Most important math

Top 10 Branches of Mathematics

Last Updated on November 13, 2021

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.

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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.

By Parinita Gupta

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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.

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.

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.

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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

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.

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:

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• 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.

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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.

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.

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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.

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.

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.

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.

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.

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.

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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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.

Top 5 Math Classes to Prepare for the Future

What does your child want to be when they grow up? Many kids start thinking about their future career options as they go into high school. As a parent, you probably wonder what math classes they should take to compete in tomorrow’s job market. Across all industries, there is a growing demand for advanced math skills.

The demand fields like science, computer programming, medicine, and engineering is increasing daily. These fields have always required advanced math. Now many creative arts fields, such as animation and special effects, also require advanced math skills because these fields also rely on technology.

Sometimes children don’t know yet what they will be when they grow up. Even if they think they have a career goal now, it will likely change before they turn 25. That’s why at Mathnasium of St Peters North, we want kids in high school to get the math education to prepare for any career. Remember, the most exciting jobs of tomorrow don’t even exist today. Your child’s education plan should include 3 or more of the following classes:

• Statistics
• Trigonometry
• Calculus
• Advanced Linear Algebra
• Game Theory

Statistics: The mathematical field concerned with the collection, analysis, interpretation, and presentation of data. Statisticians, forecasters, and analysts, are used in most industries to help formulate implementation plans and strategies, create risk assessments, coordinate logistics, track performance, maximize profitability, and to inform a wide variety of decision making. Statistics is used by:

• economists
• political analysts
• psychologists
• epidemiologists
• veterinarians

Trigonometry: The branch of mathematics which studies angles and their relationships. The fundamental mathematical component of both navigation and astronomy. Trigonometry is used by:

• engineers
• mathematicians
• medical technicians
• actuaries
• statisticians
• chemists
• physicists
• photographers
• animators
• special effects designers

Calculus: The mathematics of determining how processes or objects will change over time.  Calculus provides the framework that makes a wide variety of modeling systems possible. Calculus has applications across a wide variety of technical and scientific fields.  Calculus is used by:

• all types of engineers
• pharmaceutical sciences
• financial analysts

Advanced Linear Algebra: This area of mathematics deals primarily with vector spaces, linear transformation, dimension counting and transformation. While still valued across a very wide range of science and technology careers, linear algebra is increasingly becoming valuable in the visual arts fields. Advanced linear algebra is used by:

• animators
• designers
• special effects directors
• engineers
• biologists
• biomedical researchers

Game Theory: The area of mathematics concerned with logical decision making in humans, animals, and computers, through mathematical models of conflict and cooperation. Game theory is used by:

• political scientists
• economists
• philosophers
• psychologists
• biologists
• computer scientists
• game designers
• educational designers

What if my child struggles with math already?

Mastering advanced math relies on developing basic math skills.   Correcting math gaps in your child’s fundamental math skills will boost their confidence and reduce math anxieties. Mastery of advanced math topics will help with taking the ACT and the SAT.  High school students with high math test scores and grades get a significant advantage when applying for college admissions and scholarships.  Students who bring advanced skills with them to university don’t have to waste time and money on remedial courses.

It takes a map to get there.

Whether your child dreams of being an astronaut, animator, sports statistician, scientist, financial consultant, special effects engineer, or game designer, strong math skills will allow them compete in the global job market.

Globalization means children from St Peters North will compete for jobs with people from around the globe. Children from China, South Korea, Japan, Switzerland, Estonia, and Finland score better than children from the U.S. on the math portion of the international test known as “PISA. ”

Creating a plan increases your children’s chances of reaching their goals.  To help them, evaluate where your child is right now in terms of skill, comfort, and confidence, with math. Talk with your children about math as it relates to their current career interests. 

Once you understand their goals, comfort level, confidence, and the math skills they will need to get there, call us to setup a free trial session, or a no-risk assessment. Our assessment will determine if your child is at or above grade level, which subjects to target, and any math gaps they may need assistance with in order to be well prepared to pursue their dreams.  Call Macy of Mathnasium of St Peters North today at (636) 812-MATH.

Why do we need mathematics in human life?

Interesting facts about mathematics

Mathematics is not only arithmetic problems. This is a special language that teaches to think and reason.

Mathematics is called an interdisciplinary science because it is closely related to physics, geography, geology, and chemistry. Sociology and economics are inseparable from mathematics, so many conclusions from humanitarian research are based on mathematical concepts and logical laws.

The world has changed and become more technological, so many options for professional development are open for math lovers.

If 15 years ago the spheres of marketing and jurisprudence were promising, today IT is in the lead.

Professional demand = understanding of technology + ability to solve non-standard problems. And the key to success is the knowledge of mathematics.

What distinguishes mathematics from other school subjects:

• one problem can have several correct solutions;
• there are problems for which there is no solution - instead, you need to form a proof;
• in mathematics there are many tools: numbers, formulas, graphs, diagrams, theorems. Don't get bored!

Math Demo Lesson

Find out which topics are “lame” for you, and then analyze them without cramming formulas and boring lectures.

Mathematics develops thinking

Why do physical education? The answer is simple - for the health and beauty of the body.

Why study mathematics? The answer to this question seems less obvious.

Mathematics is gymnastics for the mind. Like it or not, but in the process of studying, the qualities that influence the way of thinking will grow stronger. To do this, it is not necessary to study in a specialized class and participate in olympiads - solving even the simplest problems with proportions or percentages gives a significant effect.

Generalization, reduction, analysis, systematization, highlighting the important, searching for patterns, formulating hypotheses and proving theories - all this helps to develop thinking, make it more flexible. In the same way that physical exercises make our body more mobile, give a boost of strength and train endurance, mathematics trains the mind.

Mathematics develops the intellect. The set of rules and functions that we learn in school make our thinking consistent and logical. This is reflected in the ability to reason, formulate thoughts and notice relationships. And the most exciting thing is that this knowledge can (and should!) be applied not only at school, but also in non-standard situations: to choose the most profitable bank card, calculate liters of paint for repairs or create a treasure map so as not to forget where they are hidden.

Mathematics is a universal international language that is spoken by almost all people on earth. This knowledge will be useful in any country and can be the subject of an interesting conversation.

Life hack!

An unusual way to get acquainted is to ask a person about his attitude to mathematics, where he uses it and whether he remembers how to take the square root of a number. Yes, it will seem strange to some, but you will definitely be remembered. 🤓

What to understand, why study mathematics at school, just imagine how nice it is when there is no “porridge” and confusion in reasoning in the head. In this regard, back in the last century, the great scientist Lomonosov said: "Mathematics only then needs to be taught, that it puts the mind in order." How can one argue?

Mathematics courses will help you improve your grades, prepare for tests, VLOOKUP and exams.

Mathematics builds character

Knowledge alone is not enough to solve mathematical problems correctly. We need such qualities of character as attentiveness, perseverance, consistency, accuracy and accuracy. The more regularly we practice, the stronger these traits become stronger. And another bonus: these qualities can be applied not only in the classroom, but also in other areas of life.

The more complex the math problems, the more effort and skill you need to put in to solve them.

Thanks to mathematics, you can get rid of bad habits:

Math trains memory

Scientists from Stanford University in the USA studied how a person solves mathematical problems and found that adults use the skill to "get" answers from memory based on past experience.

Why do teachers insist on regular attendance? The point is not in their harmfulness, but in the fact that when solving mathematical problems, we “get” answers from memory based on past experience. And in order to consolidate this experience, you need to repeat the material and train in solving examples. This is the only way to remember all the rules and formulas. 🤓

In the journal Nature Neuroscience in 2014, a study was published about the role of certain areas of the brain in the development of cognitive activity in children. It turned out that the interest in knowledge is strongly influenced by the hippocampus, the part of the brain that is responsible for memory.

Interesting fact! Certain areas of the brain influence the development of children's cognitive activity. For example, interest in knowledge is influenced by the part of the brain that is responsible for memory - the hippocampus. Therefore:

• in order for a child to avoid problems with mathematics, it is necessary to train memory at an early age;
• solving mathematical problems develops the memory of schoolchildren and motivates them to study even more.

Mathematics is a magician, not otherwise! Let's systematize all the magical properties and repeat what skills can be developed with the help of mathematics:

• The ability to generalize and find the role of the particular in the general.
• Ability to analyze situations and make informed decisions.
• The ability to see patterns.
• The ability to correctly and clearly formulate thoughts.
• Ability to think logically.
• Ability to think quickly and make decisions.
• Planning and forecasting skill.
• Abstract Thinking Skills: The ability to sequence concepts or operations and keep them in mind.

Deprimo!

(a spell that removes obstacles to knowledge)

Why do we need mathematics? Why study, the benefits of doing mathematics

Can you clearly explain to the child why he needs to do math? After all, the study of concepts, the laws of mathematics and logic, the solution of mathematical and logical problems requires mental effort. And why is it needed at all?

We reviewed a number of scientific studies and identified real evidence for the benefits of doing math.

Even if you are convinced that your child’s life will not be connected with mathematics, we recommend that you still read our article in order to at least easily answer the questions of the little “why”.

1. Mathematics develops thinking

By studying mathematics and solving problems, the child learns:

• summarize and highlight the important;
• analyze and systematize;
• find patterns and establish cause-and-effect relationships;
• reason and draw conclusions;
• think logically, strategically and abstractly.

Just as regular sports training “pumps” the body, makes it healthy, strong and resilient, so regular math exercises “pump” the brain - develop intelligence and cognitive abilities, broaden horizons.

See also: In the article "5 reasons to learn to think like a mathematician" we have analyzed in detail what is the power of mathematical thinking and why to develop it.

2. Mathematics trains memory

Scientists from Stanford University in the USA studied the process of solving mathematical problems by a person and found out that adults use thinking and the skill, brought to automatism, to “get” the answers already there from memory.

Children under 7 often resort to the help of fingers and toes, as well as various substitutes (real objects, counting sticks). In the "transitional period", at the age of 7 to 9, schoolchildren form the "adult" skill of "thinking", comprehending and remembering information.

An interesting study was published in the journal Nature Neuroscience in 2014. First of all, it was devoted to the study of the role of the hippocampus (an area in the brain) in the development of cognitive activity in children. But his indirect conclusions are as follows:

• if you want your child to have no problems with math at school, train your memory at an early age;
• solving mathematical problems develops memory.

3. Math builds character

For the correct solution of mathematical and logical problems, attentiveness, perseverance, responsibility, accuracy and accuracy are needed.

The more regularly a child trains these "muscles of character", the stronger they become, the more often they help the child in solving not only educational problems, but also life problems.

LogicLike is the right training platform for 20-60 minutes a day. Solve problems, participate in olympiads in logic and mathematics, develop the will to win and the ability to win!

We create both simple and Olympiad problems that you want to solve:

• tasks for grade 1;
• assignments for grade 2;
• assignments for grade 3.

4. Music for mathematics, mathematics for music

A comprehensive study by Barbara H. Helmrich of the College of Notre Dame in Baltimore found that children who played musical instruments in middle school did significantly better in math in high school.

Scientists have found that the same part of the brain is responsible for solving algebraic problems and processing musical information.

"The largest average difference in algebra scores between any two groups of subjects was found between African-American 'instrumental' groups and groups of 'non-musical' students."

Paradoxically, scientists didn't seem to be interested in feedback.
After all, if the same part of the brain is responsible for the development of mathematical and musical abilities, it is possible that doing mathematics improves musical abilities.

I remember Sherlock Holmes, who was both an excellent detective and a talented violinist. Many will say that the famous English detective is just a fiction, but he had his own real prototype, a mentor and friend of Arthur Conan Doyle. The greatest physicist Albert Einstein was also a passionate violinist.

5. Math Helps You Succeed in the Humanities

It is early mathematical abilities that are a sure prerequisite for the fact that in the future the child will not only understand mathematics well, but also succeed in other school disciplines. Next in importance for contributing to academic success are reading skills and the ability to manage one's attention.

Such conclusions were reached by scientists in the field of education and social policy at Northwestern University in Evanston. During the study, they assessed the relationship of key elements of school readiness (basic skills for school admission - "academic" readiness, attention, social-emotional skills) with further academic success.

Mathematics is an interdisciplinary science, it is closely related to physics, geography, geology, and chemistry. Sociology and economics are inseparable from mathematics, and many of the conclusions of even the usual humanities, such as linguistics, journalism, are based on mathematical models and concepts, mathematical and logical laws.

6. Develops skills for solving everyday problems

Barbara Oakley, PhD, brain stem cell researcher and author of Think Like a Mathematician, emphasizes:

“Mathematics saves us from “magical thinking” - we strive to delve into the essence of things and do not rely on chance and higher powers. ”

The more difficult the math problems become, the more skills are required to solve them. The child learns to reason, build sequences, think through algorithms, juggle several concepts at once, and these skills become a habit.

Thanks to mathematics, we get rid of bad habits:

• we do not speculate, but operate only in exact terms;
• we do not just mechanically memorize information and rules, but evaluate it, analyze it, reflect in order to understand and learn new material, a new life lesson.

7. Mathematics is the basis of a successful career

If 10-15 years ago the study of foreign languages ​​was considered promising, now you will not surprise anyone with fluency in several languages. Now professional demand largely depends on the understanding of technology, the ability to think, abstract and the ability to solve non-standard problems. It is extremely difficult for those who want to work in the IT field to do without knowledge of mathematics.

Abstract, critical and strategic thinking, analytical skills, the ability to build algorithms are a “must-have” for a good developer.

TOP 5 soft skills. Source: amazonaws.com

Successful mathematics classes give self-confidence, because success in it requires perseverance in striving to solve the most complex, sometimes, at first glance, “unsolvable” tasks and problems.

Test your strength: Math puzzles to help you: 9 selected well-known tasks for ingenuity. How many can you decide?

8. Problem Solving Builds Mental Resilience

Solving mathematical problems helps to improve the emotional background - this activity can relieve anxiety, helps control emotions and prevents stress.

These conclusions were reached by scientists from Duke University in the United States, who were able to prove this in a study published in the journal Clinical Psychology in 2016.

9. Pleasure from "x"

For a serious student of mathematics, mathematical formulas, equations and other logical and mathematical problems embody beauty, harmony and provide the same aesthetic pleasure as music, art and a good joke, says a group of researchers from several universities in the UK.

With the help of functional magnetic resonance imaging, the activity of the brain activity of the subjects was recorded during the demonstration of mathematical equations, formulas and tasks. The results of the study were published in the journal Frontiers in Human Neuroscience in 2014.

How to learn to experience the joy and pleasure of doing mathematics tells the famous American mathematician, a graduate of Harvard University, Stephen Strogatz. Applied Mathematics teacher, award-winning math and teacher in the pages of his book "The Pleasure of X" enthusiastically explains the most significant mathematical ideas in a simple and understandable way.

Try logic and math classes at LogicLike.com!

We are convinced that children, especially those aged 5-9, do not need to be told how important it is to study mathematics. It is much more important to give the child the opportunity to plunge into the world of entertaining interactive mathematics.

Learning on the LogicLike platform, children solve interesting logical problems, earn their first "star" awards for correct answers, play modern logic games - and get not only benefit, but also real pleasure from such mathematics.

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