Difference Between Mathematics and Applied Mathematics

Mathematics vs Applied Mathematics

Mathematics first emerged from the daily necessity of the ancient people to count. Trading, referring to time, and measuring the crop or land required numbers and values to represent them. Search of creative ways of solving above problems resulted in the basic form of mathematics, which resulted in natural numbers and their computations. Further development in the field led to the introduction of zero, then negative numbers.

Through thousands of years of developments mathematics have left the fundamental form of computation and transformed into more abstract study of the mathematical entities. Most interesting aspect of this study is that these concepts can be used in the physical world for prediction and for countless other uses. Therefore, mathematics has a very important position in any developed civilization in the world.

The abstract study of the mathematical entities can be considered as pure mathematics while the methods describing their application for specific cases in the real world can be considered as applied mathematics.


Simply put, mathematics is the abstract study of quantity, structure, space, change, and other properties. It has no strict universal definition. Mathematics originated as a means of calculating, though it has developed into a field of study with a wide variety of interests.

Mathematics is governed by logic; supported by the set theory, category theory and theory of computation give structure to the understanding and investigating mathematical concepts.

Mathematics is basically divided into two fields as pure mathematics and applied mathematics. Pure mathematics is the study of entirely abstract mathematical concepts. Pure mathematics has sub fields concerning the quantity, structure, space, and change. Arithmetic and number theory discuss the computations and quantities. Larger, higher structures in the quantities and numbers are investigated in the fields such as algebra, number theory, group theory, order theory, and combinatorics.

Geometry investigates the properties and objects in the space. Differential geometry and topology give a higher level understanding of space. Trigonometry, fractal geometry, and measure theory also involve the study of space in a general and abstract manner.

The change is the core interest of the fields like calculus, vector calculus, differential equations, real analysis and complex analysis, and chaos theory.

Applied Mathematics

Applied mathematics focus on the mathematical methods used in real life applications in engineering, sciences, economics, finance, and many more subjects.

Computational mathematics and statistical theory with other decision sciences are the major branches of applied mathematics. Computational mathematics investigates the methods for solving mathematical problems difficult for ordinary human computational capacity. Numerical analysis, game theory, and optimization are among several of the important computational mathematics fields.

Fluid mechanics, mathematical chemistry, mathematical physics, mathematical finance, control theory, cryptography, and optimization are fields enriched by methods in computational mathematics. The computational mathematics extends into computer science too. From internal data structures of large databases and performance of algorithms to very design of computers rely on sophisticated computational methods.

What is the difference between Mathematics and Applied Mathematics?

• Mathematics is the abstract study of the quantity, structure, space, change, and other properties. It is generalized in most cases, to represent the higher structure in the mathematical entities and, therefore, sometimes difficult to comprehend.

• Mathematics is based on mathematical logic, and some fundamental concepts are described using the set theory and category theory.

• Calculus, Differential equations, algebra etc. provide means of understanding the structure and properties of quantity, structure, space, and change in abstract ways.

• Applied mathematics describes the methods in which mathematical concepts can be applied in the real world situations. Computational sciences such as optimization and numerical analysis are fields in applied mathematics.