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Combinatorial Model Category
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to 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 gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, Graph (discrete mathematics), graphs, and Statement (logic), statements in Mathematical logic, logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumeration, enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics". The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plutarch
Plutarch (; , ''Ploútarchos'', ; – 120s) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo (Delphi), 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 (). Family 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 brothers, Timon and Lamprias, are frequently mentioned in his essays and dialogues, which speak of Timon in particular in the most affectionate terms. Studies and life Plutarch studied mathematics and philosophy in Athens under Ammonius of Athens, Ammonius from AD 66 to 67. He attended th ... [...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 species; 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 Among historians Ancient historians In the 19th century, scholars used to study ancient Greek and Roman historians to see how generally reliable they were. In recent decades, however, scholars have focused more on the constructions, genres, and meanings that ancient historians sought to convey to their audiences. History is always written with contemporary concerns and ancient hist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Greece
Ancient Greece () was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity (), that comprised a loose collection of culturally and linguistically related city-states and communities. Prior to the Roman period, most of these regions were officially unified only once under the Kingdom of Macedon from 338 to 323 BC. In Western history, the era of classical antiquity was immediately followed by the Early Middle Ages and the Byzantine period. Three centuries after the decline of Mycenaean Greece during the Bronze Age collapse, 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 Greece, from the Greco-Persian Wars to the death of Alexander the Great in 323 BC, and which included the Golden Age of Athens and the Peloponnesian War. The u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sushruta Samhita
The ''Sushruta Samhita'' (, ) is an ancient Sanskrit text on medicine and one of the most important such treatises on this subject to survive from the ancient world. The ''Compendium of Sushruta, Suśruta'' is one of the foundational texts of Ayurveda (Indian traditional medicine originating from the Atharvaveda), alongside the ''Charaka Samhita, Charaka-Saṃhitā'', ''the Bhela Samhita, Bhela-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. The oldest surviving manuscript of the ''Suśrutasaṃhitā'' is MS Kathmandu KL 699, a palm-leaf manuscript preserved at the Kaiser library, Kaiser Library, Nepal that is datable to 878 CE. History Date The most detailed and extensive considerati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sushruta
Suśruta (, ) is the listed author of the '' Suśruta Saṃhiāa'' (''Suśruta's Compendium''), considered to be one of the most important surviving ancient treatises on medicine. It is also considered a foundational text of Ayurveda. The treatise addresses all aspects of general medicine, including diet, surgery, nosology, anatomy, developmental biology, therapeutics, toxicology, pediatrics and other subjects. The inclusion of particularly impressive and historically important chapters on surgery has wrongly led some to believe that this is the work's primary focus. The treatise consists of 186 chapters. The ''Compendium of Suśruta'' locates its author in Varanasi, India. Authorship The printed editions of the work normally contain the phrase "as Lord Dhanvantari declared" (Sanskrit ''यथोवाच भगवान्धन्वन्तरिः'') at the start of each chapter, framing the work as Dhanvantari's discourse. However, the earliest manuscripts of the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physician
A physician, medical practitioner (British English), medical doctor, or simply doctor is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through the Medical education, study, Medical diagnosis, diagnosis, prognosis and therapy, 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 Specialty (medicine), specialities—or they may assume responsibility for the provision of continuing and comprehensive medical care to individuals, families, and communities—known as general practitioner, general practice. Medical practice properly requires both a detailed knowledge of the Discipline (academia), academic disciplines, such as anatomy and physiology, pathophysiology, underlying diseases, and their treatment, which is the science of medicine, and a decent Competence (human resources ... [...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. Also see the list of governors-general of India, list of prime ministers of India and list of years in India. Pre-historic India Pre-90th century BCE (BC) 90th–50th century BCE Bronze Age India 50th–40th century BCE 30th– 20th century BCE 19th century BCE 18th century BCE Iron Age India 17th century BCE 16th century BCE 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 Classical India 3rd century BCE 2nd century BCE 1st century BCE 1st century 2nd century 3rd century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summation
In mathematics, summation is the addition of a sequence of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined. Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article. The summation of an explicit sequence is denoted as a succession of additions. For example, summation of is denoted , and results in 9, that is, . Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands. Summation of a sequence of only one summand results in the summand itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0. Very often, the elements of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composition (combinatorics)
In mathematics, a composition of an integer ''n'' is a way of writing ''n'' as the summation, sum of a sequence of (strictly) positive integers. Two sequences that differ in the order of their terms define different compositions of their sum, while they are considered to define the same integer partition of that number. Every integer has finitely many distinct compositions. Negative numbers do not have any compositions, but 0 has one composition, the empty sequence. Each positive integer ''n'' has 2''n''−1 distinct compositions. A weak composition of an integer ''n'' is similar to a composition of ''n'', but allowing terms of the sequence to be zero: it is a way of writing ''n'' as the sum of a sequence of non-negative integers. As a consequence every positive integer admits infinitely many weak compositions (if their length is not bounded). Adding a number of terms 0 to the ''end'' of a weak composition is usually not considered to define a different weak composition; in other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Series
In mathematics, a geometric series is a series (mathematics), series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant. For example, 1/2 + 1/4 + 1/8 + 1/16 + ⋯, the series \tfrac12 + \tfrac14 + \tfrac18 + \cdots is a geometric series with common ratio , which converges to the sum of . Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same way that each term of an arithmetic series is the arithmetic mean of its neighbors. While Ancient Greek philosophy, Greek philosopher Zeno's paradoxes about time and motion (5th century BCE) have been interpreted as involving geometric series, such series were formally studied and applied a century or two later by Greek mathematics, Greek mathematicians, for example used by Archimedes to Quadrature of the Parabola, calculate the area inside a parabola (3rd century BCE). Today, geometric series are used in mathematical finance, calculati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
