We can mathematics in three major groups - Quantitative, Formulation, and Logic. They are meant to solve a problem depending on situations or problem at hand. The fundamental in knowing mathematics is understanding Addition, multiplication, subtraction and division. Quantitative mathematics help us solve problems in numbers, amount etc e.g. finding total population of people in a country, number of things(animals, cars, pens, bags etc); Formulation is a way we build, construct, engineer objects out of concept, emulation or transformation; Logic is thinking in numbers for instance, statistics, probability, percentage. This are predictions and assumptions of things based on facts we have. Calculus, algebra etc are mathematics of both quantity and formulation while Discrete mathematics etc deals with logic of things.
Many books particularly in early years of education e.g. primary and secondary schools accumulated all mathematics sub-sections in a single book. In higher learning however, there is specialization hence you will find a person do only one of the three.