The Islamic Empire established across the Middle East, North Africa, and in parts of India in the 8th century preserved and translated much of the Greek mathematics which was at that time largely forgotten in Europe. Indian mathematics, and the introduction of the Hindu-Arabic numerals, also had a major influence on Islamic mathematics. Like the Hindu mathematicians, Islamic mathematicians were especially interested in astronomy. The works of Brahmagupta were translated into Arabic circa 766. Al-Khwarizmi, the 9th century Persian astr ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Early written mathematics 2000 BC - 600 BC, History of mathematics - India 800 BC - 300 BC, History of mathematics - Greece and Hellenistic mathematics 400 BC - 200 BC, History of mathematics - Arab and Persian mathematics 650 - 1200, History of mathematics - Developing the concept of number through equations, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - Arab and Persian mathematics 650 - 1200

See also:

History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - Arabic and Persian mathematics 650 - 1500

In Europe at the dawn of the Renaissance, most of what is now called school mathematics -- addition, subtraction, multiplication, division, and geometry -- was known to educated people, though the notation was cumbersome: Roman numerals and words were used, but no symbols: no plus sign, no equal sign, no zero, and no use of x as an unknown. Almost all of the mathematics now taught in college had yet to be d ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - European Renaissance mathematics 1200 - 1600

The mathematics of humour, or the humour of mathematics? You're kidding. They're as different as chalk and cheese. Or are they?

We're familiar with those witty mathematical puzzles which delight children of all ages. We speak of a comedian's sense of 'timing', a term suggestive of arithmetical calibration. We talk of jokes that 'click', like tumblers falling into place in a numerical combination lock.

(See also: Mathematics, Faith and Belief, Spiritual Guidance, God and Religion, Peace on Earth, Peace of Mind, Love and Happiness, Life and Beyond, Body Mind and Soul)

Mathematics is often defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions. Practical mathematics, in nearly every society, is used for such purposes as accounting, measuring land, or predicting astronomical events. Mathematical discovery or research often involves discovering and cataloging patterns, without regard for application. Today, the natural sciences, engineering, economics, and medici ...

Including:

• Mathematics - History
• Mathematics - Inspiration pure and applied mathematics and aesthetics
• Mathematics - Notation language and rigor
• Mathematics - Is mathematics a science?
• Mathematics - Overview of fields of mathematics
• Mathematics - Major themes in mathematics
• Mathematics - Quantity
• Mathematics - Structure
• Mathematics - Space
• Mathematics - Change
• Mathematics - Foundations and methods
• Mathematics - Discrete mathematics
• Mathematics - Applied mathematics
• Mathematics - Important theorems
• Mathematics - Important conjectures
• Mathematics - History and the world of mathematicians
• Mathematics - Mathematics and other fields
• Mathematics - Common misconceptions

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In mathematics, a sheaf F on a topological space X is something that assigns a structure F(U) (such as a set, group, or ring) to each open set U of X. The structures F(U) are compatible with the operations of restricting the open set to smaller subsets and gluing smaller open sets to obtain a bigger one. A presheaf is similar to a sheaf, but it may not be possible to glue. Sheaves enable one to discuss in a refined way what is a local property, as appl ...

Including:

• Sheaf mathematics - Introduction
• Sheaf mathematics - The formal definition
• Sheaf mathematics - Definition of a presheaf
• Sheaf mathematics - The gluing axiom
• Sheaf mathematics - Examples
• Sheaf mathematics - Morphisms of sheaves
• Sheaf mathematics - Stalks of a sheaf at a point and germs of functions
• Sheaf mathematics - The étale space of a sheaf
• Sheaf mathematics - Generalizations
• Sheaf mathematics - History

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Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. These topics are often studied in the context of real numbers, complex numbers, and their functions. However, they can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or "distance" (a metric space). Mathematical analysis ...

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• Mathematical analysis - History
• Mathematical analysis - Subdivisions

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The Persian Empire is the name used to refer to a number of historic dynasties that have ruled the country of Persia (Iran). Persia's earliest known kingdom was the proto-Elamite Empire, followed by the Medes; but it is the Achaemenid Empire that emerged under Cyrus the Great that is usually the earliest to be called "Persian." Successive states in Iran before 1935 are collectively called the Persian Empire by Western historians. Persian Empire - The name Persia. Persia has long ...

Including:

• Persian Empire - The name Persia
• Persian Empire - The rise and fall of empires in Persia
• Persian Empire - The first Persian state: Achaemenid Persia 648 BC-330 BC
• Persian Empire - Hellenistic Persia 330 BC-150 BC
• Persian Empire - Parthian Persia 150 BC-AD 226
• Persian Empire - Sassanid Persia AD 226-650
• Persian Empire - Islam and Persia 650-1219
• Persian Empire - Persia under the Turkic rule 1037-1219
• Persian Empire - Persia under the Mongols and their successors 1219-1500
• Persian Empire - A new Persian empire: the Safavids 1500-1722
• Persian Empire - Persia and Europe 1722-1914
• Persian Empire - Persia in World War One 1914-1918
• Persian Empire - Persia after World War One 1919-1935
• Persian Empire - List of Kings and Emperors of Persia

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1200 - Events. University of Paris receives charter from Philip II of France the Kanem-Bornu Empire was established in northern Africa around the year 1200 Mongol victory over Northern China — 30,000,000 killed 1200 - Births. Al-Abhari, Persian philosopher and mathematician (died 1265) Ulrich von Liechtenstein, German nobleman and poet (died 1278) Adam Marsh, English Franciscan (approximate date; died 1259) John ...

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• 1200 - Events
• 1200 - Births
• 1200 - Deaths

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The Persian Gulf states are a group of six Arab countries that border the Persian Gulf. These countries are Kuwait, Saudi Arabia, Bahrain, Qatar, Oman and the United Arab Emirates. These six countries form the members of the Cooperation Council for the Arab States of the Gulf. It is useful to view the Persian Gulf states as a group because they share similar economies and a similar culture. Persian Gulf Arab States - Economy. The Persian Gulf states all have significant revenues from oil and gas and have co ...

Including:

• Persian Gulf Arab States - Economy
• Persian Gulf Arab States - Culture

Read more here: » Persian Gulf Arab States: Encyclopedia - Persian Gulf Arab States

Events Arab conquest of Persia completed, Islam established as state religion in Iran Hindu empire in Sumatra Croats and Serbs occupy Bosnia Khazars conquer Great Bulgarian Empire in southern Russia building of St. Martin's Church, Canterbury, England first surgical developments in India, with bladder, peristalsis and plastic operations < ...

Read more here: » 650: Encyclopedia - 650

The cognitive science of mathematics is the study of mathematical ideas using the techniques of cognitive science. Specifically, it is the search for foundations of mathematics in human cognition. This approach was long preceded by the study, in cognitive sciences proper, of human cognitive bias, especially in statistical thinking, most notably by Amos Tversky and Daniel Kahneman, including theories of measurement, risk and behavioral finance from these and other authors. These studies suggested that mathematical practice and p ...

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• Cognitive science of mathematics - Topics

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The aim of this page is to list all areas of modern mathematics, with a brief explanation about their scope and links to other parts of this encyclopedia, set out in a systematic way. The way research-level mathematics is internally organised is mostly determined by practitioners, and does change over time; this is in contrast with the apparently timeless syllabus divisions used in mathematics education, where calculus can seem to be much the same over a time scale of a century. Calculus itself does not appear as a major heading — m ...

Including:

• Areas of mathematics - Foundations / general
• Areas of mathematics - Algebra
• Areas of mathematics - Analysis
• Areas of mathematics - Geometry
• Areas of mathematics - Applied mathematics
• Areas of mathematics - Probability and statistics
• Areas of mathematics - Computational sciences
• Areas of mathematics - Physical sciences
• Areas of mathematics - Non-physical sciences

Read more here: » Areas of mathematics: Encyclopedia - Areas of mathematics

In mathematics, especially geometry, a configuration is an arrangement of points in a certain way. Other related archivesgeometry, mathematics

Read more here: » Configuration mathematics: Encyclopedia - Configuration mathematics

In China, in 212 BC, the Emperor Qin Shi Huang (Shi Huang-ti) commanded that all books be burned. While this order was not universally obeyed, it means that little is known with certainty about ancient Chinese mathematics. Another problem is that the Chinese wrote on bamboo, a perishable medium. Dating from the Shang period (1500 BC - 1027 BC), the earliest extant Chinese mathematics consists of numbers scratched on tortoise shell. These numbers use a decimal system, so that the number 123 is written (from top to bottom) as the symbol ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - Chinese mathematics 200 BC - AD 1200

Long before the earliest written records, there are drawings that indicate a knowledge of mathematics and of measurement of time based on the stars. For example, paleontologists have discovered ochre rocks in a cave in South Africa adorned with scratched geometric patterns dating back more than 70,000 years [1]. Also prehistoric artifacts discovered in Africa and France, dated between 35000 BC and 20000 BC, indicate early attempts to quantify time Evidence exists that early counting involved women who kept records of their monthly biological ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - Mathematics in prehistory

The 17th century saw an unprecedented explosion of mathematical and scientific ideas that not only fascinated philosophers but had industrial applications that began to make major changes in the way people lived. Copernicus, a Pole, had written that planets orbit the Sun. Galileo, an Italian, observed the moons of Jupiter in orbit about that planet, using a telescope based on a toy imported from Holland. Tycho Brahe, a Dane, had gathered an enormous quantity of mathematical data describing the positions of the planets in the sky. His ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - 17th century

The oldest mathematics text discovered so far is the Moscow papyrus, which is an Egyptian Middle Kingdom papyrus dated circa 2050 BC - 1800 BC. Like many ancient mathematical texts, it consists of what are today called "word problems" or "story problems", which were apparently intended as entertainment. One problem is considered to be of particular importance because it gives a method for finding the volume of a pyramid: "If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top. You are to square thi ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC

As we have seen, knowledge of the natural numbers, 1, 2, 3,..., as preserved in monolithic structures, is older then any surviving written text. The earliest civilizations, in Mesopotamia, Egypt, India, and China, knew arithmetic. One way to view the development of the various number systems of modern mathematics is to see new numbers invented to answer questions about arithmetic performed on older numbers. In prehistoric times, fractions answered the question: what number, when multiplied by 3, gives the answer 1. In India and China, ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - 18th century

When the complex numbers were introduced, there were many who argued that they were imaginary constructs to solve the cubic, and that they should not be considered 'real'. This is the origin of the terms imaginary and real for the numbers. However, mathematicians found the new world of complex numbers to be elegant and compelling. To represent a solution to the equation shown above (i.e., X * X + 1 = 0) mathematicians eventually settled on the letter i. However, in the early 19th century, one fu ...

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History of mathematics, History of mathematics - Mathematics in prehistory, History of mathematics - Egyptian and Babylonian mathematics 2000 BC - 600 BC, History of mathematics - Ancient Indian mathematics 800 BC - 200 BC, History of mathematics - Greek and Hellenistic mathematics 550 BC - 200 BC, History of mathematics - Chinese mathematics 200 BC - AD 1200, History of mathematics - Classical Indian mathematics 200 BC - AD 1600, History of mathematics - Arabic and Persian mathematics 650 - 1500, History of mathematics - European Renaissance mathematics 1200 - 1600, History of mathematics - 17th century, History of mathematics - 18th century, History of mathematics - Complex numbers, History of mathematics - Miscellaneous historical notes, History of mathematics - Notes

Read more here: » History of mathematics: Encyclopedia II - History of mathematics - Complex numbers