The word algebra originates from the Arabic word al-jabr which translates to the reunion of broken parts.
Algebra is a branch of mathematics that deals with the study of mathematical symbols and letters. It involves variables, such as x, y, and z, and has been greatly used to solve problems across many fields. Famous fields like set theory, probability, statistics, and others involve the use of algebra. Algebra in schools is taught at all levels starting from elementary school where basics are taught up to colleges where advanced algebraic expressions are taught. A simple algebraic expression can be in this form: 2a+12=28
For an algebraic expression to be complete, it should be composed of constants, variables, and arithmetic operations, such as addition, multiplication, subtraction, and division. An expression like this 5x+4=39 qualifies to be algebra since it has all the components of an algebra:
5 is a coefficient
X is a variable
+ Is an arithmetic operation
4 and 39 are constants
Branches of Algebra
There are up to five branches of algebra, and they are classified according to their complexity:
Elementary Algebra- This branch is often known as algebra 1, as it contains the most basic concept of algebra. Elementary algebra is mostly concerned with teaching general guidelines of algebra and is usually taught up to high school. Students are always advised to understand elementary algebra to their best, as it acts as a foundation to the advanced levels of algebra.
Advanced Algebra- This is commonly referred to as algebra 2. This branch is more complex and detailed than the branch mentioned above. It entails solving various mathematical operations, such as trigonometry, matrices, sequences and series, equalities and inequalities, probability, and polynomial equations.
Abstract Algebra- This branch is commonly known as modern algebra. It deals with the use of abstract groups, such as rings, groups, vector spaces, etc.
Commutative Algebra- This is a branch that studies the commutative rings and their ideals (polynomial rings, algebraic and p-adiac integers). It has played an important role in modern pure mathematics since many mathematical operations rely on commutative algebra in various ways, such as general topology, invariant theory, and differential theory.
Linear Algebra- This involves the study of lines, mappings, and vector spaces. It is used in almost all areas of mathematics. For example, linear algebra is primary in the presentation of geometry and functional analysis. It is also used in engineering, specifically machine learning. Main topics covered in linear algebra include matrices and matrix decomposition, vector spaces, relations, and computations.
History of Algebra
There are many histories and critics about the development of algebra, but there are two main histories mentioned about algebra. The early history of algebra states that the development of algebra can be traced to the ancient Babylonians where they used it to solve equations or problems, which are today called quadratic equations. Ancient algebra explains that algebra never used symbols like it is seen currently, but it underwent three stages: rhetorical, syncopated, and symbolic stages. In the rhetorical stage, equations were written in words. Algebra was quite lengthy at this stage which then led to the shortened or syncopated stage. The syncopated stage involved the use of some symbols. It then evolved to a symbolic stage where full symbols are used, which is the algebra we use and solve currently.
Uses of Algebra
Algebra has been used in everyday life to solve problems or predict future events across all fields. In our daily life, we even apply algebra without our knowledge. A good example is if you are a chef or if you are in a kitchen cooking a particular meal. You are using a recipe that was intended to cook a meal for two to prepare a meal enough for 20 people without altering the taste. Algebra will help you cook the correct amount of food. There are a lot of applications of algebra in real life but I can highlight a few:
Predicting Profits for a Business
In a business, there are expenses, and they should be at their lowest for you to make a profit while the quality of your products should not be altered. This is where algebra comes in handy. Algebra is used in making the structure of the business, such that the expenses and revenue can be altered to obtain an optimal profit.
The current world is made up of technological inventions which all trace back to programmers then further to algebra. A programmer can use or assign conditions in the use of datasets and variables to establish a connection, which brings in a result that can be seen on the front end. Linear algebra has been known to be a great tool for the development and compiling of datasets to create a program that can be used in robotics or machine learning as a whole.
Astronomy involves the study of the positioning and movement of celestial objects. Astronomers can predict the movement of these objects with the help of algebra. They can establish the relationship between the position of the planet at a chosen period, the planet’s revolution speed, and so on. All these calculations involved are algebra.
Solved Example of Algebra
Solve the equation 7x-3=5x+5
Adding both sides by 3:
Subtract 5x from both sides:
Divide both sides by 2:
Algebra is a great tool that enables you to carry out various daily life activities. Every line of operation involves the use of algebra. From the discussion above, algebra should be deeply understood in schools, as it is a preparation for you to handle life and its ideals.