Arithmetic is about manipulating numbers (addition, multiplication, etc.).
Algebra finds patterns between numbers:
a^2 + b^2 = c^2 is a famous relationship, describing the sides of a right triangle.
So Algebra finds entire sets of numbers — if you know a and b, you can find c.
Calculus finds patterns between equations:
you can see how one equation (circumference = 2 * pi * r) relates to a similar one (area = pi * r^2).
An Algorithm is a step by step method of solving a problem
If you have to establish an Algorithm to recognize shapes like circle, triangle etc. and it needs modifications to recognize the additional shapes then it is Analytics.
If the algorithm is complete in itself to perform the task in this case shape recognition and does not require any further changes then it is Machine Learning.
If the algorithm is based in a hardware and functions without any human interface then it is Artificial Intelligence.
