The solution of systems of linear equations leads to the study of linear algebra , in which the elements are matrices and vectors. Classical algebra, which is concerned with solving equations , uses symbols instead of specific numbers and uses arithmetic operations to establish ways of handling symbols. Modern algebra has evolved from classical algebra by increasing its attention to the structures within mathematics. Mathematicians consider modern algebra to be a set of objects with rules for connecting or relating them. Abstract algebra is a more general branch of mathematics that analyzes algebraic axioms and operations with arbitrary sets of symbols.
Abstract algebra is the study of systems that satisfy certain sets of axioms.
Some of these structures are fields, rings, groups, and domains . The elements used in abstract algebra may be numbers, vectors, or even geometric transformations. A number system is any of various sets of symbols and the rules for using them to express quantities as the basis for counting, comparing amounts, performing calculations, determining order, making measurements, representing value, setting limits, abstracting quantities, coding information, and transmitting data. Mathematics , Number Recommended Sites Math League Math League Help Facility. A reference guide for math topics for grades 4-8, complete with examples, definitions, and explanations.