Branches of Mathematics

Introduction

Branches of mathematics are Algebra, geometry, arithmetic, number theory, etc. Over time, the scope of mathematics has expanded. There are two types of mathematics: pure mathematics and applied mathematics. The mathematics that can be used to solve real- world problems is known as applied mathematics.

Mathematics has evolved over time into a vast and diverse subject. Mathematical advancements continue to make significant contributions. Algebra, Geometry, Arithmetic, Trigonometry, Calculus, and other branches of mathematics exist. In this tutorial, we will discuss branches of mathematics.

Mathematics

Maths is the science of quantity, pattern, order, structure, and relation, which has evolved over time from basic practices such as counting, measuring, and the symmetric study of shapes.

It primarily involves using logical reasoning and quantitative computation to solve problems. It is widely regarded as an essential computational tool in the fields of engineering, biology, medicine, and natural sciences.

Branches of Mathematics

The following branches of mathematics exist −

• Arithmetic is the most basic and oldest branch of mathematics. It's all about numbers and the fundamental operations of addition, subtraction, multiplication, and division.

• Algebra is a branch of mathematics that employs unknown quantities in addition to numbers. We can generalize formulas and rules by using letters, and we can also help you find unknown missing values in algebraic expressions and equations.

• Geometry is the most practical branch of mathematics, dealing with figure shapes, sizes, and properties. Geometry's fundamental elements are points, lines, angles, surfaces, and solids.

• Trigonometry is the study of relationships between angles and sides of triangles. It is derived from two Greek terms, trigon (means triangle) and metron (means measurement).

• The analysis is the branch of mathematics that studies the rate of change in various quantities. Calculus is the foundation of analysis.

Analysis: Real and Complex

Real − The union of rational and irrational numbers yields real numbers. They can be either positive or negative and are represented by the letter "R." This category includes all natural numbers, decimals, and fractions.

Complex − Complex numbers are created by adding imaginary and real numbers together.

A complex number normally has the form $\mathrm{a\:+\:ib}$ and is represented by the symbol z. Re(z) is utilized to represent the value "a" as the real component in this instance because both a and b are real integers, Im(z) is used to represent the value "b" as the imaginary part, and ib are also referred to as an imaginary number.

Algebra: General and Abstract

• The study of algebraic structures rather than examples ("models") of algebraic structures is the focus of universal algebra (also known as general algebra). For example, in universal algebra, rather than studying specific groups, one studies the class of groups.

• Abstract algebra (also known as modern algebra) is the study of algebraic structures in algebra (an already broad field of mathematics). Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras.

Geometry: 2D and 3D

• A 2D form is a flat shape with only two dimensions - length and width - and no thickness or depth, hence the name "two-dimensional shape." A sheet of paper, for example, has a two-dimensional shape.

• It has two dimensions: length and breadth, but no depth or height. Squares, rectangles, triangles, circles, and hexagons are examples of typical 2D shapes.

• 3D shapes are solids with three dimensions: length, width (width), and height. The term 3D shapes refer to three-dimensional objects.

• Every 3D geometric shape takes up some space based on its dimensions, and we can see many 3D shapes in our daily lives. 3D shapes include the cube, cuboid, cone, and cylinder.

Arithmetic

An arithmetic progression is a number sequence in which each successive term is the sum of the term before it and a fixed number.

Calculus: Differential and Integral, Univariate and Multivariate

Differential

A derivative in calculus is the rate of change of a quantity y with respect to another quantity x. Another term for this is the derivative from y to x. Differentiation is the process of determining a function's derivative.

Integral

Function integrals are another name for anti-derivatives. The process of determining the antiderivative of a function is referred to as integration. Finding integrals is the opposite of finding derivatives. A function's integral represents a family of curves.

Univariate

A univariate object in mathematics is an expression, equation, function, or polynomial with only one variable.

Multivariate

Multivariable calculus (also known as multivariate calculus) is the extension of one-variable calculus to calculus with functions involving multiple variables − the differentiation and integration of functions involving multiple variables rather than just one.

Statistics and Probability

Statistics

Statistics is a field of mathematics related to research that collects, analyzes, interprets, presents, and organizes data in specific ways.

Statistics are defined as the process of collecting data, classifying it, presenting it for easy interpretation, and then analyzing it. Statistics are also referred to as concluded sample data collected through surveys or experiments.

Probability

Probability is the possibility of happening an event.

$$\mathrm{Probability(event)\:=\:\frac{favorable\:outcomes}{toatl\:outcomes}}$$

Probability is the percentage of success. Probability is used to describe an outcome function for fixed parameter values.

Conclusion

Algebra, number theory, geometry, and arithmetic are the four major branches of mathematics.

Maths is the science of quantity, pattern, order, structure, and relation, which has evolved over time from basic practices such as counting, measuring, and the symmetric study of shapes.

Algebra, Geometry, Arithmetic, Trigonometry, Calculus, and other branches of mathematics exist.

FAQs

1. What do you mean by complex numbers?

Real and imaginary numbers are combined to form complex numbers. The format for complex numbers is $\mathrm{a\:+\:ib}$. where ib is the imaginary part and a is the real part.

2. What do you mean by multivariate?

Multivariable calculus (also known as multivariate calculus) is the extension of one-variable calculus to calculus with functions involving multiple variables: the differentiation and integration of functions involving multiple variables rather than just one.

3. What do you mean by statistics?

Statistics is a field of mathematics related to research that collects, analyzes, interprets, presents, and organizes data in specific ways.

4. What is general algebra?

The study of algebraic structures rather than examples ("models") of algebraic structures is the focus of universal algebra (also known as general algebra). For example, in universal algebra, rather than studying specific groups, one studies the class of groups.

5. What do you mean by integrals?

Function integrals are another name for anti-derivatives. The process of determining the antiderivative of a function is referred to as integration. Finding integrals is the opposite of finding derivatives.

6. What do you mean by 2D and 3D shapes?

A 2D form is a flat shape with only two dimensions - length and width - and no thickness or depth, hence the name "two-dimensional shape." A sheet of paper, for example, has a two-dimensional shape.

3D shapes are solids with three dimensions: length, width (width), and height. The term 3D shapes refer to three-dimensional objects.