Abstract algebra is the study of algebraic structures and include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term abstract algebra was coined in the early 20th century to distinguish this area of study from the other parts of algebra.
- Book: Introduction to Algebraic Structures (Denton)
- An algebraic structure is a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. Examples of algebraic structures include groups, rings, fields, and lattices.
- Book: Applied Geometric Algebra (Tisza)
- Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These course notes attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools.