Algebraic Number Theory

Algebraic Number Theory is a branch of mathematics that studies numbers in a broader sense than just whole numbers or fractions. It focuses on properties of numbers that can be expressed as solutions to polynomial equations, particularly using algebraic structures like rings and fields. This field explores concepts like prime numbers, divisibility, and the relationships between different types of numbers, including integers and their roots. By analyzing these structures, mathematicians can uncover deep insights about the nature of numbers and their relationships, which has applications in areas like cryptography and coding theory.