Top 10 Branches of Mathematics

Mathematics, as they call it is the language of the universe. Just like any other field of study, mathematics has been divided into major and minor branches of study as well. This division and subdivision of the subject are necessary so that people can focus and specialize at a particular thing from within the field. In this post, we will look at the different branches of mathematics.

Mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are the power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and even effective communication skills.

To begin with, the subject can be broadly categorized into two fields – pure mathematics and applied mathematics. These two fields then further branch out into various other divisions, which we’re going to list down here.

Branches of Mathematics

By Parinita Gupta

1. Algebra

The word algebra has been derived from an Arabic term “al-Jabr” which means ‘bringing broken things together by force’, and technically that is exactly what we do in algebra. We fix a broken equation, put it together, and come up with a solution.

What is Algebra?

Within the broad field of mathematics, this fascinating branch is all about solving the complicated generic (or non-generic) algebraic expressions by manipulating them to come up with an answer. It also involves complicated formulas, and a set of rules to help you manipulate the equations and derive solutions from the problems posed. 

The quantities within the said equations are unknown to us and therefore not represented via numerical digits, instead, they are represented within the equation via a variable, which could be any character from the English lexicon, ‘a’,’x’,’b’ or ‘c’. Sometimes Greek and Latin lexicons are used as well.

However, within the equation, only a few numbers are known to us, through which we manipulate the equations and come down to an answer.

Applications of Algebra

Algebra is one of the most important branches of study for mathematics and is applied in various other fields of study as well such as physics, chemistry, biology, engineering, biotechnology, and even economics and accounting.

Some example applications of algebra in common life are:

  • Making a schedule of activities
  • Preparing the food or doubling or halving the recipe
  • A kid developing spatial intelligence
  • Tax calculations
  • Astrological calculations
  • Technological developments
  • Budgeting

2. Number theory

This is where the number’s games begin. Number theory is one of the oldest branches of mathematics which is very well researched upon and yet there remains plentiful more to discover in this branch with the evolution of computers and the internet.

Despite being one of the oldest branches of mathematics, it continues to evolve and change every day. The number theory involves establishing a relationship between a set of real numbers, integers, whole numbers, and natural numbers.

Number theory also includes identifying the properties of numbers such as addition, subtraction, multiplication, modulus which further branches out to the associative and dissociative properties.

Furthermore, the number theory also deals with the concept of encryption, binary, cryptography, game theory and so much more.

Applications of Number Theory

The best-known application of number theory is public-key cryptography, such as the RSA algorithm. Public key cryptography in turn enables many technologies we take for granted, such as the ability to make secure online transactions. In addition to cryptography, number theory has been applied to other areas, such as:

  • Error correcting codes
  • Numerical integration
  • Computer arithmetic
  • Random and quasi-random number generation

3. Arithmetic

This branch of mathematics involves dealing with numbers and their applications in calculations etc. Properties such as simple addition, subtraction, multiplication, and division come into play here. Despite being simple, it is the root reason why we are now able to solve the most complex of the problems and come up with a solution.

Arithmetic also involves more complex concepts of mathematics such as limits, exponents, etc. This is the simplest and the most essential branch of mathematics since it’s used in our everyday life and also at the same time, used for computation, etc.

Applications of Arithmetic in Daily Life

You use some basic math concepts continually and never even realize it. If you want to have a healthy life, and one in which you do not waste money, you use arithmetic all the time. Every time you go to the grocery store, you should be calculating which item of the several offered is the best buy.

4. Geometry

This is the branch of pure mathematics which is rather a little head if not exactly “advanced” and gets out of just numbers and deals with real-world problems.

One might say that shapes such as squares, circles, rectangles, and triangles are hardlyreal-world problems. But if you think about it practically, it quite literally is. Not just shapes, but angles, tangents, volumes, and what not.

This is where mathematics jumps out of numbers and comes into the application in the practical world. Geometry is not really a branch of “applied mathematics”, since geometry only deals with the most basic fundamentals of it.

It involves the study of angles, shapes, sizes, figures, or any geometrical object in both the dimensions, i.e., 2D and 3D. When talking about 3-dimensional figures, 3D shapes like cubes, cones, bars, spheres come into play. Special properties of these shapes are also studied in this branch.

5. Trigonometry

One could call this an extension to the geometry branch, but the study has evolved so much so that it needed its own name. Trigonometry is one of the advanced branches of mathematics and involves the study of triangles, and triangles only whereas geometry involves the study of all shapes and angles.

Trigonometry specifically focuses on studying the angles and sides of the triangle in order to determine its distances, lengths, and other properties. It also establishes a correlation between its sides and angles and at the end of the day, it is all about triangles, different types of them, and their properties.

6. Topology

This is one of the newest branches of mathematics that is concerned with the deformations and changes in different shapes due to stretching, crumpling, twisting, bedding, etc. However, deformations like cutting and tearing do not include in the study of topologies.

Topology is applied in calculus, knot theory, Riemann surfaces, etc.

7. Combinatorics

This is a branch of mathematics that mainly involves counting to obtain solutions to the problems of selection and arrangement. It is also used to determine certain properties and of finite structures or discrete systems and operations within them.

8. Mathematical Analysis

One of the advanced branches of pure mathematics, the analysis deals with limits, and theories related to it such as to measure, infinite series, analytics functions, and pre-calculus, i.e., differentiation and integration.

These are studied in the context of the real and complex numbers and their functions. Though it could be said to be different from geometry, it does involve application in geometrical objects to come up with solutions to geometrical problems.

9. Calculus

One of the most complex and highly advanced branches of mathematics, which in fact itself has levels to it, be it Pre-calculus, advanced calculus, Accelerated Multivariable Calculus, differential calculus, integral calculus, etc.

With its advent, the field of mathematics was itself brought into a revolutionary change, which is quite ironic since this branch aims to study the ‘rate of change’ to be put simply. Previously, mathematics only involved calculations with static objects, but with the evolution or much rather, the birth of calculus, the mathematical principles were beginning to be applied to objects in motion.

Calculus is today used in a vast number of fields one of the most fundamental branches of pure mathematics that are used the most in applied mathematics.

10. Statistics and Probability

This is one of the most important and underrated branches of mathematics. It is also one of the easiest, or at least easier when compared to branches like calculus.

This branch utilizes mathematical concepts to predict events that are likely going to happen. It does so by organizing, analyzing, and interpreting a collection of data. It also involves a set of rules and formulas in order to carry out the prediction.

Despite being the most underrated, it is now one of the most indispensable branches of mathematics. By now you have probably heard of the market demand for data analysts and scientists.

Statistics is all about that and now with the evolution of technology, more important and impactful than ever. It is applied in various fields of natural and social sciences such as marketing.

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About Parinita Gupta:

Parinita is a full-time banking professional. Additionally, she is also a passionate blogger and digital marketer.

She mostly writes about the Banking & Finance, Technology, and FinTech sector. But, she also enjoys writing on other topics as well.  You can follow her on Twitter.

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