chapters on real analysis by Rudin.

 

A tad more detail would help pin down your difficulty.

Two good, modern, very clear first year university texts are

Mathematical Analysis by Binmore (He also has a good book called Calculus)

Fundamentals of Mathematical Analysis by Haggarty

Older books that bridge tha gap between sixth form and university are

Mathematical Analysis by Quadling

Mathematics for Science by Ferrar

 

Quite simply it is the degree of rigor in stating propositions and offering proofs. I've fallen down the stairs quite hard each time I tried to mix it up with the mathematical rigor folks.

I can grasp the Ito Calculus, but Stochastic Processes leave me with a cold empty feeling.

 

O.K, basically, I'm a fish that's got too big for the tank and in looking for more exotic math' methods I'm now a minnow in the Atlantic Ocean; the shift is too abrupt.

Coming from an engineering background, formal methods are not a requisite but more of an interest/hobby of mine. Engineering maths is starting to become too boring for me now, it's cumbersome grunge prone to error with a mix up of signs etc etc.

I want to start proving formally what I already know and that led me to real analysis but the change is just too abrupt, I just want to be put in a new fish tank that will allow me to start growing gradually again.

 

There is no help for what ails you, but you might try numerical analysis and counting problems. They might ease the transition.

You might also try Polya, How to Solve It

 

By engineering math do you mean numerical analysis? I found numerical analysis to be lively and entertaining. It's amazing, in fact. The fact that I had taken the course got me the job according to one of my interviewers. Programming a computer to use an iterative approach helped me to understand what the calculus was all about.