This is a starting point for the branches of Mathematics.

• The structure for this subject is focused on definition and application.
• The structure also focuses on definitions that are simple for the reader to currently choose what subject aligns with their interests most. The definitions come from Oxford, Merriam-Websters, and similar well-articulated dictionaries.

• Mathematics: The study of human enquiry involving the study of numbers, quantities, data, shape and space and their relationships, especially their generalizations and abstractions and their application to situations in the real world.

We can divide Mathematics into two categories: Pure & Applied.

• Pure Mathematics: The study of the relationships between abstract quantities according to a well-defined set of rules.
• Applied Mathematics: The application and use of mathematics in the context of the real world.

Algebra:

• Algebra (General): The area of mathematics related to the general properties of arithmetic. Relationships can be summarized by using variables, usually denoted by letters x, y, n, … to stand for unknown quantities, whose value(s) may be determined by solving the resulting equations.
• Abstract Algebra: The area of mathematics concerned with algebraic structures, such as groups, rings and fields, involving sets of elements with particular operations satisfying certain axioms.

Arithmetic:

• Arithmetic (General): The area of mathematics relating to numerical calculations involving only the basic operations of addition, subtraction, multiplication, division and simple powers.
• Number Theory (Advanced Arithmetic): The area of mathematics concerning the study of the arithmetic properties of integers and related number systems such as prime numbers.

Calculus:

• Calculus (General): A method of computation or calculation in a special notation. Methods comprise differential and integral calculus.
• Differential Calculus: The part of mathematics that develops from the definition of the derivative of a function or the gradient of a graph. The subject is concerned essentially with the rate of change of one quantity with respect to another.
• Integral Calculus: The subject that arose from the problem of trying to find the area of a region with a curved boundary.

Geometry:

• Geometry (General): The area of mathematics related to the study of points and figures, and their properties.

Topology:

• Topology (General): The area of mathematics concerned with the general properties of shapes and space, especially properties unchanged by continuous distortions such as stretching.

Trigonometry:

• Trigonometry (General): The area of mathematics relating to the study of trigonometric functions in relation to measurements in triangles and the behavior of wave functions.

Accounting:

• Accounting (General): The system of recording and summarizing business and financial transactions and analyzing, verifying, and reporting the results.

Mechanics:

• Mechanics (General): The area of mathematics relating to the study of the behavior of systems acted on by forces, whether in equilibrium or in motion.
• Quantum Mechanics: The area of mechanics concerned with the behavior of particles at small scales where the discrete nature of matter becomes important, giving rise to wave–particle duality.

Statistics:

• Statistics (General): A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data.

Probability:

• Probability (General): A branch of mathematics concerned with the study of possibility.