As far as applying advanced math to music... Not sure how it applies (certainly not my field) but I've heard that some music follows fractal math.
As far as the value to the "average citizen"... My opinion: being scientifically and technically literate is more and more important in making informed decisions about who to vote for, how relatively important different issues of the day are, which companies to patronize (and which to avoid supporting, voting with your money), evaluating options in medical treatment, things like this.
Electrical engineering is based almost entirely on complex math once you get past DC electricity in EE101 as a freshman.
This is actually an interesting background story on the evolution of electric power from DC to AC. Edison, as brilliant as he was, could not grasp complex math and thus was stuck with DC current which uses non-complex math.
Tesla on the other hand could do complex math easily and as such mastered alternating current where everything is based on complex math.
You will use complex math later in engineering or maybe somedaywhen yu are on the "would you like to win lotsa money and Be Rich TV show" and they ask you a complex math question for a billion buks. Oh CWAP, Batman. shoulda learnt that stuff. Now what's the probability that that could happen? Oops, probability. How come they ask me all this stuff I don't know? the real reason is DO yOU want to graduate?
Oh well, philomel.
It is necessary if you want to do something in a field that involes math. You need a lot of math to do physics with can be useful when designening a simple game such as asteroids to tell how fast a object is traveling on the screen
Honestly, you will never use anything past like middle school math in real life (unless your job requires it, which very few do). However, math is worth learning because it expands your ways of thinking and is mentally enriching. It's one of those things where you should learn it simply for the sake of learning it.
I KNOW RIGHT seriously from 1st grade to 12th grade we learn math, reducing fractions and all that but I wonder when we actually will use it!
no one uses it all necessary calculations are done on computers or calculators
So, I completely understand that everyone should be able to add, subtract, multiply, and divide and simple things around those areas. But why and when would we actually use complex math? I understand some professions require certain skills but I go to a school of the arts for piano and chorus, so why should I personally learn it?