A Little Background
I'm 28 today, and I've never had any formal training in software development, but I do have two higher education degrees equivalent to a B.A in Public Relations and an Executive MBA focused on Project Management. I've worked on those fields for about 6 years total an then, 2,5 years ago I quit/lost my job and decided to shift directions.
After a month thinking things through I decided to start freelancing developing small websites in WordPress. I self-learned my way into it and today I can say I run a humble but successful career developing themes and plugins from scratch for my clients - mostly agencies outsourcing some of their dev work for medium/large websites.
But sometimes I just feel that not having studied enough math, or not having a formal understanding of things really holds me behind when I have to compete or work with more experienced developers. I'm constantly looking for ways to learn more but I seem to lack the basics.
Unfortunately, spending 4 more years in Computer Science is not an option right now, so I'm trying to learn all I can from books and online resources. This method is never going to have NASA employ me but I really don't care right now. My goal is to first pass the bar and to be able to call myself a real programmer.
I'm currently spending my spare time studying Java For Programmers (to get a hold on a language everyone says is difficult/demanding), reading excerpts of Code Complete (to get hold of best practices) and also Code: The Hidden Language of Computer Hardware and Software (to grasp the inner workings of computers).
So, my current situation is this: I'm basically capable of writing any complete system in PHP (with the help of Google and a few books), integrating Ajax, SQL and whatnot, and maybe a little slower than an experienced dev would expect due to all the research involved.
But I was stranded yesterday trying to figure out (not Google) a solution for the FizzBuzz test because I didn't have the
if($n1 % $n2 == 0)
method modulus operator memorized.
What would you suggest as a good way to solve this dilemma? What subjects/books should I study that would get me solving problems faster and maybe more "in a programmers way"?
EDIT - Seems that there was some confusion about what did I not know to solve FizzBuzz.
Maybe I didn't express myself right: I knew the steps needed to solve the problem. What I didn't memorize was the modulus operator. The problem was in transposing basic math to the program, not in knowing basic math.
I just used this as an example of how not having dealt with math in a computer environment before makes me lose time looking up basic things like modulus operators to be able to solve simple problems.