Theories
Mathematics is basically the study of quantity, structure, change and space. These can also be regarded as the fields of mathematics.
Quantity is basically concerned with number, integers, rational numbers and complex numbers. The number theory is basically concerned with these numbers, their properties and the issues that arise from their study.
The next field is structure which basically deals with functions and sets, the structures that exist with themselves. The relevant theories in this aspect are the number theory, the group theory, the order theory, the ring theory, the field theory.
The next field is space and this is basically studied with the help of geometry and trigonometry. The relevant theories in this aspect are the string theory, the theory of perspective, the geometric theory of dynamical systems, the topology theory, the geo-metric group theory, the Lie theory, the dimension theory, the scheme theory, the singularity theory, the sheaf theory and many more.
The next field is change and this basically is concerned with obtaining an understanding and then describing change. The study of calculus, vectors comes under this field. The relevant theories are the measure theory, the distribution theory, the chaos theory, the theory of dynamical systems, the stability theory, and the theory of differential equations.
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