Branches of Mathematics
Numerous new fields have developed with mathematics as its core and foundation, from the primitive number system to the contemporary research fields of computer sciences and probability. Different disciplines of mathematics need to be categorized as a result of the subject’s growing applications and scope.
Different Branches of Mathematics
1. Pure Mathematics:
- Number Theory
- Algebra
- Geometry
- Arithmetic
- Combinatorics
- Topology
2. Applied Mathematics
- Calculus
- Statistics and Probability
- Set Theory
- Trigonometry
Number Theory
Studying the connection between the various types of numbers is made easier by the number theory. There are numerous categories among natural numbers. Here are the various types of numbers: even numbers, odd numbers, square numbers, cube numbers, prime numbers, co-prime numbers, composite numbers, modulo 4 numbers, triangular numbers, and Fibonacci numbers.
Algebra
One of the earliest areas of mathematics that deals with number theory, geometry and analysis is algebra. Algebra is the study of mathematical rules and symbols through the manipulation of those mathematical symbols. It covers a wide range of topics, from the study of abstractions to the solution of simple equations.
Geometry
Geometry is concerned with the dimensions, sizes, forms, and angles of a wide range of everyday objects. Geometry comes from the ancient Greek terms ‘geo’ and ‘metron’, which both imply ‘measuring’. There are two-dimensional shapes and three-dimensional shapes in Euclidean geometry. Flat shapes in plane geometry include 2-dimensional shapes like triangles, squares, rectangles, and circles. Three-dimensional shapes like cubes, cuboids, cones and other related shapes are referred to as solids in solid geometry. The coordinate geometry of points, lines, and planes are the foundations of fundamental geometry.
Arithmetic
It is the study of numbers, particularly the characteristics of conventional operations like addition, subtraction, multiplication and division. The arithmetic operators ‘+’, ‘-’, ‘\(\times\)’ and ‘\(\div\)’ are based on these operations.
Combinatorics
A branch of mathematics called combinatorics is concerned with the investigation of finite discrete structures. Enumerations of sets of elements and the study of permutations and combinations are covered in this branch. It describes the characteristics of mathematical relations. The term ‘Combinatorics’ is used by mathematicians to describe a more extensive subset of discrete mathematics. The formulas are commonly derived using computer science, and it is also used to estimate and analyze algorithms.
Topology
Topology is the study of the characteristics of spaces that are unaffected by continuous deformation. Because, the objects may be stretched and contracted like rubber sheets and yet they cannot be broken. It is frequently referred to as ‘rubber-sheet geometry’. A figure 8 cannot be bent into a square without breaking it, whereas a square can. Consequently, a square differs from a figure 8 yet is topologically equivalent to a circle.
Mathematical Analysis
The theories of differentiation, integration, measure, limits, infinite series, and analytic functions are all part of the discipline of mathematical analysis. The context of real and complex numbers and functions is typically used when these theories are studied. Calculus, which includes the fundamental ideas and methods of analysis, is where analysis originated. Geometry can be considered to be separate from analysis, although it can be applied in the context of objects where specific distances between objects need to be defined.
Calculus
The study of continuous change in functions is the purpose of classical calculus. The majority of these quantities are time functions, such as velocity, which is equal to the change in distance over time. Two central ideas of calculus are derivatives and integrals. The area under the curve is measured by the integral, whereas the rate of change of a function is measured by the derivative. The integral adds up the discrete values of a function over a range of values, whereas the derivative explains the function at a particular point.
Statistics and Probability
The two key ideas in math are probability and statistics. Probability is based on chance, while statistics focuses more on the methods we use to handle different types of data. It aids in the representation of complex data in a very simple and clear manner. Data science professionals use statistics extensively. Professionals make business predictions using statistics. They can use it to forecast the company’s future gain or loss.
Set Theory
In set theory, we study sets and their characteristics. A set is a grouping or collection of objects. These things are frequently referred to as elements or set members. A set is, for instance, a team of baseball players. We can say that this set is finite because a baseball team can only have 26 players at a time. A collection of English vowels is another illustration of a finite set. However, many sets, including the sets of whole numbers, imaginary numbers, real numbers, and natural numbers, among others, are sets that are unlimited.
Trigonometry
One of the most significant areas of mathematics, trigonometry has a wide range of applications. The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as ‘trigonometry’. Therefore, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently employed in computations.
The main branches of pure mathematics are:
- Algebra
- Geometry
- Trigonometry
- Calculus
- Statistics and Probability
There are two other sub-branch classifications for trigonometry, they are plane trigonometry and sphere trigonometry.
Mathematics in higher grades involves the following types:
- Analysis
- Discrete Math
- Applied Mathematics
- Cartesian Geometry
- Matrix Algebra
- Combinatorics
- Topology
- Order theory
Calculus is one of the branches of mathematics that deals with the study of continuous change. Calculus mainly deals with the concepts of limits, derivatives and integrals of various functions.