How many types of mathematics are there

Topology is a type of geometry developed in the 19th century. Unlike the other types of geometry, it is not concerned with the exact dimensions, shapes, and sizes of a region.

It studies the physical space a surface unaffected by distortion contiguity, order, and position. Topology is applied in the study of the structure of the universe and in designing robots. Number theory, or higher arithmetic, is the study of positive integers, their relationships, and properties.

Logic is the discipline in mathematics that studies formal languages, formal reasoning, the nature of mathematical proof, probability of mathematical statements, computability, and other aspects of the foundations of mathematics. Probability is the branch of mathematics calculating the chances of some things to take place based on the number of the possible cases to the whole number of cases possible.

Numbers from are used to express the chances of something to occur. Real-life applications are in gambling, lottery, sports analysis, games, weather forecasting, etc.

Even the chance of an earthquake or a volcano erupting are given a probability. Statistics are the collection, analysis, measurement, interpretation, presentation and summarization of data. Statistics is used in many fields such as business analytics, demography, epidemiology, population ecology, etc.

Game theory is a branch of mathematics which also involves psychology, economics, contract theory, and sociology. It analyses strategies for dealing with competitive strategies where the outcome also depends on other actions of other partaker in the activity. Functional analysis is under the field of mathematical analysis. Its foundation is the study of vector spaces that has limit-related structure such as topology, inner product, norm, etc. It was developed through the study of functions and the formulation of properties of transformation.

Functional analysis is found to be useful for differential and integral equations. Algebraic geometry is a branch of mathematics that uses algebraic expressions to describe geometric properties of structures.

Differential geometry is a field in mathematics that utilizes different mathematical techniques differential calculus, integral calculus, linear algebra, and multilinear algebra to study geometric problems. It is used in different studies of electromagnetism, econometrics, geometric modeling, digital signal processing in engineering, study of geological structures.

Dynamical Systems also referred to as chaos theory is a mathematical concept where the relationship of a point in space to time is described a fixed set of rules. This concept explains the swinging of a clock pendulum, flow of water in a pipe, number of fish in a lake during springtime, etc. Numerical analysis is an area in mathematics which develops, evaluates, and applies algorithms for numerically solving problems that occur throughout the natural sciences, social sciences, medicine, engineering and business.

Set theory is a discipline in mathematics that is concerned with the formal properties of a well-defined set of objects as units regardless of the nature of each element and using set as a means of expression of other branch of math. Every object in the set has something similar or follows a rule, and they are called the elements.

Do you often wonder about the shapes and sizes of various objects? Then geometry is the branch you must explore. Dealing with the shape, sizes, and volumes of figures, geometry is a practical branch of mathematics that focuses on the study of polygons, shapes, and geometric objects in both two-dimensions and three-dimensions.

Congruence of objects is studied at the same time focussing on their special properties and calculation of their area, volume, and perimeter. The importance of geometry lies in its actual usage while creating objects in practical life. Amongst the prominent branches of mathematics used in the world of technology and science to develop objects, trigonometry is a study of the correlation between the angles and sides of the triangle.

It is all about different triangles and their properties! It is one of the advanced branches of mathematics and studies the rate of change.

With the advent of calculus, a revolutionary change was brought about in the study of maths. Earlier maths could only work on static objects but with calculus, mathematical principles began to be applied to objects in motion. Used in a multitude of fields, the branch can be further categorized into the differential and integral calculus both starkly different from each other.

A branch with mind-numbing questions, calculus is an interesting concept introduced to students at a later stage of their study in mathematics. The abstract branch of mathematics, probability and statistics use mathematical concepts to predict events that are likely to happen and organize, analyze, and interpret a collection of data.

Amongst the relatively newer branches of mathematics, it has become indispensable because of its use in both natural and social sciences. The scope of this branch involves studying the laws and principles governing numerical data and random events. Presenting an interesting study, statistics, and probability is a branch full of surprises. As the name suggests, Number theory is one of the oldest branches of Mathematics which established a relationship between numbers belonging to the set of real numbers.

The basic level of Number Theory includes introduction to properties of integers like addition, subtraction, multiplication, modulus and builds up to complex systems like cryptography , game theory and more. Topology is a much recent addition into the branches of Mathematics list. It is concerned with the deformations in different geometrical shapes under stretching, crumpling, twisting and bedding.

Deformations like cutting and tearing are not included in topologies. Its application can be observed in differentiable equations, dynamical systems, knot theory, and Riemann surfaces in complex analysis. There are a vast number of advanced branches which are a part of the major branches mentioned above. These branches are studied at an advanced level and involve complex concepts that need strong computational skills.

Such advanced branches are listed below. Pure mathematics can be simply described as the study of mathematical concepts purely based on maths and independent of any concept outside of mathematics. Here is the list of branches of Pure Mathematics:. Applied Mathematics uses the applications of varied other disciplines and combines it with mathematical concepts. It is simply the combined application of mathematics with specialised knowledge.

For aspirants wishing to establish a career in mathematics, the first step is to pursue a course in your chosen branch of Mathematics.

Many renowned universities of the world offer lauded degrees in mathematics and its varied branches. Being aware of the major picks available to one helps in reducing the dilemma that comes with choosing the university. Tabulated below are some of the top class universities offering esteemed mathematics programs. Algebra is the hardest branch of Maths.

Mathematics is broadly divided into pure mathematics and applied mathematics. Applied mathematics is which can be applied to real world problems. There are many branches of mathematics namely Algebra, Geometry, Arithmetic, Trigonometry, calculus etc. Algebra is from the Arabic word al-jabr which means a reunion of broken parts. It is one of the broad parts of mathematics.

In general terms, algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is the unifying thread of all the mathematics. It includes everything from solving the study of abstractions to solving the elementary equations. The most basic part is the elementary algebra and the most abstract part is the modern or abstract algebra. Elementary algebra is considered to be essential for any study of mathematics, science or engineering as well as in economics and medicine.

Likewise, abstract algebra is a major area in advanced mathematics, studied mainly by professional mathematicians. For Example:. Using the formula:. Arithmetic is one of the branches of maths that is composed of the properties of the application in addition, subtraction, multiplication, and division, and also the study of numbers.

It is a part of elementary number theory. The fundamental arithmetic procedures include addition, multiplication, subtraction, and division also these add more advanced operations such as square roots, exponentiation, logarithmic functions, percentages, and also trigonometric functions.

It is the basic sign in the four operations of arithmetic. The addition of two whole numbers is the total amount of those sums combined.

The Addition has several important properties. It is commutative. Commutative means the order does not matter. Commutative Property of Addition:. And the other is Associative. Associative means when one adds more than two numbers, the order in which the addition is performed does not matter.

Associative Property of Addition:. If the addition is done for the number in the braces i. Identity Element:. It is that when adding any number to zero the quantity does not change. It is also known as additive identity. Successor and Predecessor:. The successor and predecessor refer to the numbers directly after or directly before a given number. For example, if the given number is The successor number is 19 and the predecessor number is Every whole number has a successor.

Subtraction is also an arithmetic operation next to addition. It represents the operation of removing objects from a collection. The result of subtraction is called the difference. It represents decreasing abstracts and physical quantities using different kinds of objects including negative numbers, fractions, vectors, decimal, matrices etc.