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 Greek mathematics 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 – considered mathematics only as a way to solve practical problems as opposed to the Greek view. One of the great examples is that how Romans had to solve problems with geometric methods over trigonometric methods, and they were calling mathematicians as geometers because the term mathematician was considered derogatory.

In addition to degradation of mathematicians and their way of work, Romans looked down on to the Greek schools teaching math to students. They have never supported them – those schools were usually state funded – and actually harassed them. That forced the whole mathematical education system to deteriorate;...

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

...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]Greekmathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...
There are many Greek influences that still affect us today such as Democracy. The Greeks created the world’s first democracy. Athens started out as a monarchy and then advanced to and oligarchy until it finally reached a democracy. The government consisted of over 6,000 assembly members all of whom were adult male citizens. The assembly voted on issues throughout Athens, and passed laws. The required number of votes to pass a law was simply the majority but in order to banish or exile someone 6,000 votes were needed. Today we still use a democracy but now instead of using a direct democracy we use a representative democracy where the citizens democratically vote on who should make the decisions in the country, while in Greece a direct democracy was used and the citizens actually voted on the decision rather than choosing which people to make the decision.
Another Influence that we got from Greece is The Alphabet. The Greeks were the first civilization to use an alphabet. The Alphabet was developed after the Dark Age when the Greeks stopped using their previous written language. The Greek alphabet had 24 letters and believe it or not the word "alphabet" originates from the first 2 letters of the Greek alphabet; alpha, and beta. Today many letters of our modern alphabet originate from the Greek alphabet such as the letters A, B, E, and O.
Libraries are also another thing...

...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...

...concrete model.
Looking on the locality of the paper, I highly acknowledge the fact that the researchers described the current state of math education in the Philippines. They emphasized the fact that we are more focused on procedural knowledge rather than the more desired conceptual knowledge. That is our disadvantage because we usually train students to perform math without understanding or making connections on what they are doing. By mentioning this, the readers would really have an idea that the paper itself could be a solution to the problem mentioned. Moreover, it makes the thesis more realistic.
To sum up everything that was tackled, I could say that the thesis served to have an important purpose in the current state of Mathematics Education in the Philippines. It is very informative and feasible. Since it is a small study because it only involved 6 average students, we could propose more studies rooting from this which would have a bigger scope such as implementing the same study but now comparing it to the results gathered from high and low performing students....

...INTRODUCTION
As the greatest Mathematician “GAUSS” has said –“MATHS IS THE QUEEN OF SCIENCE”, maths is truly the guiding force of human soul. Maths is the purest form of study of nature which comprise of a deep and rational comparison of quantities, structures, spaces, nature of change of different inter-relations and much more. Mathematicians seek out various patterns and formulate new conjectures. Mathematicians counter examines the facts by repeated and repeated logical transformations these experiments may take years and years of thorough research and dedication.
USE OF MATHS IN EVERY DAY LIFE
“I love those who love geometry”-said Plato, the famous Greek philosopher and thinker.Algebra, Arithmetic, Geometry are three major components of maths. Algebra is study of symbols, Arithmetic deals with numbers and geometry plays with figures. The structure of any railway bridge is supported with triangular shaped support system(geometry),saving is vital for ones peaceful oldage (arithmetic),the combinations of different dresses one should wear so that no continues days has same pattern(algebra),all these are nothing but some simple yet important usage of maths in ones daily life.
Where to go for shopping, choosing a shampoo or planning a holiday, all these things of our daily routine has something in common-its maths. Numerical and logical thinking plays a vital part in each of these every day activities. A good understanding of maths is essential for making...

...mother of Europe's languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity... of self-government and democracy. In many ways, Mother India is the mother of us all."
- Will Durant, American Historian 1885-1981
Mathematics is an important field of study. Mathematics is essential as it helps in developing lots of realistic skills, in fact study of mathematics itself include the concepts related to the routine lives of human. It not only develops mathematical skills and concepts, it also helps in developing the attitudes, interest, and appreciation and provides opportunities to develop one’s own thinking. So, mathematics is undoubtedly a discipline which is imperative to know and study. Figure 1 clearly specifies all the skills that are developed by the mathematics. Mathematics starts from simple things and linear thinking that lead towards the more complex things and higher order thinking skills. Mathematics has taken centuries to develop in its present form and that’s why it will be really fruitful to know about its development.
Fig. 1, Importance of MathematicsC:\Users\naveen\Desktop\Untitled.png
Mathematics has played a very significant role in the progress and expansion of Indian culture for centuries. Mathematical ideas that originated in the Indian subcontinent have had a...

...Question 1: (three pages maximum)
Homer in 750 B.C. wrote The Iliad and The Odyssey. Hesiod another Greek poet wrote Works and Days in 700 B.C. Compare and Contrast both authors as it relates to Greek Society.
Homer, known as the great epic poet of ancient Greece, though when he lived is unknown, Herodotus estimates that he lived 400 years before his own time, which would place him at around 850 B.C. Others ancient sources puts him nearer to the supposed time of the Trojan War, in the early 12th century BC. However, most modern researchers place Homer in the 7th or 8th centuries BC. Of all is works, his greatest contribution can be said to that of Literature i.e. considering that about fifty percent speeches, provided models in persuasive speaking and writing (one of the many Greek influence on the western world). Two particular works that stood out being The Iliad and The Odyssey. For Homer, these works were written in his point of view of the Gods illustrating how men were pawns to their will. Equally, however, Homer through these epic stories, showed the resilience of men to overcome struggles in their achievement of power, glory and heroism i.e. the Homeric approach “doer of great deeds”.
Homer’s The Iliad gives account for the ten year battle between Greece (the Greek King Agamemnon) and Troy (Priam, the Trojan King). This epic story tells of a war started as a result to Priam’s son Paris who took with him on...

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