The study of algebraic structures is known as abstract algebra, also referred to as contemporary algebra, and it is one of the many branches of algebra in mathematics. Groups, rings, fields, modules, vector spaces, lattices, and algebras are examples of algebraic structures. The use of variables to represent numbers in calculation and reasoning is known as elementary algebra. The word abstract algebra was first used in the early 20th century to describe this branch of mathematics.
Mathematical categories are formed by algebraic structures and the homomorphisms that go with them. A formalism called category theory enables a unified means of describing features and constructions that are common to many different types of structures. Abstract Algebra is getting tough day by day because of tough assignments. Well, if you face any difficulty regarding Abstract algebra then you can take Abstract Algebra Assignment Help from our experts.
In a related field called universal algebra, different kinds of algebraic structures are examined as singular objects. For instance, in universal algebra, the variety of groups, or the structure of groups, is a single entity.
History of Abstract Algebra
Similar to other areas of mathematics, abstract algebra has benefited greatly from the use of real-world examples and problems. Many of these issues—possibly the majority—up to the turn of the twentieth century have anything to do with the theory of algebraic equations. The main themes are:
The discovery of linear algebra through the solution of systems of linear equations
The discovery of groups as abstract representations of symmetry was the consequence of efforts to obtain formulas for solutions of general polynomial equations of increasing degree.
Mathematical studies of higher-degree quadratic forms and diophantine equations, which immediately gave rise to the concepts of a ring and an ideal.
Numerous textbooks in abstract algebra start with axiomatic definitions of various algebraic structures and then proceed to establish their properties. This creates a false impression that in algebra axioms had come first and then served as a motivation and as a basis of further study. The true order of historical development was almost exactly the opposite. For example, the hypercomplex numbers of the nineteenth century had kinematics and physical motivations but challenged comprehension. Most theories that are now recognized as parts of algebra started as collections of disparate facts from various branches of mathematics, acquired a common theme that served as a core around which various results were grouped, and finally became unified on a basis of a common set of concepts. An archetypical example of this progressive synthesis can be seen in the history of group theory.
Other sources:
https://www.kukulaland.com/profile/statanalytica/profile
https://www.sijnn.co.za/profile/statanalytica/profile
Comments
Post a Comment