Personally I feel that programming, as a skill, is simply another means of communicating.
Although my examples may tangent, I will attempt to readjust to your questions.
-----Programming as another means of communication-----
If you decide to make a language translation program, you will need to know the specified languages and possibly their patterns/differences.
If you make a art program, if would be significantly more useful if you understand art.
If you make a math program, you must know math.
Same applies to music and gaming.
When folks view games they see interaction, art, and enjoyment.
Programmer may see it differently: physics, calculations, memory control, network messaging, and much more.
-----Answering your questions-----
Also a new beginner's question?
How much does programming language rely on mathematics? How much of it relies more on familiar pattern sequences?
Which one plays more of a role of importance?
It would be dependent on your concentration
both, since they heavily correlate with one other; even simple math.
|How much does programming language rely on mathematics?|
Math is a necessity. Try to build a physics engine without it. Deciding whether or not to allocate processing power to objects who're varying distances away from the host. You might seek the need of theta, x, y, and possibly z. You can't be afraid of math in game programming - unless someone else is doing it for you.
|How much of it relies more on familiar pattern sequences?|
Everything is a pattern, including your game loop. Your program must eventually end.
As a hobby, drawing images to the screen, creating music players, and developing system/networking tools are pretty fun/challenging; the first two requiring very little to no math.
If you aren't doing graphics and such, the most math you'll be using is simple basic math. But you still must be able to count loops and weigh branchs and such. And possibly to count comparisons and such, as a means to test performance; though you'll not likely care about that if it's a hobby.
Let's not talk about the cons... ^^