History And Importance Of Algebra Mathematics Essay

In this project I will talk about starting of history of the algebra which is one of most important branches of arithmetic and Founder of the algebra and meaning of algebra and its benefit of our daily life, how we can learn and teach best way.

History of algebra

Algebra is an ancient and one of the most basic branches of mathematics. although inventor is Muhammad Musa Al-Khwarizmi, It was not developed or invented by a single person but it evolved over the centuries. The name algebra is itself of Arabic origin. It comes from the Arabic word ‘al-jebr’. The word was used in a book named ‘The Compendious Book on Calculation by Completion and Balancing’, written by the famous Persian mathematician Muhammad Musa al-Khwarizmi around 820 AD. Various derivations of the word “algebra,” which is of Arabian origin, have been given by different writers. The first mention of the word is to be found in the title of a work by Mohammed Musa al-Khwarizmi , who flourished about the beginning of the 9th century. “The full title is ilm al-jebr wa’l-muqabala (algebra equations opposite) , means Science, which contains the ideas of restitution and comparison, or opposition and comparison or resolution and equation, jebr being derived from the verb jabara,  to reunite, and muqabala, from gabala, to make equal. (The root jabara is also met with in the word algebrista, which means a “bone-setter,” and is still in common use in Spain.) The same derivation is given by Lucas Paciolus (Luca Pacioli), who reproduces the phrase in the transliterated form alghebra e almucabala, and ascribes the invention of the art to the Arabians.”1

Although the term “algebra” is now in universal use, various other appellations were used by the Italian mathematicians during the Renaissance.

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Algebra is one of the main areas of pure mathematics that uses mathematical statements such as term, equations, or expressions to relate relationships between objects that change over time. Many authors flourished algebra. by contributing specific field As well as

Cuthbert Tunstall

Cuthbert Tunstall (1474 -1559) was born in Hackforth, Yorkshire, England and died in Lambeth, London, England.

He was a significant royal advisor, diplomat, and administrator, and he gained two degrees with great proficiency in Greek, Latin, and mathematics.

In 1522, he wrote his first printed work that was devoted to mathematics, and this arithmetic book ‘De arte supputandi libri quattuor’ was based on Pacioli’s “Suma”.

Robert Recorde

1Robert Recorde (1510-1558) was born in Tenby, Wales and died in London, England.

He was a Welsh mathematician and physician and in 1557, he introduced the

equals sign (=).

In 1540, Recorde published the first English book of algebra ‘The Grounde of Artes’.

In 1557, he published another book ‘The Whetstone of Witte’ in which the equals sign was introduced.

John Widman

John Widman (1462-1498) was born in Eger, Bohemia, currently called Czech Republic and died in Leipzig, Germany.

He was a German mathematician who first introduced + and – signs in his arithmetic book ‘Behende und hupsche Rechnung auf Allen kauffmanschafft’.

How is Algebra used in daily life?

We use Algebra in finances, engineering, and many scientific fields. It is actually quite common for an average person to perform simple Algebra without realizing it. For example, if you go to the grocery store and have ten dollars to spend on two dollar candy bars. This gives us the equation 2x = 10 where x is the number of candy bars you can buy. Many people don’t realize that this sort of calculation is Algebra; they just do it.

1. http://wiki.answers.com/Q/Where_is_Algebra_used_in_daily_life#ixzz1KS594VsI

Basic laws of Algebra .

 There are five basic laws of algebra governing the operations of addition, subtraction, multiplication and division. And is expressed using the variables can be compensated for any number was. These laws are:

1 – substitution property of the collection. And write x + y = y + x. Means that the order is not important when collecting two issues as the result is the same. For example, 2 + 3 = 3 + 2 (-8) + (- 36) = (-36) + (-8).

2 – the property of the aggregate collection. And write C + (r + p) = (x + y) + p, which means that when you raise three issues or more, it can collect any form of first, and then complete the collection without affecting the final product, for example, 2 + (3 + 4) = (2 + 3) + 4 or 2 + 7 = 5 + 4.

3 – property substitution beaten. And write xy = y Q. Means that the order is not important when you hit the two issues as the result is the same. For example, (2) (3) = (3) (2) and (-8) (- 36) = (-36) (-8).

4 – aggregate property beaten. And write Q (r p) = (xy) p. Means that when you hit three or more numbers, it can hit any of them to form first, then complete the battery without affecting the final output. For example, 2 (3 Ã- 4) = (2 Ã- 3) 4 or 2 (12) = (6) 4.

5 – Distribution of property of multiplication over addition. And writes:

Q (r + p) = xy + x p.

Clarify this important property in algebra the following example:

3 (4 + 5) = (3 Ã- 4) + (3 Ã- 5). The multiplication of two numbers in the total number such as 3 (4 + 5) or 3 Ã- 9 equals the sum of multiplying the number one of the two numbers and multiplied by the number the second number. Note that:

3 (4 + 5) = 3 (9) = 27 as well.

(3 Ã- 4) + (3 Ã- 5) = 12 + 15 = 27.

Other definitions. It is important to know some other words used in algebra. Valmkdar o 2-2 XY + R contains three parts linked to the processes of addition or subtraction, called an end to every part of it. The amount of so-called compulsory component of the limit and only one Bouhid met, for example, 5 o r single limit, although it contains three elements (5, x, y) multiplied with each other and called each factor. And know how much that amount binomial component of their double-edged reference collection or ask, for example, both x + y, 3, a 2-4 with a double-edged. The polynomial is how much the component of the double-edged or more linked with each other or ask a reference collection, for example, Q – r + p polynomial. Note that the binomial is not only a special case of polynomial.

That means the amounts set side by side in algebra they multiplied, Fidel expression on the 5 A product of a five-Issue 5 and is called a factor. Since that 5 times the symbol a in algebra is called a gradient of the number 5. As well as in the formula a (x + r) is a factor (x + y) and (x + y) is a factor. Since a = 1 Ã- a, we can always replace a formula 1a.

Combination. Similar to the process of bringing in algebra to a great extent than in the account. For example, the sum of A and A is 2a. We call a and 2 a similar double-edged because they contain the same variable. And to collect two quantities Ghebretin or more similar use property of the distribution of multiplication over addition, for example.

2x + 3 x + 4 h is (2 + 3 + 4) Q 9 or Q, but we can not express the sum of two quantities is similar with a single. For example, the sum of A and B written A + B. And to collect 3a, 4 b 0.6 a and b use his replacement and assembly of the collection process. It is clear that these special Tsaaadanna to collect any series of the border, written in any order. And the compilation of similar border, we find that:

3a +6 a = 9 a and 4 b + b b = 5.

So 3a +4 b + 6 a + b = 9 a + 5 b.

The solution could be organized as follows:

And to collect similar amounts of non-negative or positive, we were using a private distribution of multiplication over addition. To make it clear that use the collection:

(2a – b ² c + d 6 b ² + 2 d ) and

4 (a + 3 b ² c – 4 d b ² – 3 d ) and

3 (a + 2 b ² c + d 2 b ² – 4 d ) and

(-2 A – 8 b ² c + d 6 b ² + 6 d ).

And the number 3, which appears in the border such as 2 a means that a variable multiplied by itself three times. See: the cube. Before the process of collecting such amounts arrange the border in the columns.

Algebra equations

Algebra equation include letters represent unknown numbers.

It is one of the main branches of algebra in mathematics, where the mastery of mathematics depends on a proper understanding of algebra. And uses the engineers and scientists algebra every day, and counts commercial and industrial projects on the algebra to solve many of the dilemmas faced by them. Given the importance of algebra in modern life, it is taught in schools and universities all over the world.

Symbolizes the number of anonymous letters in algebra, such as X or Y. In some of the issues can be replaced only one number is indicated. As an example note that even a simple sentence becomes + 3 = 8 should be correct to compensate for x number 5 because 5 + 3 = 8.

In some other issues, it can compensate for the code number or more. For example, in order to achieve the health of sentence constraint x + y = 12 may put Q equals 6 and Y equals 6, or Q equal to 4, and Y equal to 8. In such sentences arrest, you can get several values ​​for x makes true if the sentences given for r different values.

And admire many of the students of his ability and usefulness of algebra big, as using algebra, one can solve many of the issues that can not be resolved by using the only account. For example, say the plane cut a distance of 1710 km in four hours if the flight in the direction of the wind blowing, but cut 1370 km in five hours if the flight was blowing the opposite direction of the wind. Using algebra, we can find the speed of the plane and wind speed.

Terminology used in algebra

Exponent of the number placed on the number or variable from the left to indicate the number of times where it is used as a factor.

Signals the assembly , brackets []. And are used in algebra formulas to account for arrest.

Square or second-degree variable multiplied by the same user as any ¸ twice •.

Binomial term in algebra consists of two double-edged symbol + or the symbol -.

The number of fixed or variable scope set of one item.

Roots of the equation numbers that make the equation correct a report when you replace the variables in the equation.

Algebra is a branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can include real numbers, complex numbers, matrices, vectors. Moving from Arithmetic to Algebra will look like this: Arithmetic: 3 + 4 = 3 + 4 in Algebra it would look like: x + y = y + x

The name ‘algebra’ is derived from the treatise written by the Persian mathematician 

Muhammad bin MÅ«sā al-KhwārizmÄ« titled (in Arabic “Al-Kitab al-Jabr wa-l-Muqabala” 

The development of algebra is outlined in these notes under the following headings: Egyptian algebra, Babylonian algebra, Greek geometric algebra, Diophantine algebra, Hindu algebra, Arabic algebra, European algebra since 1500, and modern algebra.

Since algebra grows out of arithmetic, recognition of new numbers – irrationals, zero, negative numbers, and complex numbers – is an important part of its history.

And later became known to science in general mathematical equations

Best way to learn and teach algebra

As you already know, algebra is an essential subject. It’s the gateway to mathematics. It’s used extensively in the sciences. And it’s an important skill in many careers.

Yet for many people Algebra is a nightmare. It causes more stress, homework tears and plain confusion than any other subject on the curriculum.

Well the good news is you don’t have to struggle with Algebra for a minute longer. Because now there’s a solution that explains Algebra in a way that anyone can quickly understand.

Algebra is an Arabic word and a branch of mathematics and its name came from the book world of mathematics, astronomy and traveller Muhammad ibn Musa Khurazmi (short book, in the calculation of algebra and interview) which was submitted by the governing algebraic operations to find solutions to linear and quadratic equations.

The algebra is three branches of basic math in addition to geometry and mathematical analysis and the theory of numbers and permutations and combinations. And takes care of this science to study algebraic structures and symmetries, including, relations and quantities.

And algebra is the concept of a broader and more comprehensive account of the primary or reparation. It does not deal with numbers, but also formulate dealings with symbols, variables and categories as well. And formulate Alibdehyat algebra and relations by which can represent any phenomenon in the universe. So is one of the fundamentals governing the methods of proof

The Start of Algebra

Algebra is an ancient and one of the most basic branches of mathematics. It was not developed or invented by a single person but it evolved over the centuries. The name algebra is itself of Arabic origin. It comes from the Arabic word ‘al-jebr’. The word was used in a book named ‘The Compendious Book on Calculation by Completion and Balancing’, written by the famous Persian mathematician Muhammad ibn Musa ibn al-Khwarizmi around 820 AD. Various derivations of the word “algebra,” which is of Arabian origin, have been given by different writers. The first mention of the word is to be found in the title of a work by Mahommed ben Musa al-Khwarizmi (Hovarezmi), who flourished about the beginning of the 9th century. The full title is ilm al-jebr wa’l-muqabala, means Science, which contains the ideas of restitution and comparison, or opposition and comparison or resolution and equation, jebr being derived from the verb jabara, to reunite, and muqabala, from gabala, to make equal. (The root jabara is also met with in the word algebrista, which means a “bone-setter,” and is still in common use in Spain.) The same derivation is given by Lucas Paciolus (Luca Pacioli), who reproduces the phrase in the transliterated form alghebra e almucabala, and ascribes the invention of the art to the Arabians.

Although the term “algebra” is now in universal use, various other appellations were used by the Italian mathematicians during the Renaissance.

Algebra is one of the main areas of pure mathematics that uses mathematical statements such as term, equations, or expressions to relate relationships between objects that change over time. Many authors flourished algebra. by contributing specific field As well as

Cuthbert Tunstall

Cuthbert Tunstall (1474 -1559) was born in Hackforth, Yorkshire, England and died in Lambeth, London, England.

He was a significant royal advisor, diplomat, and administrator, and he gained two degrees with great proficiency in Greek, Latin, and mathematics.

In 1522, he wrote his first printed work that was devoted to mathematics, and this arithmetic book ‘De arte supputandi libri quattuor’ was based on Pacioli’s “Suma”.

Robert Recorde

1Robert Recorde (1510-1558) was born in Tenby, Wales and died in London, England.

He was a Welsh mathematician and physician and in 1557, he introduced the equals sign (=).

In 1540, Recorde published the first English book of algebra ‘The Grounde of Artes’.

In 1557, he published another book ‘The Whetstone of Witte’ in which the equals sign was introduced.

John Widman

John Widman (1462-1498) was born in Eger, Bohemia, currently called Czech Republic and died in Leipzig, Germany.

He was a German mathematician who first introduced + and – signs in his arithmetic book ‘Behende und hupsche Rechnung auf Allen kauffmanschafft’.

How is Algebra used in daily life?

Mathematics is one of the first things you learn in life. Even as a baby you learn to count. Starting from that tiny age you will start to learn how to use building blocks how to count and then move on to drawing objects and figures. All of these things are important preparation to doing algebra..

We use Algebra in finances, engineering, and many scientific fields. It is actually quite common for an average person to perform simple Algebra without realizing it. For example, if you go to the grocery store and have ten dollars to spend on two dollar candy bars. This gives us the equation 2x = 10 where x is the number of candy bars you can buy. Many people don’t realize that this sort of calculation is Algebra; they just do it.2

———————-

2. http://wiki.answers.com/Q/Where_is_Algebra_used_in_daily_life#ixzz1KS594VsI

Basic laws of Algebra .

 There are five basic laws of algebra governing the operations of addition, subtraction, multiplication and division. And is expressed using the variables can be compensated for any number was. These laws are:

1 – substitution property of the collection. And write x + y = y + x. Means that the order is not important when collecting two issues as the result is the same. For example, 2 + 3 = 3 + 2 (-8) + (- 36) = (-36) + (-8).

2 – the property of the aggregate collection. And write C + (r + p) = (x + y) + p, which means that when you raise three issues or more, it can collect any form of first, and then complete the collection without affecting the final product, for example, 2 + (3 + 4) = (2 + 3) + 4 or 2 + 7 = 5 + 4.

3 – property substitution beaten. And write xy = y Q. Means that the order is not important when you hit the two issues as the result is the same. For example, (2) (3) = (3) (2) and (-8) (- 36) = (-36) (-8).

4 – aggregate property beaten. And write Q (r p) = (xy) p. Means that when you hit three or more numbers, it can hit any of them to form first, then complete the battery without affecting the final output. For example, 2 (3 Ã- 4) = (2 Ã- 3) 4 or 2 (12) = (6) 4.

5 – Distribution of property of multiplication over addition. And writes:

Q (r + p) = xy + x p.

Clarify this important property in algebra the following example:

3 (4 + 5) = (3 Ã- 4) + (3 Ã- 5). The multiplication of two numbers in the total number such as 3 (4 + 5) or 3 Ã- 9 equals the sum of multiplying the number one of the two numbers and multiplied by the number the second number. Note that:

3 (4 + 5) = 3 (9) = 27 as well.

(3 Ã- 4) + (3 Ã- 5) = 12 + 15 = 27.

Other definitions. It is important to know some other words used in algebra. Valmkdar o 2-2 XY + R contains three parts linked to the processes of addition or subtraction, called an end to every part of it. The amount of so-called compulsory component of the limit and only one Bouhid met, for example, 5 o r single limit, although it contains three elements (5, x, y) multiplied with each other and called each factor. And know how much that amount binomial component of their double-edged reference collection or ask, for example, both x + y, 3, a 2-4 with a double-edged. The polynomial is how much the component of the double-edged or more linked with each other or ask a reference collection, for example, Q – r + p polynomial. Note that the binomial is not only a special case of polynomial.

That means the amounts set side by side in algebra they multiplied, Fidel expression on the 5 A product of a five-Issue 5 and is called a factor. Since that 5 times the symbol a in algebra is called a gradient of the number 5. As well as in the formula a (x + r) is a factor (x + y) and (x + y) is a factor. Since a = 1 Ã- a, we can always replace a formula 1a.

Combination. Similar to the process of bringing in algebra to a great extent than in the account. For example, the sum of A and A is 2a. We call a and 2 a similar double-edged because they contain the same variable. And to collect two quantities Ghebretin or more similar use property of the distribution of multiplication over addition, for example.

2x + 3 x + 4 h is (2 + 3 + 4) Q 9 or Q, but we can not express the sum of two quantities is similar with a single. For example, the sum of A and B written A + B. And to collect 3a, 4 b 0.6 a and b use his replacement and assembly of the collection process. It is clear that these special Tsaaadanna to collect any series of the border, written in any order. And the compilation of similar border, we find that:

3a +6 a = 9 a and 4 b + b b = 5.

So 3a +4 b + 6 a + b = 9 a + 5 b.

The solution could be organized as follows:

And to collect similar amounts of non-negative or positive, we were using a private distribution of multiplication over addition. To make it clear that use the collection:

(2a – b ² c + d 6 b ² + 2 d ) and

4 (a + 3 b ² c – 4 d b ² – 3 d ) and

3 (a + 2 b ² c + d 2 b ² – 4 d ) and

(-2 A – 8 b ² c + d 6 b ² + 6 d ).

And the number 3, which appears in the border such as 2 a means that a variable multiplied by itself three times. See: the cube. Before the process of collecting such amounts arrange the border in the columns.

Algebra equations

Algebra equation include letters represent unknown numbers.

It is one of the main branches of algebra in mathematics, where the mastery of mathematics depends on a proper understanding of algebra. And uses the engineers and scientists algebra every day, and counts commercial and industrial projects on the algebra to solve many of the dilemmas faced by them. Given the importance of algebra in modern life, it is taught in schools and universities all over the world.

Symbolizes the number of anonymous letters in algebra, such as X or Y. In some of the issues can be replaced only one number is indicated. As an example note that even a simple sentence becomes + 3 = 8 should be correct to compensate for x number 5 because 5 + 3 = 8.

In some other issues, it can compensate for the code number or more. For example, in order to achieve the health of sentence constraint x + y = 12 may put Q equals 6 and Y equals 6, or Q equal to 4, and Y equal to 8. In such sentences arrest, you can get several values ​​for x makes true if the sentences given for r different values.

And admire many of the students of his ability and usefulness of algebra big, as using algebra, one can solve many of the issues that can not be resolved by using the only account. For example, say the plane cut a distance of 1710 km in four hours if the flight in the direction of the wind blowing, but cut 1370 km in five hours if the flight was blowing the opposite direction of the wind. Using algebra, we can find the speed of the plane and wind speed.

Terminology used in algebra

Exponent of the number placed on the number or variable from the left to indicate the number of times where it is used as a factor.

Signals the assembly , brackets []. And are used in algebra formulas to account for arrest.

Square or second-degree variable multiplied by the same user as any ¸ twice •.

Binomial term in algebra consists of two double-edged symbol + or the symbol -.

The number of fixed or variable scope set of one item.

Roots of the equation numbers that make the equation correct a report when you replace the variables in the equation.

Algebra is a branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. Algebra can include real numbers, complex numbers, matrices, vectors. Moving from Arithmetic to Algebra will look like this: Arithmetic: 3 + 4 = 3 + 4 in Algebra it would look like: x + y = y + x

The name ‘algebra’ is derived from the treatise written by the Persian mathematician 

Muhammad bin MÅ«sā al-KhwārizmÄ« titled (in Arabic “Al-Kitab al-Jabr wa-l-Muqabala” 

The development of algebra is outlined in these notes under the following headings: Egyptian algebra, Babylonian algebra, Greek geometric algebra, Diophantine algebra, Hindu algebra, Arabic algebra, European algebra since 1500, and modern algebra.

Since algebra grows out of arithmetic, recognition of new numbers – irrationals, zero, negative numbers, and complex numbers – is an important part of its history.

And later became known to science in general mathematical equations

Best way to learn and teach algebra

As you already know, algebra is an essential subject. It’s the gateway to mathematics. It’s used extensively in the sciences. And it’s an important skill in many careers.

Yet for many people Algebra is a nightmare. It causes more stress, homework tears and plain confusion than any other subject on the curriculum.

Well the good news is you don’t have to struggle with Algebra for a minute longer. Because now there’s a solution that explains Algebra in a way that anyone can quickly understand. about “How to learn algebra the easy way”. Algebra is not that difficult as everyone thinks. With some practice & hard work anyone can master it.

How to learn algebra easy way

The learning of any subject needs to understand well, and algebra is not exception to other branches of maths , as we know the maths is first thing we learn before anything else even before we go to school ,therefore it is easier than other subjects in my opinion . And started counting fingers even when you buying sweet .every one of us has knowledge of some collections like books ,cars, and so on ,it is good to use as groups we know as rats, cow ,pen . Some student surprise if you say 5x+4=24 but it will be easy to say 5cars=20£ how much the price of one car?

When we use variable numbers and letters instead of numbers only it is algebra, truly it is very fun and easy if we make more effort with understanding.

To understand it needs to make more practice and follow up the rules, addition ,subtraction, multiplication, division and equality of equations because changing sign from side to side is very important and algebra is not exception to other branch of maths .

Understanding and practice whenever you make more practice sure you will be mathematician person ,it is not difficult as many people afraid or think

1

LEARN ALGEBRA THE EASY WAY :

The key to learn and understand Mathematics is to “practice” and Algebra is no exception. Understanding the concepts is very vital, without which you are going to have difficulty learning algebra. Algebra helps in problem solving, reasoning, decision making, and applying solid strategies which is important in your day to day life especially in a job atmosphere. Consider Algebra to be a game and you would find how easy it is, you’ll see the miracle !

2

There are several techniques that can be followed to learn Algebra the easy way. Learning algebra from the textbook can be boring. Though textbooks are necessary it doesn’t always address the need for a conceptual approach. There are certain techniques that can be used to learn algebra the fun and easy way. Listed below are some of the techniques that can be used. Do some online research and you will be surprised to find a whole bunch of websites that offer a variety of fun learning methods which makes learning algebra a pleasant experience and not a nightmare. But the key is to take your time in doing a thorough research before you choose the method that is best for you, or you can do a combination of different methods if you are a person who looks for variety to boost your interest.

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1. ANIMATED ALGEBRA : You can learn the basic principles of algebra through this method. Animation method teaches the students the concepts by helping them integrate both teaching methods. When the lessons are animated you actually learn more !

2. ALGEBRA QUIZZES : You can use softwares and learn at your own pace & best of all you don’t need a tutor to use it. What you really need is something that can help you with your own homework, not problems it already has programmed into it that barely look like what your teacher or professor was trying to explain. You can enter in your own algebra problems, and it works with you to solve them faster & make them easier to understand.

3. INTERACTIVE ALGEBRA : There are several Interactive Algebra plugins that allows the user to explore Algebra by changing variables and see what happens. This promotes an understanding of how you arrive at answers. There are websites that provide online algebra help and worksheets. They also provide interactive online games and practice problems and provide the algebra help needed.

It is difficult to recommend better methods for studying and for learning because the best methods vary from person to person. Instead, I have provided several ideas which can be the foundation to a good study program. If you just remember all the rules and procedures without truly understanding the concepts, you will no doubt have difficulty learning algebra. So the magic word is “concept”. The above techniques can help you in learning the concepts without pain in a fun environment

Read more: How to learn algebra the easy way ! | eHow.com http://www.ehow.com/how_4452787_learn-algebra-easy-way.html#ixzz1M8en5qcH

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