Number Theory
Number Theory is a branch of mathematics that explores the properties and relationships of numbers. Instead of dealing with calculations and operations, it focuses on understanding the fundamental nature of integers and their patterns. In other words, it’s like studying the building blocks of numbers.
Whole Numbers
Whole numbers are the numbers we use for counting things. They start from zero and go on without any fractions or decimals. They are the natural numbers we use in our daily lives for simple counting and basic calculations.
Prime Numbers
Prime numbers are a central concept in Number Theory. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers, except for 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11. The fundamental theorem of arithmetic states that every natural number greater than 1 can be uniquely expressed as a product of prime numbers.
Divisibility Rules
Divisibility rules are guidelines that help determine whether one number is divisible by another without performing the actual division. These rules are practical tools in Number Theory for understanding the relationships between numbers.
- Divisibility Tests
- Prime Factorization
Number System
The number system is a method of representing and expressing quantities using numerical symbols. It encompasses different types of numbers, such as natural numbers, integers, rational numbers, and irrational numbers. The number system provides a structured way to count, measure, and perform mathematical operations.
Complex Number
A complex number is a mathematical concept that combines both real and imaginary components. It is expressed in the form a+bi, where a is the real part, b is the imaginary part, and i represents the imaginary unit (√-1). Complex numbers find applications in various fields, including engineering and physics, for solving equations that involve square roots of negative numbers.
Key Concepts of Number Theory:
Branches of Mathematics
Branches of Mathematics: Mathematics is the study of amount, pattern, arrangement, structure, and connection. It keeps growing from simple actions of counting, measuring, and examining symmetrical shapes. The main thing is to use logical thinking and numerical calculations to discover the best solutions to problems. Maths is the solution to many problems and hence has various branches, that give solutions in different fields.
Mathematics is broadly classified into two parts— pure mathematics and applied mathematics. This article will cover the concept of branches in mathematics— Arithmetic, Geometry, Algebra, Calculus, Topology, Trigonometry, Number theory, Probability and Statistics, and the various sub-categories of these branches
Table of Content
- What are Main Branches of Mathematics?
- Table – Branches of Mathematics with Key Topics
- Number Theory
- Arithmetic
- Geometry
- Algebra
- Calculus
- Trigonometry
- Probability and Statistics
- Topology
- List of Branches of Mathematics