Whats the difference between applied mathematics and academics math?
This sounds similar to Australia, where most Universities distinguish between “Pure Mathematics” and “Applied Mathematics”. The names mean what you would expect: maths with particular applications in mind. Algebra, Trig and Geometry would all be “Pure Mathematics”, as would be Number Theory and the analysis part of Calculus. Applied maths would be things like Differential Equations, Waves, Optimisation, and sometimes some overlap with computing and statistics. As an example, check out these Senior (3rd year University) Pure and Applied subjects at the University of Sydney.