Math concepts list

Branches, Fundamentals, Important Topics, Preparation Tips

Math is the science of quantity, pattern, order, structure and relation that has continuously evolved from basic practices of counting, measurements and symmetric study of shapes. It primarily involves applying logical reasoning and quantitative computation to find optimal solutions to problems. It has been worldwide recognized as an indispensable computational tool in the field of engineering, biology, medicine and natural sciences.

Math As A Subject

Math as a subject is an important part of the curriculum that plays a significant role in shaping a child’s future. It involves studying many useful concepts and topics relevant to practical life. Although math is an interesting subject, students often find it boring and complex due to the way it is taught conventionally. Cuemath helps students to explore and understand fundamental concepts in a fun and intuitive manner.

Fundamentals of Math

Fundamentals of math are the basic building blocks that help students form a solid mathematical foundation. Math learning entirely relies on the understanding of these fundamental concepts. If children lack the basic understanding of division or subtraction, then algebra automatically becomes confusing for them. Therefore, it is imperative that children must have a crystal clear knowledge of all fundamentals of math.

Addition and Subtraction of Whole Numbers
Multiplication and Division of Whole Numbers
Exponents, Roots, and Factorization of Whole Numbers
Introduction to Fractions and Multiplication and Division of Fractions
Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions
Decimals and Fractions
Ratios and Rates
Techniques of Estimation
Measurement and Geometry
Signed Numbers
Algebraic Expressions and Equations

Branches of Mathematics

Mathematics involves complex studies of interlinked topics and several concepts that overlap each other. Generally, it can be categorized into the following branches:

Arithmetic

Arithmetic is the most basic branch of mathematics that deals with the elementary aspects of numbers, mensuration and numerical computations. This term is derived from the Greek word ‘arithmos’ which means number. It generally involves studying numbers and their relationships to solve problems that include the operations of addition, multiplication, subtraction, division, extraction of roots and raise to power.

Algebra

Algebra is an important and ancient branch of math that covers basic operations and symbols to represent numbers in formulas and equations. The word Algebra means the science of restoring and balancing. Learning algebra enables students to understand many real-life phenomena around them. It is a symbolic representation of numbers and how they work together to provide structure to equations. It forms the basis for advanced study in many fields like science, medicine, engineering, etc. It allows mathematicians to write formulas and solve maths problems more efficiently.

Geometry

Geometry is the branch of math which deals with computation of various dimensions of solid shapes including height, width, area, volume, perimeter and angles. It has several useful applications from the construction of homes to interior designs.

Trigonometry

Trigonometry is an important branch of math that involves studying the relationship between angles, lengths, heights and distance. The applications of trigonometry can be found in many spheres including architecture, physics, surveying, electronics, satellite navigation, astronomy and engineering.

List of Branches of Maths

Important Math Topics

A thorough understanding of all important math topics will benefit students throughout their lifetime. Some of the essential math concepts that students must have an in-depth understanding of are based on the topics listed below.

BODMAS Rule
Prime and Composite numbers
HCF and LCM
Basic Menstruation
Divisibility Rules
Decimal and Fractions
Ratio and Proportion
Three-dimensional shapes
Geometry
Probability

Math Calculators

Students often find math challenging due to complex mathematical calculations. Math Calculators are handy tools to resolve all such problems. It makes calculations simple and quick. With the use of math calculators, calculations ranging from elementary arithmetic operations to complicated equations can be solved within a few seconds.

List of important calculators for students to solve problems quickly and get accurate solutions.

Important Math Formulas

Math formulas are expressions created after several years of research to help solve problems easily. Performing simple numerical operations like addition, subtraction and division are easy. However, to solve algebraic expressions, and other complex operations we use mathematical formulas. These are quite useful in obtaining the answers precisely. Cuemath provides formulas for each math topic along with the illustrated steps of equations for students to understand them logically.

List of important formulas that students must learn and memorize.

Tips And Tricks To Learn Math Fast

Although math is a vast subject there are some tips and tricks to learn math fast. These tips and tricks will help students improve along their math journey.

Clear All Basic: The first and foremost step in learning mathematics is to clearly understand all basics. It will not only allow you to learn math faster but will also help in establishing links between various math topics.

Set Objectives: After clearing all basics, set goals for what you need to focus on. Once you understand your objective, start working on it. Explore various resources that can help you improve and get well versed in those topics.

Practice Daily: Math requires daily practice, implementing a proper study routine will help in grasping concepts better.

Take Guidance: Heading in the right direction is necessary as it will ensure good results. Consider taking help from your teacher or a math tutor if you feel doubtful about topics and concepts.

FAQs on Math

What Exactly is Math?

Math is the science involving numbers, shapes and patterns which is present in almost everything around us. It helps us to derive analytical solutions to practical problems. It is applied in various fields such as engineering, finance, physical science, etc. It has a great impact in every domain of our life and we can find many mathematics applications around us.

How to Get Better at Math?

Getting better at math requires enforcing a study routine and analyzing mistakes. Students must try to understand and rectify their mistakes through daily practice. Doing so will also help them clear all their doubts. Students with better mathematical abilities achieve higher academic success. Thus, it is crucial to cultivate math interest in children at an early age. Cuemath’s visually-enriched math concepts enhance a child’s interest in mathematics and make it easier to learn the subject.

Why is Math Important in Our Daily Life?

Math is highly important in our daily life as there are several applications of mathematics in real-world situations. Statistics or probability theory are examples of applied maths.

What are the Fundamentals of Mathematics?

Fundamentals of mathematics are the building blocks for a solid math foundation. Students must possess a clear knowledge of all the fundamentals of mathematics to study advanced mathematical concepts. These fundamentals of mathematics are given below.

Addition and Subtraction of Whole Numbers
Multiplication and Division of Whole Numbers
Exponents, Roots, and Factorization of Whole Numbers
Introduction to Fractions and Multiplication and Division of Fractions
Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions
Decimals and Fractions
Ratios and Rates
Techniques of Estimation
Measurement and Geometry
Signed Numbers
Algebraic Expressions and Equations

How many Branches of Mathematics do we Have?

The branches of mathematics can be broadly categorized as:

Arithmetic: Arithmetic involves studying numbers and their relationships to solve problems that include the operations of addition, multiplication, subtraction, division, extraction of roots and raise to power.
Algebra: Algebra is the symbolic representation of numbers that provides structure to equations. It forms the basis for advanced study in many fields like science, medicine, engineering, etc.
Geometry: Geometry is the calculation of various dimensions of solids including height, width, areas, volumes, perimeter and angles. It has many practical applications in architecture and other fields.
Trigonometry: trigonometry deals with the study of the relationship between angles, lengths, and heights. The applications of trigonometry can be found in many spheres including architecture, physics, surveying, electronics, satellite navigation, astronomy and engineering.

What are the Most Important Math Topics?

Some of the most important math topics are prime numbers, composite numbers, BODMAS rule, geometry, probability, divisibility rules, HCF, LCM, three-dimensional shapes, basic menstruation, decimal, fractions, ratio and proportion. An in-depth understanding of all important math topics will enable students to score well in exams.

How Math is Used in Sports?

Math is used in sports to accumulate data, study conditions and generate performance statistics which are considered for planning and optimizing the training session. The data collected in these mathematical calculations is also helpful for taking strategic decisions based on the team’s performance.

How Maths is Related to Other Subjects?

Math is related to other subjects, especially chemistry, physics, computer science and engineering. In chemistry, mathematics is used to write and balance equations. In physics. It is applied to calculate mass, velocity and acceleration. In computer science, math is used to build algorithms and solve problems.

Main Branches of Mathematics Tree | PDF | Pure & Applied

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

Branches of Mathematics

Main Branches of Mathematics

YouTube: DOS- Domain of Science

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.

Word Problems on Arithmetic Operations

Arithmetic Reasoning

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.

Algebra Questions

Algebra Formulas

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 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.

Coordinate Geometry Formulas

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!

Trigonometry Formulas

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 mind-numbing 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.

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.

Statistics Formulas for Competitive Exams

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 set-theoretic 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

Applied Mathematics and Computation

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.

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

What are the four branches of Mathematics?

Algebra, Geometry, Calculus and Statistics & Probability are considered to be the 4 main branches of Mathematics.

What is the hardest branch of Maths?

Algebra is the hardest branch of Maths. Abstract algebra particularly is the most difficult portion as it includes complex and infinite spaces.

Who is the father of Mathematics?

Archimedes [287 – 212 BC] is the father of Mathematics

Who invented Math?

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.

BSc Mathematics

MSc Mathematics

Are you intrigued by numbers and have a flair for doing difficult numeric calculations? Then, Mathematics is an all-encompassing 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