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Combinatorial Pattern Matching
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Countable Set
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements. In more technical terms, assuming the axiom of countable choice, a set is ''countable'' if its cardinality (its number of elements) is not greater than that of the natural numbers. A countable set that is not finite is said countably infinite. The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers. A note on terminology Although the terms "countable" and "countably infinite" as defined here are quite co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schröder–Hipparchus Number
In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin :1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, ... . They are also called the super-Catalan numbers, the little Schröder numbers, or the Hipparchus numbers, after Eugène Charles Catalan and his Catalan numbers, Ernst Schröder and the closely related Schröder numbers, and the ancient Greek mathematician Hipparchus who appears from evidence in Plutarch to have known of these numbers. Combinatorial enumeration applications The Schröder–Hipparchus numbers may be used to count several closely related combinatorial objects:.. *The ''n''th number in the sequence counts the number of different ways of subdividing of a polygon with ''n'' +&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. He is known to have been a working astronomer between 162 and 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. He was the first whose quantitative and accurate models for the motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (fifth century BC), Timocharis, Aristyllus, Aristarchus of Samos, and Eratosthenes, among others. He developed trigonometry and constructed trigonometric tables, and he solved sever ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chrysippus
Chrysippus of Soli (; grc-gre, Χρύσιππος ὁ Σολεύς, ; ) was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of the Stoic philosopher Cleanthes. When Cleanthes died, around 230 BC, Chrysippus became the third head of the Stoic school. A prolific writer, Chrysippus expanded the fundamental doctrines of Cleanthes' mentor Zeno of Citium, the founder and first head of the school, which earned him the title of the Second Founder of Stoicism. Chrysippus excelled in logic, the theory of knowledge, ethics, and physics. He created an original system of propositional logic in order to better understand the workings of the universe and role of humanity within it. He adhered to a deterministic view of fate, but nevertheless sought a role for personal freedom in thought and action. Ethics, he thought, depended on understanding the nature of the universe, and he taught a therapy of extirpating the unrul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plutarch
Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''Parallel Lives'', a series of biographies of illustrious Greeks and Romans, and ''Moralia'', a collection of essays and speeches. Upon becoming a Roman citizen, he was possibly named Lucius Mestrius Plutarchus (). Life Early life Plutarch was born to a prominent family in the small town of Chaeronea, about east of Delphi, in the Greek region of Boeotia. His family was long established in the town; his father was named Autobulus and his grandfather was named Lamprias. His name is derived from Pluto (πλοῦτον), an epithet of Hades, and Archos (ἀρχός) meaning "Master", the whole name meaning something like "Whose master is Pluto". His brothers, Timon and Lamprias, are frequently mentioned in his essays and dialogues, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Historian
A historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the study of all history in time. Some historians are recognized by publications or training and experience.Herman, A. M. (1998). Occupational outlook handbook: 1998–99 edition. Indianapolis: JIST Works. Page 525. "Historian" became a professional occupation in the late nineteenth century as research universities were emerging in Germany and elsewhere. Objectivity During the ''Irving v Penguin Books and Lipstadt'' trial, people became aware that the court needed to identify what was an "objective historian" in the same vein as the reasonable person, and reminiscent of the standard traditionally used in English law of "the man on the Clapham omnibus". This was necessary so that there would be a legal benchmark to compare and contrast the scholar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of culturally and linguistically related city-states and other territories. Most of these regions were officially unified only once, for 13 years, under Alexander the Great's empire from 336 to 323 BC (though this excludes a number of Greek city-states free from Alexander's jurisdiction in the western Mediterranean, around the Black Sea, Cyprus, and Cyrenaica). In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Roughly three centuries after the Late Bronze Age collapse of Mycenaean Greece, Greek urban poleis began to form in the 8th century BC, ushering in the Archaic period and the colonization of the Mediterranean Basin. This was followed by the age of Classical G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sushruta Samhita
The ''Sushruta Samhita'' (सुश्रुतसंहिता, IAST: ''Suśrutasaṃhitā'', literally "Suśruta's Compendium") is an ancient Sanskrit text on medicine and surgery, and one of the most important such treatises on this subject to survive from the ancient world. The ''Compendium of Suśruta'' is one of the foundational texts of Ayurveda (Indian traditional medicine), alongside the '' Charaka-Saṃhitā'', ''the Bheḷa-Saṃhitā'', and the medical portions of the Bower Manuscript. It is one of the two foundational Hindu texts on the medical profession that have survived from ancient India. The ''Suśrutasaṃhitā'' is of great historical importance because it includes historically unique chapters describing surgical training, instruments and procedures which is still followed by modern science of surgery. One of the oldest ''Sushruta Samhita'' palm-leaf manuscripts is preserved at the Kaiser Library, Nepal. History Date Over a century ago, the scholar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sushruta
Sushruta, or ''Suśruta'' (Sanskrit: सुश्रुत, IAST: , ) was an ancient Indian physician. The ''Sushruta Samhita'' (''Sushruta's Compendium''), a treatise ascribed to him, is one of the most important surviving ancient treatises on medicine and is considered a foundational text of Ayurveda. The treatise addresses all aspects of general medicine, but the impressive chapters on surgery have led to the false impression that this is its main topic. The translator G. D. Singhal dubbed Suśruta "the father of surgery" on account of these detailed accounts of surgery. The ''Compendium of Suśruta'' locates its author in Varanasi, India. Date The early scholar Rudolf Hoernle proposed that some concepts from the ''Suśruta-saṃhitā'' could be found in the '' Śatapatha-Brāhmaṇa'', which he dates to the 600 BCE, and this dating is still often repeated. However, during the last century, scholarship on the history of Indian medical literature has advanced substantially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physician
A physician (American English), medical practitioner (Commonwealth English), medical doctor, or simply doctor, is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through the study, diagnosis, prognosis and treatment of disease, injury, and other physical and mental impairments. Physicians may focus their practice on certain disease categories, types of patients, and methods of treatment—known as specialities—or they may assume responsibility for the provision of continuing and comprehensive medical care to individuals, families, and communities—known as general practice. Medical practice properly requires both a detailed knowledge of the academic disciplines, such as anatomy and physiology, underlying diseases and their treatment—the ''science'' of medicine—and also a decent competence in its applied practice—the art or ''craft'' of medicine. Both the role of the physician and the meaning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timeline Of Indian History
This is a timeline of Indian history, comprising important legal and territorial changes and political events in India and its predecessor states. To read about the background to these events, see History of India. See also the list of governors-general of India, list of prime ministers of India and Years in India. __NOTOC__ Pre-90th century BCE 90th–50th century BCE 50th–40th century BCE 30th century BCE- 20th century BCE 19th century BCE 18th century BCE 17th century BCE 16th century BC 15th century BCE 14th century BCE 13th century BCE 12th century BCE 11th century BCE 10th century BCE 9th century BCE 8th century BCE 7th century BCE 6th century BCE 5th century BCE 4th century BCE 3rd century BCE 2nd century BCE 1st century BCE 1st century 2nd century 3rd century 4th century 5th century 6th century 7th century 8th century 9th century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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