# What is the difference between algebra and analysis

## What is the difference to algebra, arithmetic and analysis?

Arithmetic describes the simple mathematics of natural numbers with the operations adding, subtracting, multiplying and dividing with the associated arithmetic operators +, -, *,:. You learn this in elementary school.

The elementary algebra describes equations and inequalities with variables, you learn this in the secondary school (secondary school, secondary school, high school, ..)

Higher algebra deals with algebraic structures such as groups, rings, bodies, modules and, above all, vector spaces over a body. She studies the properties of such structures. In further developments such as category theory, algebraic structures are also examined in relation to other mathematical sub-areas, such as in algebraic geometry and algebraic topology. You learn the basics of it at school, but most of it during your studies.

The analysis is mainly based on calculus (i.e. integrating and differentiating). In it properties of functions, series and sequences are examined. You learn this in school.

In multidimensional analysis, properties of functions of higher dimensions are sought. Terms like partial differential equation and triple integral are important here. There are also many integral clauses and other deepening of infinitesimal calculus that are no longer taught in school. There is also functional analysis, but it is too complicated to be explained here.