Abstract algebra is a branch of mathematics that deals with mathematical structures, such as groups, rings, fields, and modules. It is a fundamental subject in mathematics, which has applications in various fields, including physics, computer science, and engineering. In this article, we will explore the definition and meaning of abstract algebra, its origins, associations, synonyms, antonyms, and example sentences.
Definitions
Abstract algebra is defined as the study of algebraic structures, such as groups, rings, fields, and modules, using abstract concepts, rather than specific numbers or symbols. It is concerned with the properties and relationships between these structures, and how they can be manipulated and transformed.
Another definition of abstract algebra is that it is the study of algebraic structures that are independent of any particular set of objects or operations. It is a generalization of classical algebra, which deals with specific numbers and symbols.
Origin
The origins of abstract algebra can be traced back to the 19th century, when mathematicians began to investigate the properties of algebraic structures that were independent of any particular set of objects or operations. The term “abstract algebra” was first used by the mathematician Emil Artin in the 1920s, to describe the study of algebraic structures using abstract concepts.
Meaning in different dictionaries
According to the Oxford English Dictionary, abstract algebra is “the branch of mathematics concerned with the study of algebraic structures using abstract concepts, rather than specific numbers or symbols.”
The Merriam-Webster Dictionary defines abstract algebra as “a branch of mathematics dealing with algebraic structures that are independent of any particular set of objects or operations.”
Associations
Abstract algebra is associated with various branches of mathematics, including number theory, geometry, and topology. It is also used in physics, computer science, and engineering, where it is used to model and solve problems in these fields.
Synonyms
Some synonyms of abstract algebra include modern algebra, algebraic structures, and algebraic systems.
Antonyms
There are no specific antonyms of abstract algebra, as it is a specialized branch of mathematics. However, classical algebra, which deals with specific numbers and symbols, can be seen as an antonym of abstract algebra.
The same root words
The root words of abstract algebra are “abstract” and “algebra.” Abstract refers to something that is conceptual or theoretical, rather than concrete or specific. Algebra refers to the branch of mathematics that deals with the manipulation and solving of equations and formulas.
Example Sentences
- “Abstract algebra is a fundamental subject in mathematics, which has applications in various fields.”
- “The study of algebraic structures using abstract concepts is the essence of abstract algebra.”
- “Abstract algebra is used to model and solve problems in physics, computer science, and engineering.”
- “Modern algebra and algebraic systems are synonyms of abstract algebra.”
- “Classical algebra can be seen as an antonym of abstract algebra.”