Math

Imagine a world without mathematics. Sounds chaotic right?

Math is the most essential branch of science, as it deals with concepts such as trigonometry, arithmetic, and geometry, which are applied everywhere. Fundamental arithmetic operations like addition, subtraction, multiplication, and division are used in mathematics. Mathematics and its concepts are crucial when dealing with numbers, as different problems may require different ideas to solve. Math has formulas and equations that are used as tools to simplify and solve complex problems.

Math trains the brain to make precise decisions and think critically. Learning math in depth opens up careers in STEM subjects, such as engineering, physics, chemistry, computer science, AI, economics, and many more branches. It includes planar and solid geometry, as well as natural numbers. Galileo Galilei once said, “Mathematics is the language with which God has written the universe”. A few crucial branches of Mathematics are described below

Math has been a part of human existence ever since the ancient times. The earliest traces of math being used for calculation and measurement purposes can be traced back to the ancient Mesopotamia and Egyptian civilizations around 3000-2000 BCE. Math was used simply as a tool in the ancient times to perform basic calculations such as counting, measuring etc. The evolution of math occurred with the change in applications of math. 

Math generally uses a set of pre-defined formulas that solve particular problems. But some of the most basic and essential formulas were discovered hundreds or even thousands of years ago. The formula for calculations of volume was introduced by Archimedes around the 225 BCE. Aryabhatha who is also known as the father of Indian mathematics used the number '0' as a placeholder in decimal numbers back in 499 CE. Similarly, there have been numerous other scientists who have made significant discoveries in the field of mathematics that helped the ancient math evolve into what it is today. 

Some historical discoveries in the field of mathematics can be credited to mathematicians and scientists, such as Pythagoras discovered the Pythagorean theorem for a right-angled triangle around 530 BCE, Diophantus discovered Arithmetica which is basic methods of solving equations with unknowns around the year 250 CE, Al-Khwarizmi discovered algebra around 820 CE and numerous others contributed in helping math evolve over the years. 

Then came a time in the 17th century when advanced calculations were needed to find out terms such as motion, velocity, gravity etc. To felicitate these new and more complex discoveries' math had to keep evolving. Sir Isaac Newton discovered calculus, which made it possible to calculate motion of objects, gravitational forces and a lot more. Numerous more discoveries in the field of math made it possible to develop other forms of sciences too. Since pre-historic times, math has been evolving with the needs and requirements of the world.

Math is the most essential and fundamental subject that needs to be taught and learned, as it is used by everyone, regardless of their age or profession. The subject of mathematics requires skills such as critical thinking and problem-solving, which in turn enhance overall cognitive development. Math is also a subject commonly used in our daily lives, as even the simplest calculations and measurements require the application of various forms of mathematics. Math is a part of academics from kindergarten. Math is applied in fields such as engineering, medicine, physics, and others. Pure and applied math are the branches of mathematics. Therefore, math is taught as a compulsory subject from the very beginning.

Humans use math every day, right from the moment we wake up to the moment we sleep again. Math has been embedded so deeply into our brains that, without even thinking about it, we use mathematical tools such as counting, multiplication, and addition throughout our daily lives. The importance of mathematics in our lives is unmatched and irreplaceable. A few points are listed below that can help us understand the importance of mathematics better:

• Math is used to calculate dates, times, years, and other quantities. Without mathematics, it would be impossible to calculate any of these.
• Math is used for scheduling; it helps in dividing and allocating work based on the amount of work and the number of hours allotted to it.
• All finance-related activities require some mathematics, such as budgeting, allocating funds, calculating taxes, or even basic tasks like counting money. All financial activities are incomplete without math.
• Apart from being a form of science itself, math has been the most crucial building block in the evolution of other sciences as well. For example, physics extensively uses math and its concepts while solving equations and form its own set of equations. Another form of science that relies heavily on mathematics is chemistry, as it also employs a wide range of mathematical formulas and equations.
• Math is used to calculate and measure distances, heights, slopes, speed, and gravity, among other quantities, using branches of mathematics such as trigonometry and algebra. Graphical solutions for various problems are also created using math.

Math encompasses a wide range of concepts, which originate from the fundamental principles of mathematics. Fundamentals of mathematics are the basic terms and operations that can be performed using math. A few fundamentals of mathematics are listed below:
1. Number: One of the most basic concepts of mathematics is numbers, and numbers are the fundamental arithmetic values used to represent quantity. There are various types of numbers, including integers, rational numbers, irrational numbers, prime numbers, even numbers, and odd numbers. Example:
Integers: -5, -4, 0, 1, 2
Rational numbers: 12, 57, 0.35
Irrational numbers: √15, √6, π
Prime numbers: 2, 3, 5, 7
Even numbers: 2, 4, 6, 8
Odd numbers: 1, 3, 5, 7
2. Operations: There are four basic operations in math, which are addition, subtraction, multiplication, and division. These operations are for real numbers. Each operation is represented using different signs, such as + (plus) for addition, — (minus) for subtraction, × (times sign) for multiplication, and ÷ (division sign) for division. 
Addition: In this operation, two numbers are added together to produce a value called 'sum'.
Example: 2 + 5 = 7
Subtraction: Here, A number is subtracted from another number.
Example: 5 - 3 = 2
Multiplication: In multiplication, numbers are multiplied together to get a product. 
Example: 5 × 6 = 30
Division: A larger number is broken down into smaller numbers. 
Example: 8 ÷ 2 = 4
3. Geometry: The concept of geometry deals with shapes, structures, angles, and dimensions of different objects. There are several types of geometry, including plane geometry, three-dimensional geometry, and solid geometry, among others.
4. Algebra: The relationship between the things that change is expressed using mathematical statements. Variables such as x, y, and z are used.
5. Calculus: The study of changes and motion is performed using calculus. Integrals and derivatives are used to solve calculus equations
6. Trigonometry: The study of the relationship between angles, length, height, and distance is called trigonometry. The basic functions are cosine, tangent, cotangent, secant, and cosecant.

Mathematics encompasses a wide range of topics, categorized under various branches of mathematics. These branches are closely connected and often overlap with each other. Even though there are numerous branches, they can be broadly classified into two categories:

• Pure mathematics: This form of mathematics focuses primarily on concepts that have no immediate relation to real-life problems. For example, algebra, geometry, analysis, and topology, etc. 
• Applied mathematics: It deals with problems that are based on real-life applications. The branches of math under this concept focus on solving problems related to statistics, finance, probability etc.

Pure mathematics Vs. Applied mathematics

Math works on formulas, for each and every concept in math there is a formula. Some of these formulas are mentioned below: 

• Geometry formulas for 2-D shapes: 

Triangle:

Area of a triangle = 1/2bh
Here, ‘b’ is the base and ‘h’ is the height of the triangle

Circle:

Circumference of a circle = 2πr
Area of a circle = πr²
Here ‘r’ is the radius of the circle 

Square:

Area of a square = a²
Perimeter of a square = 4a
Here, ‘a’ refers to the length of a side

Rectangle:

Area of a rectangle = l × b
Perimeter of a rectangle = 2(l + b)
Here ‘l’ is the length and ‘b’ is the breadth of the rectangle 

• Quadratic formula: ax² + bx + c = 0

It is a polynomial equation of the second degree. Here, the variable is ‘x’, the real numbers are ‘a’, ‘b’, and ‘c’. Here, a ≠ 0

• Pythagorean theorem: c =  √a² + b² 

The Pythagorean theorem is applicable to a right-angle triangle. This equation is applicable to find the length of the longest side. Here, the length of the longest side is ‘c’, and ‘a’ and ‘b’ are the lengths of the other side.

• Algebra formulas:

(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a2 - b² = (a - b) (a + b)
a² + b² = (a + b)² - 2ab

• Percentage formula:

Percentage is the representation of a number as a fraction of 100.

Percentage = given value / total value × 100
 

In math, for representing operations, relations, concepts, and so on we use symbols. Each function has a unique symbol, let’s learn some of them.
 

• Plus symbol: + used in addition

• Minus symbol: - used in subtraction

• Times sign: × used in multiplication

• Division sign: ÷ used in division 

• Equal to: =

• Not equal to: ≠

• Greater than and less than: >, <

• Plus or minus sign: ±

• Exponent: a²

• Square root: √

• Cube root: ∛a

• Percentage: %

• Set: { }

• Pi: π
   

Several properties in mathematics enable us to form relations between terms and enhance the process of solving equations or sets of numbers.
The four properties of math are:

• Commutative property
• Associative property
• Distributive property
• Identity property

Commutative property:
If two numbers are added or multiplied by each other in any order, the result remains the same. It is called the commutative property.
In addition: a + b = b + a
Example: 2 + 5 = 7
5 + 2 = 7
In multiplication: a × b = b × a
Example:  2 × 5 = 10
5 × 2 = 10

Associative property:
Grouping the numbers in any sequence or format won't affect the result. However, it can be applicable only for multiplication and addition.
(a + b) + c = a + (b + c)
example (2 + 5) + 3 = 2 + (5 + 3) = 10
(a × b) × c = a × (b × c)
example (2 × 2) × 5 = 2 × (2 × 5) = 20

Distributive property:
Distributive property states that a × (b + c) = (a × b) + (a × c).
When you multiply a number'  a' with the sum of two other numbers, 'b' and 'c', the resultant will be equal to the sum of two products. Here, the products will be (a × b) and (a × c).
For example, 2 × (4 + 3) = (2 × 4) + (2 × 3) = 14

Identity property:
The identity property states that in certain operations, if an identity element is combined with another number, the value of the number remains unchanged.
Additionally, when adding 0 to a number, the sum remains the original number.
24 + 0 = 24
In multiplication: The product of multiplying a number by 1 is the number itself. 
24 × 1 = 24

Calculators are devices used to perform mathematical calculations. There are several types of calculators available based on the user's requirements, the most common being scientific calculators, graphing calculators, and programmable calculators.

Math is a subject with numerous formulas, equations, and concepts, which makes it a tricky subject to get a grasp on, so here are a few tips and tricks that can help 

• Memorizing - Memorizing the basic properties and concepts of mathematics makes working more efficient.

• Regular practice - Regular practice can help you master math. Therefore, it is essential to practice regularly to understand math concepts fully. For practice, kids can use math worksheets, work on various problem-solving techniques, and engage in online math practice.

• Remembering Formulas - For Geometry and Trigonometry, memorizing formulas is an effective way to apply them in calculations.

• Rechecking Answer Sheets - In examinations, children often make mistakes in calculations. They should spend a quality amount of time revising the answer sheets.

• Proper Writing of Symbols and Numbers - In many cases, children may get confused with symbols; it is advisable to pay close attention to those symbols.

• Online Mock Tests - For lower grades, online mock tests or online math practice can also help overcome mistakes.

Math is everywhere from home to school or work. As we use math a lot, it's hard for us to realize how often we use it. Let’s see how we use math in daily life.  
 

From all we learn, we know that math has an impact on the real world. So there are ample career opportunities for a person with a strong foundation in mathematics. Let's see some interesting career opportunities in mathematics. Mathematics teacher, accountant, computer programmer, financial analyst, finance planner, engineer, auditor, statistician, economist, etc.