The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[19] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.Evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time – days, seasons, years.[20]

More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[21] The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time.

In Babylonian mathematics elementary arithmetic (addition, subtraction, multiplication and division) first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]

Between 600 and 300 BC the Ancient Greeks began a systematic study of mathematics in its own right with Greek mathematics.[22]

Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The...

...As students, we are taught the basics about mathematics. What the core properties of addition, subtraction, multiplication and division mean. How they work, and if we are lucky, we go into a little history of these methods. For those of us who have learned history, we learned that the basis for modern mathematics came from the Greeks and their writings. While this is correct, to truly understand the historical aspect of mathematics and its origins, one must study a time before the Greeks, when math was a whole new language, and one we still today have not completely mastered.
Perhaps the most interesting group to study is one of the first known civilizations, the Babylonians from Mesopotamia; the land between the Tigris and Euphrates Rivers in modern day Iraq. The Mesopotamian people are considered the founders of the first sophisticated, urban cities, and the founders of writing and keeping records. It was then that the idea of writing evolved as a means to record the most essentials of founding a city, mathematics. As a people who flourished from the land, it has been determined that the main uses for a mathematical language were utilitarian. It is believed that agriculture was invented in Mesopotamia, as the land between the rivers provided for much fertile ground (5). Because of this, research has found that the Babylonians made a number system to represent livestock, produce, and their basic way of life....

...Mathematics is defined as the science which deals with logic of shape, quantity and arrangement. During ancient times in Egypt, the Egyptians used maths and complex mathematic equations like geometry and algebra. That is how they managed to build the pyramids.
Our day today life would be quite strenuous without maths knowledge. There are many ways in which people use maths during the day today living. Below are some ways in which people use maths in daily lives.
* Daily life would be very difficult without maths’ knowledge at all. To begin with, you need to be able to organize and count your money; as well as subtract, divide and multiply. This is a skill everyone needs to have in order to survive. Every day we visit supermarkets to buy items, without maths knowledge, we would not be able to know if we have been given the right change.
* Some DIY jobs require basic maths knowledge for them to be done effectively. For example, a person needs to work out the amount of materials required in order to decorate a house. One has to be aware of the measurement, space and shape of the area he is working on to ensure that he or she has purchased the required amount of materials. This helps in ensuring that you do not run out of essential materials before the job is finished or you do not have too much left over.
* In the field of architecture or engineering, it is essential to have more advance maths knowledge. Working on geometry and algebra...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...I consider mathematics as a very important tool in life. My first real memories with mathematics began in my elementary years. I use to bring home assignments of several pages in order to master the basic arithmetic principles. I would go over my textbook answering several pages that included addition, subtraction, multiplication and division. What a truly memorable experiences they were and still was very rewarding especially when I got the correct answers. Other than that, I could compete with my classmates in how fast we can solve the problems.
From my elementary years, mathematics became more demanding when I became a high school student. It was quite a transition period as much as I can recall. Mathematics that was taught to us became more complex and was somehow much more difficult than what I was doing in primary school. High school math was presented as something straight forward. Our teachers during that time presented examples in class and gave the homework without further explanation. I knew I had to work hard and concentrate in order to get decent grades. The problems involved a lot of time and analyzing equations. It was both difficult but fun. When I got the chance to adopt on the new concepts, I easily adjusted and was happy to get decent grades.
For me, Geometry seemed to be the most difficult at that time. It involved a lot of consideration with the principles of Pythagoras. Ever since then, I came...

...Assignment 1 Miss. Dzigbodi Ama Agbodra.
A brief history of Mathematics. Ecs/13/01/0396
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC) and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics....

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HOW DOES THE CHILD PROGRESS FROM CONCRETE TO ABSTRACT IN THE MATHEMATICS MATERIALS,
Mathematics is the most eye opening of the entire Montessori curriculum. It is full of fascinating and beautiful hands on materials that bring the mathematical concept to life. The goal of Dr. Montessori was not just to teach the children the children to recognize numbers and calculate but enable them to think logically. The mathematics materials develop the child mathematical mind, the ability to reason abstract, investigate, calculate, and measure and also exactness. Her mathematical materials allow the children to begin their mathematical journey from concrete to abstract idea”
The mathematical mind has a foundation Maria Montessori said that a mathematical mind was “a sort of mind which is built up with exactness.” The mathematical mind tends to estimate, needs to quantify, to see identity, similarity, difference, and patterns, to make order and sequence and to control error. All children have human tendencies that are related directly to the mathematical mind. Montessorians recognize the necessity for order and exactness. We place materials quite intentionally on trays, we color code activities, materials are displayed in a logical sequence, and we break down movements during presentations into series of sequential steps. Children practice calculation skills when determining how much water to pour or precisely how many drops of polish to...

...Women in Mathematics
Every human is created with a gift of some sort. Whether it is an athletic ability, a wonderful singing voice, or an ability to relate to other individuals, every one has a special gifting. For many women in history, their ability was deciphering and understanding the intricacies of math. Although various cultures discouraged women mathematicians, these women were able to re-define the standards for women in this field of study.
Hypatia of Alexandria was born in Roman Egypt and was the daughter of a teacher of mathematics, Theon of Alexandria. Hypatia studied with her father as well as with many other mathematicians. When she was older, she taught at the Neoplatonist school of philosophy. She wrote on mathematics, philosophy, as well as anatomy. Her studies covered the motion of the planets, conic sections, and number theory, which is “one of the oldest branches of pure mathematics, and one of the largest. It concerns questions about numbers, typically meaning whole numbers as well as rational numbers. Although little information about Hypatia survives, it has been discovered that she was a very popular lecturer that drew students from various locations. She is known for her invention of the plane astrolabe, which is an elaborate inclinometer with the ability to locate and predict the locations of the sun, moon, planets, and stars and the graduated brass hydrometer which was used to determine...

...Decline of the Greek Mathematics
Historically, the Greek Mathematics had reached a high level in Greece and its colonies during the Hellenic era, beginning in the sixth century B.C.E. and ending in 476 C.E. when the barbarians invaded Rome. Although there were achievements made during the Roman Empire, the Greeks have had their best productive times before the Roman Empire – the end of third century B.C.E. Although there might be many reasons why the Greekmathematics decline, I think that the changes in the political and social climate – especially during the Roman Empire – was not sufficient enough for the Greeks to continue their culture – including mathematics. Moreover, the lack of stability and security disrupted Greek schools that were very well known with their mathematical education. Lastly, I also believe that there were fundamental limitations, such as lack of algebra, to the Greek way of mathematics.
First of all, it is very logical to claim that the peace times were very beneficial for the Greek mathematics as they had leisure time and energy to spend on developing mathematics. Greeks used the axiomatic method (axiom, theorem, proof) that can also be called as doing the mathematics just because it is mathematics (not aiming to use it anywhere or using it when applicable.) On the other hand, Romans – whom invaded the Greeks –...