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There are many, many branches of mathematics. Among the most common:

Elementary arithmetic

Algebra

Geometry

Trigonometry

Calculus

Analysis

Vector Calculus

Topology

Statistics

Combinatorics

Matrix Mathematics/Linear Algebra

You could also include applied mathematical branches such as Thermodynamics and Theoretical Physics. The list is practically endless.
Some of the different branches of Math are: Algebra, arithmetic, calculus, geometry, and trigonometry.
calculus, algebra, queueing theory, String Theory, functional analysis, statistics and linear algebra
The typical progress of a student would be basic math, algebra, geometry, trigonometry, and calculus.

After calculus one might take linear algebra, differential equations, mathematical modeling, real analysis, number theory, statistical analysis, topology, group theory, and perhaps tensor calculus. (A tensor is a more generalized concept of a vector, apparently.)

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