Mathematics can be divided into various branches based on different classification schemes. A traditional division is into pure mathematics, which is studied for its own interest, and applied mathematics, which can be directly applied to real world problems. Some key branches include: Arithmetic, the oldest branch involving the study of numbers and basic operations between them. Algebra, which studies the properties of numbers and methods to solve equations, leading to abstract algebra and concepts like vectors. Mathematical analysis, concerning continuous change and theories like differentiation, integration and limits. Combinatorics, focused on discrete collections and their structures, including graph theory and counting objects. Geometry and topology, dealing with spatial relationships using axioms

1. BRANCHES OF
MATHEMATICS
By
Aswathy.u.s

2. MATHEMATICS
Mathematics has become a vastly diverse subject over history, and there
is a corresponding need to categorize the different areas of
mathematics. A number of different classification schemes have arisen,
and though they share some similarities, there are differences due in
part to the different purposes they serve. A traditional division of
mathematics is into pure mathematics, mathematics studied for its
intrinsic interest, and applied mathematics, mathematics which can be
directly applied to real world problems.[1] This division is not always clear
and many subjects have been developed as pure mathematics to find
unexpected applications later on. Broad divisions, such as discrete
mathematics and computational mathematics, have emerged more
recently.

3. Arithmetic
Arithmetic or arithmetics (from the Greek ἀριθμός
arithmos, "number") is the oldest[1] and most elementary
branch of mathematics. It consists of the study of
numbers, especially the properties of the traditional
operations between them—addition, subtraction,
multiplication and division.

4. Algebra
The study of structure begins with numbers, first the familiar
natural numbers and integers and their arithmetical operations,
which are recorded in elementary algebra. The deeper properties
of these numbers are studied in number theory. The investigation
of methods to solve equations leads to the field of abstract
algebra, which, among other things, studies rings and fields,
structures that generalize the properties possessed by everyday
numbers. Long standing questions about compass and straightedge
construction were finally settled by Galois theory. The physically
important concept of vectors, generalized to vector spaces, is
studied in linear algebra.

5. Mathematical analysis
A strange attractor arising from a differential
equation. Differential equations are an important
area of mathematical analysis with many
applications to science and engineering.
Mathematical analysis is a branch of
mathematics that studies continuous change and
includes the theories of differentiation,
integration, measure, limits, infinite series, and
analytic functions

6. Combinatorics
Combinatorics is the study of finite or discrete collections
of objects that satisfy specified criteria. In particular, it is
concerned with "counting" the objects in those
collections (enumerative combinatorics) and with
deciding whether certain "optimal" objects exist
(extremal combinatorics). It includes graph theory, used
to describe inter-connected objects (a graph in this sense
is a network, or collection of connected points). See also
the list of combinatorics topics, list of graph theory topics
and glossary of graph theory. A combinatorial flavor is
present in many parts of problem-solving.

7. Geometry and topology
Geometry deals with spatial
relationships, using fundamental
qualities or axioms. Such axioms can be
used in conjunction with mathematical
definitions for points, straight lines,
curves, surfaces, and solids to draw
logical conclusions.

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