Yes, most definitely. You might say "I don't need math to do web
programming", and you are probably right. But then, you don't need a
degree to do web programming to begin with. You do need to know how the
kidneys and the liver work to get a medical degree, even if you don't
need that knowledge to do volunteer work for the Red Cross.
Here's an example of how you would be using math while programming.
Suppose you have to shuffle an array. You can just grab a module
or cut and paste the FAQ, but what if you want (or need) to know
that the algorithm is correct, fair and efficient? You do need math.
Mostly discrete math in this case, but to do discrete math well, you
need to have your foundations in algebra and analysis.
I got a fair bit of mathematics when I did my masters in CS. And I'm
very glad I had it. It doesn't mean I'm constantly busy proving new
theorems, but the mathetical way of thinking makes me write better
programs, if only by easier spotting flaws or holes in the programs.