The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:
You might have come across specific formulas or equations where the problem is solved using alphabets and symbols. These alphabets and symbols are called ‘variables’ in algebra. When you form an equation, variables are used to determine the unknown values. However, since algebra is a vast concept, it is divided into various branches to make it easier to understand and find the correct approach to solve the problem.
1. Elementary Algebra:
Elementary algebra combines the basic arithmetic operations like addition, subtraction, multiplication, and division with the variables of algebra like a, b, x, and y to form the equations.
For example: a=1, b=5, x=2, y= 4 then the equation can be written as
a+ b= x + y
Elementary algebra is used to evaluate the equations, the equalities, and inequalities of the properties, solving equations with one or more variables, etc.
2. Advanced Algebra:
Advanced algebra helps you understand the higher level of equations to solve the other parts of algebra like:
3. Abstract Algebra:
Abstract Algebra is the algebra field that deals with the algebraic structure like vectors, lattices, rings, modules, groups, etc. These algebraic systems are not dependent on a specific nature of the algebraic operations, and hence it follows certain concepts to solve the problem.
The concepts of abstract algebra are as follows:
4. Linear Algebra:
Linear Algebra is a branch of algebra that deals with the spaces between the vectors and their mapping. Linear algebra lets you study lines and planes while also giving you an opportunity to understand the transformation properties of the linear equation. In linear algebra, you will study:
C. Linear equations
E. Computations and relations
5. Commutative Algebra:
Have you ever wondered if there is any branch in mathematics that studies the rings? Well, commutative algebra is the branch that studies the rings, such as polynomial rings and their corresponding ideals.
Two algebraic expressions can be multiplied to find the unknown variable, and the expressions can consist of integer variables and constants. For example, 2ab+5 is an expression, where a & b as variables and 4 & 9 as constants. There are certain rules that must be followed while multiplying the algebraic expression:
When solving the algebraic expressions with brackets, it is necessary that the bracket is simplified first using the BODMAS rule. BODMAS and simplification of brackets are used for expressions that have multiple arithmetic operations.
By the rule, the expression needs to be solved in the order Bracket, Order, Division, Multiplication, Addition, and Subtraction. If there are multiple bracketed expressions in an expression, then the innermost bracketed expression is solved first and then moved towards the outermost bracket.
Exponents give the idea about how many times the base number will have to be multiplied. For example, in the expression 32, 3 must be multiplied 3 times to get the result. Here, 3 is called the base number, and 2 is called the exponent.
The algebraic expressions with exponents follow a particular rule, and the rules are as follows:
RULE 3: When the exponent of the number is raised by another exponent, then multiply the exponents. For example, (32)3=3(2x3).
Exponents in algebra are used when a large number has to be represented in a simple way that can be easily understood. It shows how many times a number must be multiplied by the same number to achieve the result. For example, for the number 100, 10 must be multiplied twice, and it can be denoted as 102.
Formulas are critical, and one must understand the concept behind them. MSVgo is a learning app that is built on the philosophy that understanding a concept is the core of learning and therefore explains the concepts with examples, animations, or explanatory visualisation.
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