A Little Understanding of Mathematics and its Branches
Mathematics means "knowledge, study, learning". It includes the study of topics such as arithmetic, algebra, geometry, and mathematical analysis. It has no generally accepted definition.
Several civilizations in China, India, Egypt, Central America, and Mesopotamia equally contributed to mathematics. The counting system was first developed by the Sumerians. Mathematicians developed arithmetic, which includes basic operations, like addition, subtraction, multiplication, fractions, and square roots.
As civilizations developed, mathematicians began to work with geometry, which deals with the areas and volumes to make angular measurements. Geometry is used everywhere from home construction to fashion and interior design. Moreover, geometry is that branch of mathematics, which is concerned with spatial relationships among several objects, the shape of single objects, and the properties of space surrounding us. Geometry is considered as one of the oldest branches of mathematics while the term is derived from the Greek language as geo means earth and material means measurement, meaning earth measurement.
However, after a certain point, people began to realize that geometry does not need to be limited to the study of rigid three-dimensional objects or plane and flat surfaces, but can be put to use or represented with the most abstract images and thoughts. Besides, the major branches of geometry consist of analytic geometry, Euclidean geometry, projective geometry, non-Euclidean geometries, topology, and differential geometry. Nevertheless, students do not need to go in-depth about all these concepts.
Now, let’s discuss a bit about Algebra. It is that branch of mathematics where the students usually use symbols, letters of the alphabet to get the solutions to the given problems. Now talking about its history, it can be divided into three parts. The first one is the written stage where just words were used, the second stage included the shortened or syncopated stage where symbols came into existence in the equations. The third stage is the modern or symbolic stage. Moreover, Algebra was invented in the ninth century by a Persian mathematician, Mohammed ibn-Musa al-Khowarizmi. He also developed quick methods for multiplying and dividing numbers, which are known as algorithms. The study of algebra meant mathematicians were solving linear equations and systems, as well as quadratics solutions.
Arithmetics – Numbers and Operations
Arithmetic is one of the first few subjects that you learned in lower grades. It deals with numbers and basic operations on them. It is the foundation for studying other branches of mathematics.
Arithmetic originated from the Greek word arithmos, which is a branch of mathematics that consists of the study of counting numbers and the properties of the traditional operations on them such as addition(+), subtraction(-), multiplication(x), and division(). Arithmetic is an elementary part of number theory.
In addition to basic operations, this subject also includes more advanced operations, such as percentage, square roots, exponentiation, logarithmic functions, trigonometric functions, and many more.
The four basic operations addition, subtraction, multiplication, and division are commonly referred to as the four arithmetic operations.
The four main properties of operations are:
Commutative Property
Associative Property
Distributive Property
Additive Identity
The BODMAS or PEMDAS rule is followed for order of operation involved +, −,×, and ÷. The order of operation is:
B:- Brackets
O: -Order
D: -Division
M:- Multiplication
A: -Addition
S: -Subtraction
Geometry-Shapes
Geometry is the study of shapes. It is broadly classified into two types: plane geometry and solid geometry. Plane geometry deals with two-dimensional figures like squares, circles, rectangles, triangles, and many more. Whereas Solid geometry deals with the study of three-dimensional shapes like cube, cuboid, cylinder, cone, sphere, and many more.
The study of this shape is needed to find lengths, widths, area, volume, perimeter, and many more terms.
In mathematics, we need specific terms again and again to solve problems. It becomes difficult to write the full terms repeatedly, hence the shortcuts for these terms are discovered and it is called a symbol.
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Algebra
Algebra is one of the branches of Mathematics that deals with variables and numbers. A combination of constants and variables connected by the signs of the fundamental operation of addition, subtraction, multiplication, and division is called an algebraic expression. Various parts of an algebraic expression that are separated by the signs of + or - are called the terms of the expression. An algebraic expression is defined as a sum, difference, product, or quotient of constants and variables.
Consider,
12x + 50
Here this expression is called an algebraic expression where x varies in values so it is a variable and 50 is constant. 12x and 50 are the terms and they are separated by the sign +. We can write anything a, b, c ….z in place of variables.
Algebra consists of different methods of solving a pair of linear equations:
1. Elimination method
2. Substitution method
3. Cross multiplication method
Let us understand the difference between Arithmetic and Algebra.
Difference Between Arithmetic and Algebra
Differences between arithmetic and algebra will make the arithmetic and algebra concepts more clear.
Let us understand the difference between Algebra and Geometry
Difference Between Algebra and Geometry
Differences between algebra and geometry will make the algebra and geometry concepts more clear.
Fun Facts:
It was Babylonians who came up with Algebra in 1900 BC.
The use of signs addition(+) and subtraction(-) prove to be beneficial in performing algebraic equations. Before that, people used written words to express the functions of addition and subtraction which was a time-consuming process.
Arithmetic is something that is always around you. Just take a look at the ice tray and pick two ice cubes out of it, how many in total are left? To find the answer to it, one must subtract the total number of ice cube slots by 2.
The history of math goes a long way back but most of the mathematical symbols were not invented till the 16th century as equations were written in words before that.
There is no doubt that Greeks were keen, but they used geometry in making artwork like buildings and much more, which gives students another reason to love this subject.
The two of the most important tools of geometry that are considered powerful as they helped in the advancement and construction of the subject are straight edge and compass.
FAQs on Arithmetic, Geometry and Algebra
1. What are the simple definitions of Arithmetic, Geometry, and Algebra?
These three are fundamental branches of mathematics with distinct focuses:
- Arithmetic is the study of numbers and the basic operations between them, such as addition, subtraction, multiplication, and division. It forms the foundation of all quantitative calculations.
- Geometry is the study of shapes, sizes, positions of figures, and properties of space. It deals with concepts like points, lines, angles, surfaces, and solids.
- Algebra uses symbols and letters (variables) to represent numbers and quantities in formulas and equations. It allows for the generalization of arithmetic rules and the solving of unknown values.
2. What is the main difference between how Arithmetic and Algebra solve problems?
The main difference lies in their approach. Arithmetic deals with specific, known numbers to find a definite numerical answer (e.g., 5 + 10 = 15). In contrast, Algebra uses variables to represent unknown quantities and establishes relationships between them to find a general solution or the value of the unknown (e.g., finding the value of 'x' in the equation x + 10 = 15).
3. How is Algebra used in everyday life, beyond the classroom?
Algebra is used in many practical situations, often without us realising it. Key examples include:
- Financial Planning: Calculating interest, loan repayments, and creating a budget involves algebraic formulas.
- Technology: Computer programming and video game design rely on algebraic logic to define rules and actions.
- Cooking: Adjusting a recipe for more or fewer people requires using algebraic proportions to change ingredient quantities.
- Decision Making: Comparing different mobile plans or deals uses algebraic thinking to determine the best value based on usage.
4. What are some real-world applications of Geometry?
Geometry is essential in many fields for understanding and manipulating the physical world. For example:
- Architecture and Construction: Architects use geometric principles to design safe and stable buildings, calculating angles, area, and volume.
- Art and Design: Artists use geometry for creating perspective, patterns, and aesthetically pleasing compositions.
- Navigation and GPS: GPS systems use geometry (specifically, trigonometry and coordinate geometry) to pinpoint locations on Earth.
- Medical Imaging: Technologies like MRI and CT scans use geometric algorithms to create 3D models of the human body from 2D image slices.
5. How does understanding Arithmetic form the foundation for learning Algebra?
Arithmetic provides the essential building blocks for Algebra. Before you can work with variables (like 'x' or 'y'), you must have a strong grasp of the rules that govern numbers. Algebra is essentially a generalisation of Arithmetic. The properties you learn in arithmetic, such as the commutative property (a+b = b+a) and the order of operations (BODMAS/PEMDAS), are applied directly in algebra to manipulate and solve equations with variables.
6. Why did mathematics need to evolve from using just numbers (Arithmetic) to using symbols and letters (Algebra)?
Mathematics evolved to include Algebra to solve more complex and abstract problems that Arithmetic alone could not handle. Using symbols allows us to:
- Solve for Unknowns: Algebra provides a method to find values that are not yet known, which is impossible with pure arithmetic.
- Create General Rules: We can create formulas, like the area of a rectangle (A = l × w), that work for any length and width, not just specific numbers.
- Model Relationships: Algebra helps describe the relationship between different quantities, such as how speed, distance, and time are connected.
7. Can you solve Geometry problems without using any concepts from Algebra or Arithmetic?
While you can understand basic geometric shapes visually, almost all quantitative geometry problems rely on both Arithmetic and Algebra. You need Arithmetic to perform calculations like finding the area of a square with a known side length (e.g., 5cm x 5cm = 25 cm²). You need Algebra when a side length is unknown and you have to solve for it using a formula, such as finding the side of a square when only its perimeter is given (4x = P).
