The GRE Subject Test in Math assesses knowledge and skills in undergraduate-level mathematics, including calculus, algebra, and geometry.
Abstract algebra explores algebraic structures like groups, rings, and fields. Rather than focusing on numbers, it investigates the rules and relationships that govern sets and operations.
A group is a set with an operation that combines any two elements to form a third, following certain rules like associativity and the existence of an identity element.
Rings have two operations (like addition and multiplication), and fields add more structure, allowing division (except by zero).
Cryptography, coding theory, and advanced physics all rely on abstract algebra.
\[a + b = b + a\]
Integers with addition form a group; real numbers with multiplication (excluding zero) form a group.
Modular arithmetic is used in creating secure passwords.
Abstract algebra studies mathematical structures and the rules that connect them.