TITLE: Future learning for a math graduate in applied mathematics references
QUESTION [6 upvotes]: As a mathematics graduate with focus on programming we did a whole lot of coding of some mathematical statements (as well as proving them), but yet rarely giving real life examples and applications for given statements.
So for my future work i would like to learn some of the applications (mostly in electronics, programming, physics...) and get some references where i can continue to learn so that - given a problem i can correlate that to something i have learned before.
I am most interested in applications for these fields: 

Numerical analysis

Interpolation (Hermite, multidimensional, Newton, Spline ...)
Approximation ( Least squares, uniform approximation,..)
Numerical methods for solving differential equations
Numerical methods for finding eigenvalues and eigenvectors
Numerical Methods for solving non-linear equations
...

Mathematical analysis

Integration by curve, surface
Integrals with parameters 
Fourier series,Fourier transformation,Fourier integral
Uniform convergence (for sequence of functions, series, integrals) 
Weierstrass function, Riemann zeta function  
...

Measure theory

Lebesgue measure, Lebesgue integral 
Radon - Nikodym theorem , derivate
Monotone convergence theorem, dominant convergence theorem 
Lp spaces, norms
...

Complex analysis

Cauchy integral theorem
Picard's theorem 
Laurent series ...
Holomorphic functions 
...


References, books, websites - anything will do, just as long as there are multiple examples (also the more on the side of programming (algorithms, problem solving) and electronics the better)

REPLY [2 votes]: Probability theory is to me strictly pure mathematics, but with strong applicable properties. If you like measure theory, along with functional/modern analysis then probability theory is the area for you; The axioms of probability theory (Kolmogorov) are strictly measure theoretic. Then how one builds up expected value and so on is also integration theoretical. One integrates with respect to a probability measure, thus making the Lebesgue integral or equivalent necessary. I strongly encourage you to read the table of content in Kallenberg's Foundations of modern probability theory, to get a glimpse of what probability theory might entail, from the analytical stand point. It is sadly a bit advanced though, but I do not expect someone to read it all.
Probability theory is to some degree either very analytical or very combinatorial/graph theoretical, i.e. either you get hooked on stochastic analysis and SDE:s (along with stochastic integration and such), or you get hooked on percolation theory and Markov analysis, the latter having intimate connections with statistical mechanics (Ising's model for instance).
And as a last point, probability theory is computationally challenging, in so far as we need strong programmers as well. For instance, Monte Carlo methods are a very popular numerical method.
I hope you do not mind me diverging from your wish list, but I believe probability theory is worth a notice.