Transcendental Number Theory
Transcendental Number Theory studies the properties and relationships of numbers that are not algebraic, meaning they are not roots of any non-zero polynomial equation with integer coefficients. These numbers are called transcendental numbers and are known to be irrational. The field explores various aspects of transcendental numbers, such as their distribution, approximation, and transcendence degree over the rational numbers. It also investigates the connections between transcendental numbers and other branches of mathematics, such as analysis and geometry.