Shakuntala Devi rightly said that without mathematics, there is nothing you can do. To explore more, let’s first know the 5 main branches of mathematics, i.e. Algebra, Number Theory, Arithmetic and Geometry. In the past 2 decades or so, our modern world has introduced more branches like Probability and Statistics, Topology, Matrix Algebra, Game Theory, Operations Research derived from these oldest branches of math. Breaking the myth of mathematics being called boring, we bring to you all about branches of mathematics with their list, tree and career options!
Check Out: Vedic Maths
Tree of the Branches of Mathematics
Main Branches of Mathematics
Mathematics is a complex area of study and comprises interlinked topics and overlapping concepts. Additionally, extensive analysis of the branches of mathematics helps students in organizing their concepts clearly and developing a strong foundation. Being aware of the differences and uniqueness of branches of mathematics helps in methodically studying various concepts of maths and also guides students in deciding the branch they would like to pursue as a career.
Here are the main branches of mathematics:
 Foundations
 Arithmetic
 Algebra
 Geometry
 Trigonometry
 Calculus
 Probability and Statistics
 Number Theory
 Topology
Below explained are the important branches of mathematics with their unique features and distinct concepts. These branches are important for laying a strong foundation for mathematics.
Fun Fact: 40 °C is equal to 40 °F.
Arithmetic
“Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians.”
– Bertrand Russell
Arithmetic is one of the most basic branches of mathematics and deals with numbers and their applications in many ways. Addition, subtraction, multiplication, and division are used as the basic groundwork to solve a large number of questions and progress into more complex concepts like exponents, limits, and many other types of calculations. This is one of the most important branches because its fundamentals are used in everyday life for a variety of reasons from simple calculations to profit and loss computation.
Algebra
“The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.”
– Rudolf Clausius
A broad field of mathematics, algebra deals with solving generic algebraic expressions and manipulating them to arrive at results. Unknown quantities denoted by alphabets that form a part of an equation are solved for and the value of the variable is determined. A fascinating branch of mathematics involves complicated solutions and formulas to derive answers to the problems posed.
Fun Fact: The word “mathematics” only appears in one Shakespearean play, “The Taming of the Shrew”.
Geometry
“The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.”
Isaac Newton
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 twodimensions and threedimensions. 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.
Trigonometry
Derived from Greek words “trigonon” meaning triangle and “metron” meaning “measure”, trigonometry focuses on studying angles and sides of triangles to measure the distance and length. 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!
Calculus
“Calculus is the most powerful weapon of thought yet devised by the wit of man.”
– Wallace B. Smith
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 mindnumbing questions, calculus is an interesting concept introduced to students at a later stage of their study in mathematics.
Fun Fact: “Forty” is the only number that is spelled with letters arranged in alphabetical order.
Probability and Statistics
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.
Number Theory
“Mathematics is the queen of the sciences, and number theory is the queen of mathematics.”
– Carl Friedrich Gauss
As the name suggests, Number theory is one of the oldest branches of Mathematics that established a relationship between numbers belonging to the set of real numbers. The basic level of Number Theory includes an introduction to properties of integers like addition, subtraction, multiplication, modulus and builds up to complex systems like cryptography, game theory and more.
Topology
“The basic ideas and simplest facts of settheoretic topology are needed in the most diverse areas of mathematics; the concepts of topological and metric spaces, of compactness, the properties of continuous functions and the like are often indispensable.”
– Pavel Sergeevich Aleksandrov
Topology is a much recent addition to 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.
Fun Fact: Every odd number has an “e” in it.
Advanced Branches of Mathematics
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.
Here are the 10 branches of mathematics:
 Matrix Algebra
 Numerical Analysis
 Operations Research
 Complex Numbers
 Calculus
 Set Theory
 Game Theory
 Analysis
 Cartesian Geometry
 Combinatorics
Branches of Pure Mathematics
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:
 Algebra
 Number Theory
 Geometry
 Arithmetic
 Topology
 Combinatorics
 Mathematical Analysis
Branches of Applied 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.
Here are the branches of applied mathematics:
 Statistics and Probability
 Set Theory
 Calculus
 Trigonometry
Fun Fact: Archimedes [287 – 212 BC] is the father of Mathematics
Top Universities for Courses in Mathematics
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.
University  Country 
Imperial College London  England 
University of Dundee  Scotland 
Jacobs University Bremen  Germany 
University of Pavia  Italy 
Carleton University  Canada 
Southern Utah University  United States 
Cardiff University  Wales 
University of Almeria  Spain 
Clarkson University  United States 
EastWest University  United States 
Top Indian Colleges for Mathematics
 Fergusson College
 Mount Carmel College
 Stella Maris College
 St. Xavier’s College
 Jadavpur University
 St.Stephen’s College
 Ramakrishna Mission Vivekananda College
 Christ University
Career Options in Mathematics
If the number game attracts you and you can’t help but add or multiply any number you see, then you should pick up Mathematics as a career. You can become one of the following professionals if you choose a career in Mathematics:
 Teacher/Lecturer– You can teach mathematics at the high school level and even university level if you are qualified enough and even explore research via postgraduation.
 Statistician A statistician collects data, turns them into charts and graphs and makes interpretations which is an important aspect in all professions.
 Data Analyst/Scientist– A data analyst/scientist is similar to a statistician but with certain differences. In Data Science, you will use scientific methods of data collection, comparison and give solutions to the organisation relatively.
 Mathematician– A mathematician is involved in all fields of profession. Whether it be inventing new business valuation methods or creating a formula that sends a rocket to the ISS, a mathematician does it all.
 Cryptographer– A cryptographer is a person who encodes and decodes various symbols or modes of communication to decipher what it means. Additionally, they also create safe codes for the military or other organisations.
Every profession needs the Branches of Mathematics as the subject ties all the broken pieces and creates uniformity.
FAQs
Algebra, Geometry, Calculus and Statistics & Probability are considered to be the 4 main branches of Mathematics.
Algebra is the hardest branch of Maths. Abstract algebra particularly is the most difficult portion as it includes complex and infinite spaces.
Archimedes [287 – 212 BC] is the father of Mathematics
It is difficult to trace back the exact origins of Maths. But it is estimated that in early 6th century, Pythagoreans invented Maths. After that Euclid introduced the axiomatic method consisting of the definition, axiom, theorem, and proof.
Are you intrigued by numbers and have a flair for doing difficult numeric calculations? Then, Mathematics is an allencompassing science that deals with quantity, space and numbers and abstract concepts as well as applied maths in other fields. While at first glance it might be difficult to identify the branches of mathematics, it is imperative to possess knowledge about them for any student wishing to gain a holistic idea about the subject. We hope this blog has presented a comprehensive list of different areas of study and branches of mathematics. (Phentermine) Planning to study a degree in Mathematics? Experts at Leverage Edu can help you find the best course and university as well as assist you throughout the admission process to ensure that you send a winning application! Sign up for a free session today!
Shakuntala Devi rightly said that without mathematics, there is nothing you can do. To explore more, let’s first know the 5 main branches of mathematics, i.e. Algebra, Number Theory, Arithmetic and Geometry. In the past 2 decades or so, our modern world has introduced more branches like Probability and Statistics, Topology, Matrix Algebra, Game Theory, Operations Research derived from these oldest branches of math. Breaking the myth of mathematics being called boring, we bring to you all about branches of mathematics with their list, tree and career options!
Check Out: Vedic Maths
Tree of the Branches of Mathematics
Main Branches of Mathematics
Mathematics is a complex area of study and comprises interlinked topics and overlapping concepts. Additionally, extensive analysis of the branches of mathematics helps students in organizing their concepts clearly and developing a strong foundation. Being aware of the differences and uniqueness of branches of mathematics helps in methodically studying various concepts of maths and also guides students in deciding the branch they would like to pursue as a career.
Here are the main branches of mathematics:
 Foundations
 Arithmetic
 Algebra
 Geometry
 Trigonometry
 Calculus
 Probability and Statistics
 Number Theory
 Topology
Below explained are the important branches of mathematics with their unique features and distinct concepts. These branches are important for laying a strong foundation for mathematics.
Fun Fact: 40 °C is equal to 40 °F.
Arithmetic
“Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians.”
– Bertrand Russell
Arithmetic is one of the most basic branches of mathematics and deals with numbers and their applications in many ways. Addition, subtraction, multiplication, and division are used as the basic groundwork to solve a large number of questions and progress into more complex concepts like exponents, limits, and many other types of calculations. This is one of the most important branches because its fundamentals are used in everyday life for a variety of reasons from simple calculations to profit and loss computation.
Algebra
“The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.”
– Rudolf Clausius
A broad field of mathematics, algebra deals with solving generic algebraic expressions and manipulating them to arrive at results. Unknown quantities denoted by alphabets that form a part of an equation are solved for and the value of the variable is determined. A fascinating branch of mathematics involves complicated solutions and formulas to derive answers to the problems posed.
Fun Fact: The word “mathematics” only appears in one Shakespearean play, “The Taming of the Shrew”.
Geometry
“The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.”
Isaac Newton
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 twodimensions and threedimensions. 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.
Trigonometry
Derived from Greek words “trigonon” meaning triangle and “metron” meaning “measure”, trigonometry focuses on studying angles and sides of triangles to measure the distance and length. 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!
Calculus
“Calculus is the most powerful weapon of thought yet devised by the wit of man.”
– Wallace B. Smith
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 mindnumbing questions, calculus is an interesting concept introduced to students at a later stage of their study in mathematics.
Fun Fact: “Forty” is the only number that is spelled with letters arranged in alphabetical order.
Probability and Statistics
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.
Number Theory
“Mathematics is the queen of the sciences, and number theory is the queen of mathematics.”
– Carl Friedrich Gauss
As the name suggests, Number theory is one of the oldest branches of Mathematics that established a relationship between numbers belonging to the set of real numbers. The basic level of Number Theory includes an introduction to properties of integers like addition, subtraction, multiplication, modulus and builds up to complex systems like cryptography, game theory and more.
Topology
“The basic ideas and simplest facts of settheoretic topology are needed in the most diverse areas of mathematics; the concepts of topological and metric spaces, of compactness, the properties of continuous functions and the like are often indispensable.”
– Pavel Sergeevich Aleksandrov
Topology is a much recent addition to 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.
Fun Fact: Every odd number has an “e” in it.
Advanced Branches of Mathematics
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.
Here are the 10 branches of mathematics:
 Matrix Algebra
 Numerical Analysis
 Operations Research
 Complex Numbers
 Calculus
 Set Theory
 Game Theory
 Analysis
 Cartesian Geometry
 Combinatorics
Branches of Pure Mathematics
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:
 Algebra
 Number Theory
 Geometry
 Arithmetic
 Topology
 Combinatorics
 Mathematical Analysis
Branches of Applied 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.
Here are the branches of applied mathematics:
 Statistics and Probability
 Set Theory
 Calculus
 Trigonometry
Fun Fact: Archimedes [287 – 212 BC] is the father of Mathematics
Top Universities for Courses in Mathematics
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.
University  Country 
Imperial College London  England 
University of Dundee  Scotland 
Jacobs University Bremen  Germany 
University of Pavia  Italy 
Carleton University  Canada 
Southern Utah University  United States 
Cardiff University  Wales 
University of Almeria  Spain 
Clarkson University  United States 
EastWest University  United States 
Top Indian Colleges for Mathematics
 Fergusson College
 Mount Carmel College
 Stella Maris College
 St. Xavier’s College
 Jadavpur University
 St.Stephen’s College
 Ramakrishna Mission Vivekananda College
 Christ University
Career Options in Mathematics
If the number game attracts you and you can’t help but add or multiply any number you see, then you should pick up Mathematics as a career. You can become one of the following professionals if you choose a career in Mathematics:
 Teacher/Lecturer– You can teach mathematics at the high school level and even university level if you are qualified enough and even explore research via postgraduation.
 Statistician A statistician collects data, turns them into charts and graphs and makes interpretations which is an important aspect in all professions.
 Data Analyst/Scientist– A data analyst/scientist is similar to a statistician but with certain differences. In Data Science, you will use scientific methods of data collection, comparison and give solutions to the organisation relatively.
 Mathematician– A mathematician is involved in all fields of profession. Whether it be inventing new business valuation methods or creating a formula that sends a rocket to the ISS, a mathematician does it all.
 Cryptographer– A cryptographer is a person who encodes and decodes various symbols or modes of communication to decipher what it means. Additionally, they also create safe codes for the military or other organisations.
Every profession needs the Branches of Mathematics as the subject ties all the broken pieces and creates uniformity.
FAQs
Algebra, Geometry, Calculus and Statistics & Probability are considered to be the 4 main branches of Mathematics.
Algebra is the hardest branch of Maths. Abstract algebra particularly is the most difficult portion as it includes complex and infinite spaces.
Archimedes [287 – 212 BC] is the father of Mathematics
It is difficult to trace back the exact origins of Maths. But it is estimated that in early 6th century, Pythagoreans invented Maths. After that Euclid introduced the axiomatic method consisting of the definition, axiom, theorem, and proof.
Are you intrigued by numbers and have a flair for doing difficult numeric calculations? Then, Mathematics is an allencompassing science that deals with quantity, space and numbers and abstract concepts as well as applied maths in other fields. While at first glance it might be difficult to identify the branches of mathematics, it is imperative to possess knowledge about them for any student wishing to gain a holistic idea about the subject. We hope this blog has presented a comprehensive list of different areas of study and branches of mathematics. (Phentermine) Planning to study a degree in Mathematics? Experts at Leverage Edu can help you find the best course and university as well as assist you throughout the admission process to ensure that you send a winning application! Sign up for a free session today!

Please which branch of mathematics is induction found

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Thanks for your valuable feedback!

3 comments
Please which branch of mathematics is induction found
So grateful
Thanks for your valuable feedback!