Importance of Algebra
Algebra is the study of symbols and the rules for working with these symbols. These symbols create formulae, which define the relationship of these symbols with each other. Formulas are a part and parcel of our lives. When we drive a car, when we need to calculate distances, when we need to measure the volume in a milk container, we use algebraic formulas throughout our everyday lives without even realizing it. From calculating interest rates in Finance to taking strategic decisions at war, from taking personal buying decisions to performing surgery, algebra plays an indispensable role. This is why Algebra is considered to be the gatekeeper subject to mathematics. It unifies almost all branches of mathematics.
Basic algebra is the stepping-stone for students looking for college education and higher mathematics. This is also the reason why a large number of students fail to do well at college. Many are unable to build a strong foundation of basic mathematics. As a result, they have to perform compensatory work during college which affects their overall performance and eventually their careers. It is important to understand that one can't avoid algebra and that it's better to learn it as early as possible.
Algebra is not just important for academics only but finds application later in life as well. If you understand the routines of anyone who runs an online store, or a grocery store or a restaurant, you will realize that they all use algebra extensively. Algebra isn't complicated and yet it makes our daily lives easier.
Algebra is a main field of mathematics. It is associated to mathematics is much broader than elementary algebra, studying what happens, beyond arithmetic of normal numbers, when different rules of relations and operations are used. This leads to concepts and constructions get arises from them. This mainly involves the terms equations and polynomials. When the rules of addition and multiplication are global, their exact definitions lead to algebraic structure like groups, rings and fields, studied in the area of mathematics and so called abstract algebra.
Elementary algebra is concerned with the basic rules and operations of algebra. This is one of the important branches of arithmetic mathematics, where the rules of arithmetic deal with specific numbers and operators (example, 3 + 2 = 5).
1.) Algebra introduces variables, which are letters that stand for non-specified numbers (i.e. 3a + 2a = 5a).
2.) Algebra also explains the conventions and rules of how it is shown (called algebraic notation). For illustration, the symbol of multiplication is sometimes can be replaced with a dot (.), or even completely misplaced, because its context makes its use obvious (e.g. 3 a may be written 3a).
Abstract algebra is the math subject area that is concerned with algebraic structures like groups, rings, fields, modules, vector spaces, and algebra. The term "ABSTRACT ALGEBRA" was coined at the turn of the 20th century to differentiate this area from what was normally recognized as algebra, the study of the rules for manipulating formulae and algebraic expressions involving undefined and real/ complex numbers often now named elementary algebra.
Linear algebra is sub field of math concerning vector spaces often countably infinite or finite dimensional, with linear mappings among such spaces. Such a query is motivated initially by a system of linear equations in a variety of unknowns. Such equations are represented of course using the formalism of matrices and vectors.
Universal algebra or also known as general algebra is the field or branch of mathematics those concerned mainly algebraic structures themselves; it is not examples ("models") of algebraic structures. For clear picture, rather than take groups which are particular as the object of study. In general or universal algebra one takes "the theory of groups" as an object of study.
Difficulties faced by a student while solving Algebra problems
One of the major difficulties faced by students in solving algebra problems is converting word problems to algebra problems. Algebra finds application in many real-life practical situations. As a result, curriculums include a significant no. of word problems for algebra. Most students fail to correctly mathematize these real life situations. The second most prevalent problem is working with symbols and variables. Students struggle to give dynamic meaning to familiar symbols and variables. Moreover, information skill is the most critical aspect of solving word-problems. Research shows that out of the various problems faced by students while solving mathematical problems, lack of information skill is the most prevalent. Information skill is the way a person work with the information available to him/her. Many students struggle to solve word problems in algebra despite having a clear understanding of the concepts.
It is absolutely necessary to impart realistic mathematic education to young students. Algebraic problems must be translated to real world problems, habituating the learner to develop a problem solving approach. This situation helps in building a good understanding of algebra because the learner is already familiar with real world elements that are being used.
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