Algebra is one of the oldest branches in the history of mathematics that deals with number theory, geometry, and other analyses of mathematics. The study of mathematical symbols is usually known as algebra, but it not only deals with symbols, but it deals with other complicated numerals as well. We can also say that algebra is a concept that occupies every position in mathematics. We have been studying algebra since our childhood in our respective classes. In this article, we will try to understand some basic concepts of algebra such as, branches of algebra which include algebra 1 and 2, abstract algebra, commutative algebra, and algebraic expressions.
What is Algebra 1?
Elementary algebra also known as algebra 1 covers the traditional topics that we have been studying in modern elementary algebra courses. Algebra 1 is basically a high school maths course that teaches us how to use letters and numbers with mathematical symbols to solve problems. The arithmetic numerals include symbols like + (addition), – (subtraction), × (multiplication), ÷ (division). In the case of algebra, the numbers are often represented by symbols that are also known as variables. For example, x, a, n, y, etc. Algebra 1 typically helps students in building conceptual understanding and gaining fluency in concepts that are required for more advanced maths topics. The concepts that come under elementary algebra or algebra 1 include variables, evaluating equations and expressions, linear equations of one or two variables, properties of equalities and inequalities, etc.
Branches of Algebra
We already know that algebra is a concept that comes across unknown values known as variables. But one of the most important concepts of algebra is the algebraic equation. It undergoes various rules to perform arithmetic expressions. These rules are made in order to make sense to sets of data that involve two or more variables. In your everyday life, you may have used algebraic equations without knowing it. Algebra has been divided into various branches and subbranches such as elementary algebra, advanced algebra, abstract algebra, linear algebra, etc. Let us now try to understand some of these topics in detail. If you want to learn more about algebra or algebra 1 in detail and in an interesting and fun way, visit Cuemath.
Algebra 2 or Advanced Algebra
Advanced algebra or algebra 2 is the intermediate level of algebra after elementary or algebra 1. This stage requires a high level of equations in order to solve the equations as compared to pre-algebra. This stage of algebra will also help you to go through different parts of algebra such as Equations with inequalities, matrices, solving systems of linear equations, conic equations, polynomial equations, sequences and series, trigonometry, quadratic functions with inequalities, etc.
Abstract algebra is the third level of algebra which deals with algebraic structures such as fields, groups, modules, vectors, spaces, etc. Some of them are mentioned below:
- Sets are the collection of objects that are determined by some of the specific properties of sets. For example, a set of 2×2 of all the matrices, different forms of plane groups, etc.
- Binary operations: Whenever the idea of addiction is conceptualized, it gives us binary operations. The binary operations are related to the concept of sets. We can also state that the concept of binary operations is useless without sets.
A branch of algebra that applies both pure, as well as applied mathematics, is known as linear algebra. Linear algebra deals with the mappings between the vector spaces. It also deals with the study of planes and lines. This concept of algebra is almost used in every part of mathematics. The significant topics that are covered in linear algebra are as follows: linear equations, vector spaces, mappings, relations, and computations, etc.