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  • 03 Jan 2022

Would you consider yourself a math enthusiast? Or, is math your number one pet peeve? No matter what you think about math, it's an essential subject to learn.

What is Algebra? Definition, Types, Basics, Examples?

It's a basic skill we could not do without. For example, your grocery shopping would be impossible without math. People, we have to face reality. Mathematics matters!

Math begins with addition for most of us. After that, we learn to subtract. Our next step is to master multiplication and division after we have mastered pluses and minuses. Many of us will inevitably progress to more advanced math at some point. Where are we going with this? The majestic subject of algebra, of course!

Mathematics becomes letter-based at the point of algebra. An algebraic problem involves the study of mathematical symbols and how they are manipulated.

In this article, we will take you through the life of algebra. We guarantee you will know everything about algebra by the end of this article!

First Off, What is Algebra?

Using equations to find the unknown is what algebra is all about at its most basic level. Probably, problems encountered in everyday life influenced its development!

Symbols and the rules that apply to manipulating those symbols are at the core of algebra. It is the symbol for variables (written today as Latin and Greek letters) in elementary algebra. A mathematical equation describes the relationship between variables in the same way that sentences describe relationships between specific words. To illustrate:

There is a truck full of tomatoes. A bump unexpectedly interrupts its trip. 7 tomatoes fall off! The remaining 11 tomatoes remain intact. At the time the truck hit the bump, how many tomatoes were there? Answer this question using the algebraic formula “x - 7 = 11”. The unknown x (about how many tomatoes were on the truck at the start) is represented by x. 9 tomatoes fell off, yet 11 remain on the truck. Add seven to both sides of the equation, and you will get 17. There were 17 tomatoes on the truck before it crashed into the bump.

Amazed, Right? So, Does It Matter In Our Daily Lives, You Think!

That simple equation is just the beginning of algebra. Many students wonder when they will be able to use algebra in their daily lives. Will it be of use in the real world? Why learn it at all?

Mathematical foundations are built on algebra. It is related to other classes in your schooling. You learn how to critically think when you study algebra. It helps you to solve problems, analyze patterns, see trends, and make decisions. Many professions require an understanding of algebra, especially those in math and science. Don't want to pursue those careers? Algebra may still come in handy!

Think about this example: You need to fill up the gas tank in your car. There's only $27 left in your wallet and gas costs $5 a gallon. What amount of gas can you buy? We can solve this problem with the algebraic equation, “5x = 27.” For each side of the equation to be isolated, you must multiply it by 5. The answer to this equation is 5.4 gallons of gas since x = 27 divided by 5. What's the cost of 10 gallons of gas? Algebra gets you there!

Perhaps this example will help? Say you'd like to get a home theatre set for your house. It charges a $12 setup fee and a $25 monthly fee to Company XYZ. There's no setup fee with Company ZYX, but they charge $28 a month. What is the most cost-effective service for a year? Calculate the total cost for Company XYZ by first multiplying x by $12 + $25*12 (months in a year), and you get $312. Company ZYX's equation is x = $28 * 12, which adds up to $336. Although Company ZYX might look cheaper at first glance because they don't charge a setup fee, algebra proved otherwise!

Popular belief holds that it was invented to torture students, and this may not be out of the question. What makes algebra so special is the fact that it dates back nearly 4,000 years! Jacques Sesiano writes that he found these types of problems on a Babylonian clay tablet circa 1800 B.C. in his book “An Introduction to the History of Algebra”. The roots of algebra date back to ancient Mesopotamia, and it has contributed to many scientific advances and technological development.

Other real-world applications of algebra can be found everywhere, from finding out what time to leave your house for a meeting across town on time to compare prices on similar products in a grocery store! Ask your teacher or parent why you need to learn algebra (or wonderonto!) if you are ever in doubt. The chances are good you have a valid reason!

Algebra as a Foetus!

Algebra as a Foetus!

In the era of the golden age of Islam, algebraic thinking was transformed substantially. Babylonian mathematics was practiced in increasingly complex ways until this point by the civilizations that inherited it.

The “Aryabhatiya” is thought to be one of the earliest books on math and astronomy written by a mathematician, genius, and astronomer called Aryabhata. This work is a summary of Hindu mathematics up to that time, written in 118 verses by Aryabhata. It was written in verse, not a title, according to the University of St. Andrews.

Using the Aryabhatiya of Aryabhata by Kripa Shankar Shukla as a guide, the verse is translated as:

“By multiplying the product by four, adding the square of the difference, and taking the square root of two quantities, we can identify their difference and product. Divide the result into two. Add the difference to the first slot and deduct the difference from the second. Half each slot to get each quantity's value.”

The difference and product are written in modern algebraic notation as follows:

  • x*y = B (product)
  • x – y = A (difference)

Afterwards, the procedure looks like this:

  • x = [ √(4*B + A2) + A ]/2
  • y = [ √(4*B + A2) - A ]/2

The quadratic formula is being used here. In many civilizations like Assyria, Chaldea, Persia, ancient Greeks, the Romans, in the first century A.D., and India, in the fifth century A.D., algebra was the state of play for more than 3,500 years.

The original texts from each civilization don't mention how such procedures were determined, nor did they try to demonstrate their correctness. However, it is important to note, these procedures almost certainly emerged from geometry. It wasn't until the Middle Ages that these problems were recorded in writing!

When Algebra Hit Puberty!

When Algebra Hit Puberty

Islamic mathematics became widespread in the Muslim world during the Golden Age of Islam, a period between the mid-7th and mid-13th centuries. The Compendious Book on Calculation by Completion and Balancing was published by Al-Khwārizmī, a faculty member of the House of Wisdom of Baghdad, in AD 820.

We get our word "algebra" from the Arabic word al-jabr. The mathematician Al-Khwārizmī created some quick ways to multiply and divide numbers, which became known as algorithms –do you hear a ring of similarity between his name and the word ‘algorithms’? Moreover, he suggested that when no tens number appeared in the calculation, a circle be used instead - thus the zero was invented.

The practice of algebra shifted its focus, for the first time since its inception, from applications of procedural algorithms to means of proving and deriving such algorithms using geometry and the method of applying operations to both sides of an equation. The author writes that Al-Khwārizmī believed it was necessary to show geometrical truth of the same problems described in numbers, according to Carl B. Boyer in “A History of Mathematics 3rd Ed.”

The rhetorical algebra tradition originated in medieval Muslim scholars writing equations as sentences. Syncopated algebra is a type of symbolic and rhetorical language used in algebra over the next 800 years. It was through the Iberian Peninsula, which Arabs referred to as Al-Andalus, that the pan-Eurasian heritage of mathematics, astronomy and navigation reached Europe from the 11th century until the 13th century, mainly through the transmission of the Arabic language.

Conquests in Spain by Christian armies in 1085 and 1091 (after the Islamic conquest in 965) and Crusader battles throughout the Levant between 1096 and 1303 represented important transmission points to Europe. As well as this, Christians such as Constantine the African, Adelard of Bath, and Leonardo Fibonacci sought knowledge of Islamic sciences in Muslim lands!

Algebra Turns into aSmart Woman and Marries Geometry!

Since symbolic algebra was not recognizable until the Scientific Revolution, as explained at the beginning of the article. It was René Descartes (1596-1650) who introduced the art of graphing algebraic equations in his article “La Géométrie,” published in 1637. In “Euclid's Window: The Creation of Mathematics” (Free Press, 2002), Leonard Mlodinow asserts that Descartes' algebraic-geometric methods were so fundamental to his discoveries that he wrote, “Physics is nothing but geometry.” Since it developed into a symbolic language 800 years earlier from its procedural geometric partner, algebra has come full circle!

The Bottom Line

The concept is more than just mathematics; it is also a skill that we all rely on in our daily lives without even noticing. To learn other topics in mathematics that you will learn in the future or have already learned, you must understand algebra as a concept, rather than solving equations and finding the right answer!

Choose MyAssignmentHelpAU today to explore a new dimension of algebra and various other essentials of mathematics. From offering skilled academic support to assisting in everyday assignments, the professionals make your academic life a lot easier. Trust the experts to redefine your algebra assignments and give them a new look every time you have an academic requirement in hand. Get in touch today to know more.

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