What is the difference between algebra, linear algebra, and abstract algebra?

algebra is a broad term encompassing various branches of mathematics that deal with mathematical symbols and their manipulation. Linear algebra is a specific branch of algebra that focuses on vector spaces and linear transformations. Abstract algebra is an advanced branch of algebra that studies algebraic structures in a general and abstract context, such as groups, rings, and fields. read less

Algebra deals with the study of mathematical symbols and rules to solve equations and manipulate mathematical expressions. Linear algebra specifically focuses on vectors, matrices, and linear transformations. Abstract algebra explores algebraic structures such as groups, rings, and fields, investigating their properties and relationships in a more generalized and abstract manner. read less

Algebra Linear Algebra Abstract Algebra Algebra is a broad branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Linear algebra is a specialized branch of algebra that focuses on vector spaces and linear mappings between these spaces. Abstract algebra is a more advanced and abstract branch of algebra that generalizes the study of algebraic structures. It involves solving equations, studying relationships and structures, and dealing with mathematical operations and their properties. It involves the study of linear equations, matrices, determinants, vector spaces, and linear transformations. Instead of focusing on specific number systems or structures, abstract algebra deals with algebraic systems in a more general way, considering common algebraic properties. read less