The history of mathematics


If you have taken the first years of the history of college course – or read through a basic history textbook – you may have noticed a small gap. It is only a thousand years or so

a long time, the history of Western culture was told like this :. About the fifth century BC, mathematics, philosophy and science developed, thanks to the work of some very smart Greeks such as Thales, Plato, Archimedes and Aristotle. Then Rome over Greece and Rome fell, it went dark for a thousand years or so. Then came the Renaissance on, and thinkers like Galilei and Johannes Kepler took up where the Greeks had in fact disappeared

Thanks to new historical research -. And wider understanding of non-Western countries and very rich spiritual culture development east of the Urals – this picture of the history of mathematics, philosophy and science is changing, slowly. But still, the teachers all too often skip over one of the most interesting stories in intellectual history – the way that mathematics and logic, including the best insights Greek logician, became the property of the Muslim countries in the long twilight period, from Rome’s fall to the Renaissance when most Europeans could no longer read Greek. Without the work of these great scholars of Muslims, math today might be very different animals. The Islamic Arab Empire, beginning in the eighth century, the world intellectual capital, and Arabic became the language learning to rival Latin. Some of the best mathematical reasoning in the world was done here.

We might as well start with Muhammad ibn Musa al-Hwarizmi (9th century), the Persian astronomer deeply learned in mathematics scholar of ancient India. From his name (in Latin form) we get the word algorithm, and from one of the titles of his algebra. It is right that he should be associated with the history of algebra – after all, his books preserved most of the ancient world knew about algebra (in addition to the brilliant his innovations), and his work helped to spread the use of Arabic numerals (the numbers we know and use day) to the West, so algebra lot more feasible. (To understand why this is important, imagine trying to do algebra problems while using Roman numerals: XIIa times XXVb equals c No, thanks ?.)

Then there is Al-Karam, as 1000AD found proof by mathematical induction – one of the basic logical maneuvers in math. Poet Omar Khayyam, writing in the twelfth century, laid the foundation for not Euclidean geometry. During this period, Muslim mathematicians invented spherical trigonometry, figured out how to use places with Arabic numerals (although decimal itself had long been invented by Hindu mathematicians), and developed cryptography, algebraic calculus, analytic geometry, among other things.

As important as any of these contributions, however, was the rescue of Aristotle’s text from obscurity by Arab scholars. For a long time in the Middle Ages, Aristotle was considered by Western intellectuals as one great thinkers of the world – but most of them had not read it. Few of his works that had survived the twin falls of Greece and Rome were available in sometimes poor or rather free handed and wrong, Latin translations, and many of his most important works were not available at all. Here and survived Greek script, but almost no one, at this point, could read Greek. (Widespread teaching Greek had to wait for the Renaissance -. Even famously learned scholars as the poet Petrarch struggled over it)

The same went seminal works as Euclid’s Elements, best known treatise on geometry. During this long period, when it was thought that these brilliantly logical works were gone forever, Islamic scholars kept their own copies of the translation. When European scholars began to travel to Spain and Sicily (then under Muslim rule) in the 12th century, these works and others were rediscovered in the West, leading to great intellectual ferment, including the theology of Thomas Aquinas – and understanding of logic that helped discipline of mathematics to survive and can thrive again in Western countries.


Being a Better Artist, scientist, mathematician, engineer, inventor, Leonardo Da Vinci


Leonardo Di Vinci, painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer, who was born and a symbol of the Italian Renaissance. He is known primarily for his paintings, among which include the famous Mona Lisa, the Last Supper, and the illustration of the Vitruvian man, which is seen as cultural elements in Europe, where coins, textbooks and bags have been built. Leonardo is more revered for his technical ingenuity, which he conceived ideas helicopter, a tank, concentrated solar power, a calculator. Leonardo had achieved so much in his life, and as a tribute to the great thinker I did some research and came up with clues that will bring us further towards how this great thinker the world.

genius Leonardo can be identified by understanding where he grew up, his experience, and also by how he digested the world around him. In this article I focus on the latter, how he digested the world around him, but the first two are obviously of paramount value to understand how he came to be. It all began in 1452, where Leonardo Da Vinci was born in Vinci Tuscan hill. Interestingly, Leonardo was not born with the name of the Lord, his name Da Vinci simply means “from Vinci,” marked by his birthplace. His father was fairly wealthy peasant and mother, and about his childhood, his father, who lived with had married four different wives. By the age of fourteen Leonardo apprenticed with the artist Andrea di clones, it was here that he was exposed to what could be labeled one of the best training in the art of Florence had to offer.

In order to understand the mind of Leonardo, we are going to take advantage theory spun psychologists and other mental health experts, the world is generally three procedures, visually, kinesthetically (with emotions) and hearing. The theory holds that people have a strength in either what is vision, what we can find, or what we can hear, and it is this strength that was a significant part of people work, personality and attitude of the events taking place around them.

“If you historians or poets or mathematicians had never seen it with your eyes and you would be ill able to describe the writings. And if you, O poet, represent the history of the show it with a pen, a painter with his brush, will then do what to be easier pleasurable and less tedious to understand “

Leonardo of his work has shown a clear preference for things that are visual. This is the first step to understand why he ended up showing art as well, way in which he saw the world. If one puts a clear specific selection of all things visual, had his time has been spent wondering visual images, drawing, painting, and illustrating. Saper Vedere (“knowing how to see”), this is what Leonardo put at the forefront of how he analyzed the structures, forms, nature and the world. For Leonardo, knowledge was simply taking an idea, a concept, and then conceptualizing it clearly pictorial way.

So how Leonardo drew so well, does not only look at the world through a visual point of view. This is an excerpt of Leonardo

“When you want to know anything well of the heart that you have studied this process: Once you have drawn the same so often that it seems that you know it by heart trying to do it without the model, but have traced from the model of a thin piece of smooth glass and lay this to draw you make without making Note well where you want to have it in mind in order. not to make mistakes again. Even the back of the model to copy the part where you were so wrong times and to fix it in your mind. “

This is a similar quote of Picasso popular in our time with Steve Jobs, to read “good artists borrow, great artists steal.” I both artists agree that to learn something one must first copy it, in fact, everything we do is based on something you have seen or experienced in the past, so every creation is based on copying before seen picture. Thus to be a great artist, or think alike to Leonardo, it is important that you allow yourself to be aware of this idea that all representations are simply the result of what we have experienced in the past. To learn something, be relentless in copy form in which it has been laid out.

If one is to learn how to speed up the tie, Leonardo suggests studying various types of facial features of heart. For example, as cited in his writings, “If you want to have a facility to keep in mind the expression of the face, first to learn by heart the various different types of heads, eyes, noses, mouths, chins, necks and also neck and shoulders … when you have to draw a face from memory, carry with you a small notebook in which you have referred to such actions, and so when you cast a glance at the face of the person you want to draw you can run privately and see who mouth or nose resembles it. “

Leonardo had thought a good time to review research on the levels to be awake and asleep. While lying in bed before you sleep, and just as you wake up are times where if you go over what you’re trying to learn, it will be easier to memorize. This is now explore the concept in psychology, there is a condition called trance, a trance unconscious learning is much easier.

Leonardo believed that in order for us to understand something we have to analyze it from different angles, cited when describing how he draws the human body, “it with my drawings every part must be known to you, and all of demonstrations from three different perspectives of each part. ” When drawing the human body, he also believed that it was necessary to take into account all factors, including the purpose of organ one draws, its beginnings, and also the status of transplant patients experience death. His drawings were not just pictures, they were too abstract map of the system that he drew.

When judging own photo Leonardo believed that it is wise to consider the human spirit, we are likely to face similar drag us that if we are ugly, we must draw a grim picture. He points out that we are less likely to see defects in our work as closely as others can, thus, he suggests looking at your work through the flat mirror, or go for a walk and then evaluate your work by relaxing. He also includes a view of the work from a distance will give a similar effect, it will allow you to see your work more so as it is, but what you want it to be. “Simplicity is the ultimate sophistication,” further promoted in today’s generation of Steve Jobs. Leonardo recognized the power of simplicity has beauty and class, it is possible to have something that is simple. Compare this with the popularity of the iPad many Microsoft products, iPad is actually a very simple device, simplicity seems market appeal.

“It is easier to resist at the beginning of the end,” first step can be difficult sometimes. When you start something new it must be admitted that in the beginning may greatest reluctance. And when working on a project it is advisable to follow your experience, not your mind, that “each device needs to be experienced.”

Last lesson I will present what I had learned by reading the works of Leonardo, was his desire to create something special, as cited “I wish to work miracles . ” The desire to create content from the ceiling was written about his work, in which he compares himself to Alchemist on more than one occasion.

In short, see Leonardo Da Vinci in the world can be better understood if one decides to take time and focus on the beauty of all that is visual, if you take your time to understand the purpose of things that you see . If you appreciate the idea to learn something you have to copy it to where it can be done without a guide, and the best time to learn something new is in the state of trance, just before bedtime or just when you wake up. When learning or detect something that’s extremely important to take multiple perspectives, and the desire to achieve the miracle is also necessary mix to level. Keep in mind the simplicity of the product once it has been completed, as it is the ultimate form of sophistication. Walk around with your laptop and keep in mind the importance of experience to the job, and the first resistance that may arise when pursuing new projects.


How to learn the mathematics


When I was a student and the teacher would say, “Study your

math test! “I think,” how can I ‘trial’ for the math test? ”

I now realize that the ‘investigation’ is the wrong one. You really need

to ‘practice’ for the math test.

Math test not only need to know the material, they

need to know how to do something with this material.

This change requires a change in your preparation. Unlike other

test, there is no way to prepare for a math test night

before. At that point, you either know the material or you

not, but there’s no faking.

First, it is important to understand the common causes

students loose points on the math test. They are:

1) Do not read the directions! (This is the big one!)

2) Do not write neatly. (ie lost a number of

tens place for the one who should be in the hundreds of


3) understand math vocabulary.

4) do not do their homework regularly to get appropriate


5) Do not know basic addition, subtraction,

multiplication and / or division facts their fluent.

Simply be aware that each of these factors can affect the

rating is half the battle, but as you probably

guess, there’s more you can do

** Action Plan **

Step 1 :. Know the basic math facts! There are hundreds of

math on the internet to help you practice the facts.

They are the foundation of mathematics and will continue to hold

you back if you can not answer each of them (0-10) in


Step 2 :. When you do your homework, remind yourself that you

are actually “learning” for the next math test. Circle all

problems that you do not know how to do and ask for help

class the next day. As you correct your homework in class,

circle all the problems that you did wrong and take notes on how to

make them right

Step 3 :. Three nights for your test, learn math

vocabulary and doing 10-15 practice problems with the “wrong”

answers your homework. Repeat the next night with

different problems homework

Step 4 :. The night before the test, they dear

vocabulary and make one problem from each night’s


Step 5 :. When you first get the test, write down any

formulas or definitions you are afraid you might forget

Step 6 :. Read the instructions! Twice

Step 7 :. Write neatly. Keep the numbers right


Step 8 :. When you are stuck, do as much as you can (you can

get partial credit), should drop and move on.

Come back to it if you have time

Step 9 :. After testing is gone, make sure that you understand

any mistakes and how to correct them. If you are not

understand the subject now, you will continue to have

problem in the following sections.

** Finally **

Math can be challenging because everything you learn builds

the knowledge that you should have learned before. If you lose

something, it will catch up with you. However, if you

– Learn math facts,

– Treat your homework as it is the practice test and study

from your mistakes,

– Take time to learn math vocabulary


– Read the instructions …

… it will not be long before mathematics test scores will soar!


Tips and techniques to learn math


I started my part time job as a math teacher from my graduation and I understand the frustration of the student when he has an issue with grasping math concepts and doing homework when no one is around to help. I agree that everyone has their own strengths and weaknesses when we come to learn skills in various subjects. This does not prevent someone who is determined by studying mathematics especially when this subject is his weakness.

My advice to this student is going back to basics and review the ideas that appear in recent times. This could help the mathematical concepts are not introduced all at once, but gradually, with one based on other. With the revision of the old mathematical concepts, one is expected to have a better basic old ideas before he starts to get a new one. A proactive student not skip the speech he is to have but to confront them. He will try as hard as he could, figuring out the question and seek new ways to approach the question before asking someone. He will not see it as a daunting task, but rather challenging one. The problem is: Most student will avoid any such question at first glance, leaving them to their teachers

When help or assistance is available, resist the urge to ask for assistance .. Working out of the question as far as man can before attempting to do so. After much intense thought process and you still could not (really could not!) To figure out the first step in making the question, here comes the need to revise the section again and this shows that you do not have any knowledge of. However, if you can at least figure out the first lines of the solution, you need a certain understanding of the section you are still not sure about some techniques / methods to spread. And do you know what you do not know or unsure. Therefore, at this point of time, you need a teacher to enlighten you with / his guidance. The main thing here is, you must know what you do not know. Knowing this is going to be very effective in learning math because you can evaluate the solution presented by the instructor. You can differentiate what you know and only accept new ideas and different solution teacher is. So, a student dedicates himself more with what he did when he applied these methods compared to those receiving the projects blindly without some basic understanding.

Mathematics is all about work. Practice makes perfect and there is no shortcut in learning math. Keep practicing and expose you to different types of math questions and get as much experience as possible. This is very effective in learning calculus and trigonometry in particular because of the type of questions and their complexity to prove – you might think this method is right, but you may be wrong because there are various ways to approach this type of problem and at a certain time, you find yourself going round the question in vain without establishing a final answer. This requires a certain level of expertise that can only be achieved through experience. Keep practicing and you can rest assured that you are on the right track

Here are some tips for those who sit for the tests :.

to take into account before testing

  • Never burn the midnight oil the night before the exam. Those who do may find that they lose focus easily on the exam and some even have their mind blanking out. Start preparing your exam as soon as possible.
  • Avoid engaging in activities that could potentially make you sick.
  • Observe healthy diet to make yourself in tip-top condition.
  • Get yourself enough rest

Here are some things to consider while you sit for the exam :.

  • Ensure calculator is in good working condition. If you need to replace the battery, just replace it.
  • Do not spend too much time on one question. Students often stubbornly spend most of their time on one question just to figure it out. Exam questions are structured in such a way so that difficulties are jumbled up. You may find easier questions right after the harder one. If harder one is taking too much time, just skip it. Remember to revisit it later after you’re done with other questions.
  • Never enter the solution immediately, even if you think it’s wrong. Marks could provide from work, even if you get the answer right. Only enter it when you’re done with another solution, hopefully a better one.

I was once told by my lecturer of this fact. I feel that it is worthwhile for me to mention its offer.

All you have to learn on the internet. It is a great online resource. We are here simply just to guide you.

Happy learning math!


Mental Math Tricks


This article is about teaching mental math tricks for addition to the primary school child. Almost every child starts by counting on her fingers. This is easy to do when the sum is less than ten. It starts to get confusing when the total is more than ten. After learning these tricks, the child should be a math wizard!

get the basics

The trick to perform mental math quickly by understanding the idea of ​​groups of ten. The first thing to do is to put ten pencils on the table. Move one pencil aside; now you have a group of nine pencils and a pencil group. Ask your child what is the answer to the nine plus one. Write it out mathematically

9 + 1 = 10

Carry on this way for eight plus two, seven plus three and so on until the child knows all the combinations that make up a group of ten . The next step is to commit them to memory. One way to do this is in writing similar to this:

7 + ___ = 10

____ + 8 = 10

10-6 = ____

Another interesting way through the game. Take out a normal pack of cards. Remove all the tens and picture cards, leaving only the Aces to the nines. Shuffle the cards and place the deck face down on the table. Turns to look over the top card. Let’s say it’s three, the other person must call the number that would give a total of ten – in this case, the number seven. Your points for correct answers. The first to reach twenty points wins. Play this several times a day and your child will soon remember all groups of ten.

A variation of this game is based on the memory game. Spread out the cards face down on the table. Exchanging lifting up two cards at once. If the total of ten, you collect cards and take another turn. The player with the most cards at the end of the game wins.

less than twenty

Now the child is ready to mentally add numbers to a total of more than ten but less than twenty. For example, add seven and eight. They already know that the seven and three make ten. Split number eight in three and five. Add three to seven make ten. You are left with five so that the total is fifteen. Here’s the trick written out mathematically

7 + 8 = 7 + 3 + 5 = 10 + 5 = 15

It may seem complicated at first, but your child will get an idea very quickly . In practice, use the cards again. This time take two cards at the time of the stack. The first to add a number of works right.

larger numbers

When the child has mastered the first two tricks, it’s time to learn how to add larger numbers. Here’s what to do to add twenty-five and seventeen

25 + 17

= 20 + 5 + 10 + 7

= 30 + 5 + 5 + 2

= 30 + 10 + 2

= 42

It takes a little getting used to, but by using the idea of ​​groups of ten, the child should learn this mental math tricks in no time!


Math Concepts and skills – Repetition of Mathematics


the last two decades has been declining emphasis on the importance of repetition of math concepts and skills in learning this stuff. The focus has shifted more towards thinking skills and “working outside the square,” which means to be able to apply problem solving skills to real life situations. This has been in contact with the increase in the volume of written material in secondary mathematics textbooks and a decrease in the amount of repetitive exercises where only basic math skills are practiced.

This is good in theory, but a steady decline in standards of mathematics in Australia and the United States suggest that this method of mathematics is not as good as it seems. The problem lies with the basic assumption that students already have the basic skills needed to solve problems. In mathematics, it is not possible to “work outside the square” unless one is a town with all the skills within the square. For example, a student will not be able to solve the problem regarding the amount of wire needed to fence fence Farmer Brown, unless they can accurately calculate the perimeter first.

Freedom to complete repetitive textbook exercises does not guarantee success in the application problem. What it does do is to give students the tools they need to address problems outside the textbook. Try to solve abstract problems without a solid knowledge base is like building a house on sand; it is a futile exercise.

This situation can be compared to physical training. Can understand the benefits of being able to build muscle through exercise, but if you do this you will fail when it comes to application task weight lifting. Math works the same way. Repetition builds on basic skills so that it becomes reflex. When skill is action that can be applied to other situations. Possessing the skill does not guarantee success in the application, but it is expected that success.

role repetition of basic skills in mathematics should be reviewed in conjunction with primary and lower secondary level. Without binding basis math skills to build on, students will continue to struggle with mathematics throughout their school careers.


Aryabhatta, The Indian Mathematician


Aryabhatta (476-550 AD) was born in Patliputra in Magadha, modern Patna in Bihar. Many believe that he was born in southern India especially Kerala and lived in Magadha at the time Gupta rulers; time is known as the golden age of India. There is no evidence that he was born outside Patliputra and traveled to Magadha, the center of education and learning program where he even set up a training center. His first name “Arya” is hardly the south Indian name while “Bhatt” (or Bhatta) is a typical north Indian name even found today especially among “Bania” (or trader) community.

What this origin it is not possible to argue that he lived in Patliputra where he wrote his famous thesis on “Aryabhatta-Siddhanta” but more famously as “Aryabhatiya”, the only work to have survived. It contains mathematical and astronomical theories that have been revealed to be quite right in modern mathematics. For example, he wrote that if 4 is added to 100 and then multiplied by 8 then add the 62,000 divided by 20,000 the answer will be equal to the circumference of a circle diameter twenty thousand. This calculates to 3.1416 near real Pi (3.14159). But his greatest contribution has to be zero. Other works of his are algebraic numbers, trigonometry, quadratic equations and the sine table.

He already knew that the earth rotates on its axis, the earth moves round the sun and the moon revolves round the earth. He talks about the positions of the planets in relation to its movement around the sun. He refers to the light of the planets and the moon and the reflection from the sun. He goes so far to explain the eclipse of the moon and sun, day and night, the contours of the earth length of identical 365 days.

he even calculate the Earth’s circumference as 24 835 miles, which is close to modern calculation 24900 miles.

This remarkable man was a genius and continues to baffle many mathematicians today. His work was then later adopted by the Greeks and the Arabs.


Mathematics: History and Importance


First, let’s take a look at the origins of mathematics:

How math? Where did it start first? For many who are well versed in the origin of mathematical thought, the development of mathematics will show up consistently and continually refining (and growing) set of expressions materials.

first abstract, that many animals share with us the figures. What do I mean by that? Well, the implementation of a certain number of things, such as 2 trees and 2 bananas are similar in quantity.This their ability to recognize the amount and multiple amounts are often considered to be the first abstract.

A step up from the first abstract ability to consider and perceive abstract not physical quantities time and elementary statistics. One does not see really see the 3 items deducted 4 parts is one thing. From there, it is only natural that subtraction, multiplication and division began.

In fact, mathematics precedes written script and written communications and records of primitive methods of counting among the knotted strings or tallies. Statistical systems go as far back as the Egyptians and ancient Chinese. They were used for everything from everyday life (painting, weaving, recording time) to more complex mathematics involved arithmetic, geometry and algebra for financial considerations, such as taxes, trade, construction and time. On the subject of time, this was often based on astronomy and

ancient Egyptians and Babylonians were skilled to hire math and it really speculate Pyramids were more than tombs of ancient kings long dead. Pyramids are also the first computers. It was said issues and alignment of the pyramids assisted by the ancients in the implementation of complex calculations like how we could use log table for the widespread use of calculators.

But where was essentially theoretical mathematical start? Mathematics as we know it with geometry, vectors, differentiation, integration, mechanics, sequences, trigonometry, probability, binomials, estimation, hypothesis testing, geometric and select distribution and hyperbolic functions (to name a few of the top of my head) started in Ancient Greece as far back between 600 BC 300 f.Kr ..

From it’s humble origins tied knots, mathematics has been extended in science and has been of immense benefit to both disciplines. In fact, it is said that one who does not know mathematics can not fully appreciate the beauty of nature. I would go so far as to say that there is no truth without mathematics. Anything without a number is just an opinion. What we believe qualitative measurements are highly quantitative ones that have exceeded a certain threshold after which we pass a certain signal. For example, when we say that the drug works, what we really mean is that 70% of people who received a certain dose of the drug over a period of experienced perhaps 90% reduction in the severity of them.

threshold our say “drug works” is 70%.

To give you an idea of ​​how the world of mathematics has expanded in recent years, I shall take this article with a reference from the Monetary American Mathematical Society

“The number of articles and books in the Mathematical Reviews database in 1940 (the first year that MR) is now more than 1.9 million and more than 75,000 items are added to the database annually overwhelming majority of works in this ocean contain new mathematical theorem and accompanying them. “- Mikhail B. Sevryuk