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Article: Mathematics. Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and 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), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature or—in modern mathematics—purely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a proof consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration. Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation. Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics) but often later find practical applications. Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements.
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Wikipedia - Mathematics - Summary
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Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new fields. Since then, the interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics.
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Wikipedia - Mathematics - Summary
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Section: Areas of mathematics. Before the Renaissance, mathematics was divided into two main areas: arithmetic, regarding the manipulation of numbers, and geometry, regarding the study of shapes. Some types of pseudoscience, such as numerology and astrology, were not then clearly distinguished from mathematics. During the Renaissance, two more areas appeared. Mathematical notation led to algebra which, roughly speaking, consists of the study and the manipulation of formulas. Calculus, consisting of the two subfields differential calculus and integral calculus, is the study of continuous functions, which model the typically nonlinear relationships between varying quantities, as represented by variables. This division into four main areas—arithmetic, geometry, algebra, and calculus—endured until the end of the 19th century. Areas such as celestial mechanics and solid mechanics were then studied by mathematicians, but now are considered as belonging to physics. The subject of combinatorics has been studied for much of recorded history, yet did not become a separate branch of mathematics until the seventeenth century. At the end of the 19th century, the foundational crisis in mathematics and the resulting systematization of the axiomatic method led to an explosion of new areas of mathematics. The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. Some of these areas correspond to the older division, as is true regarding number theory (the modern name for higher arithmetic) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly considered part of geometry. Algebra and calculus do not appear as first-level areas but are respectively split into several first-level areas.
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Wikipedia - Mathematics - Areas of mathematics
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Section: Areas of mathematics > Number theory. Number theory began with the manipulation of numbers, that is, natural numbers ( N ) , {\displaystyle (\mathbb {N} ),} and later expanded to integers ( Z ) {\displaystyle (\mathbb {Z} )} and rational numbers ( Q ) . {\displaystyle (\mathbb {Q} ).} Number theory was once called arithmetic, but nowadays this term is mostly used for numerical calculations. Number theory dates back to ancient Babylon and probably China. Two prominent early number theorists were Euclid of ancient Greece and Diophantus of Alexandria. The modern study of number theory in its abstract form is largely attributed to Pierre de Fermat and Leonhard Euler. The field came to full fruition with the contributions of Adrien-Marie Legendre and Carl Friedrich Gauss. Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem. This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles, who used tools including scheme theory from algebraic geometry, category theory, and homological algebra. Another example is Goldbach's conjecture, which asserts that every even integer greater than 2 is the sum of two prime numbers. Stated in 1742 by Christian Goldbach, it remains unproven despite considerable effort. Number theory includes several subareas, including analytic number theory, algebraic number theory, geometry of numbers (method oriented), diophantine equations, and transcendence theory (problem oriented).
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Wikipedia - Mathematics - Areas of mathematics > Number theory
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Section: Areas of mathematics > Geometry. Geometry is one of the oldest branches of mathematics. It started with empirical recipes concerning shapes, such as lines, angles and circles, which were developed mainly for the needs of surveying and architecture, but has since blossomed out into many other subfields. A fundamental innovation was the ancient Greeks' introduction of the concept of proofs, which require that every assertion must be proved. For example, it is not sufficient to verify by measurement that, say, two lengths are equal; their equality must be proven via reasoning from previously accepted results (theorems) and a few basic statements. The basic statements are not subject to proof because they are self-evident (postulates), or are part of the definition of the subject of study (axioms). This principle, foundational for all mathematics, was first elaborated for geometry, and was systematized by Euclid around 300 BC in his book Elements. The resulting Euclidean geometry is the study of shapes and their arrangements constructed from lines, planes and circles in the Euclidean plane (plane geometry) and the three-dimensional Euclidean space. Euclidean geometry was developed without change of methods or scope until the 17th century, when René Descartes introduced what is now called Cartesian coordinates. This constituted a major change of paradigm: Instead of defining real numbers as lengths of line segments (see number line), it allowed the representation of points using their coordinates, which are numbers. Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically.
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Wikipedia - Mathematics - Areas of mathematics > Geometry
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Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically. Analytic geometry allows the study of curves unrelated to circles and lines. Such curves can be defined as the graph of functions, the study of which led to differential geometry. They can also be defined as implicit equations, often polynomial equations (which spawned algebraic geometry). Analytic geometry also makes it possible to consider Euclidean spaces of higher than three dimensions. In the 19th century, mathematicians discovered non-Euclidean geometries, which do not follow the parallel postulate. By questioning that postulate's truth, this discovery has been viewed as joining Russell's paradox in revealing the foundational crisis of mathematics. This aspect of the crisis was solved by systematizing the axiomatic method, and adopting that the truth of the chosen axioms is not a mathematical problem. In turn, the axiomatic method allows for the study of various geometries obtained either by changing the axioms or by considering properties that do not change under specific transformations of the space. Today's subareas of geometry include: Projective geometry, introduced in the 16th century by Girard Desargues, extends Euclidean geometry by adding points at infinity at which parallel lines intersect. This simplifies many aspects of classical geometry by unifying the treatments for intersecting and parallel lines. Affine geometry, the study of properties relative to parallelism and independent from the concept of length. Differential geometry, the study of curves, surfaces, and their generalizations, which are defined using differentiable functions. Manifold theory, the study of shapes that are not necessarily embedded in a larger space.
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Wikipedia - Mathematics - Areas of mathematics > Geometry
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Section: Areas of mathematics > Algebra. Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra. Diophantus solved some equations involving unknown natural numbers by deducing new relations until he obtained the solution. Al-Khwarizmi introduced systematic methods for transforming equations, such as moving a term from one side of an equation into the other side. The term algebra is derived from the Arabic word al-jabr meaning 'the reunion of broken parts' that he used for naming one of these methods in the title of his main treatise. Algebra became an area in its own right only with François Viète (1540–1603), who introduced the use of variables for representing unknown or unspecified numbers. Variables allow mathematicians to describe the operations that have to be done on the numbers represented using mathematical formulas. Until the 19th century, algebra consisted mainly of the study of linear equations (presently linear algebra), and polynomial equations in a single unknown, which were called algebraic equations (a term still in use, although it may be ambiguous). During the 19th century, mathematicians began to use variables to represent things other than numbers (such as matrices, modular integers, and geometric transformations), on which generalizations of arithmetic operations are often valid. The concept of algebraic structure addresses this, consisting of a set whose elements are unspecified, of operations acting on the elements of the set, and rules that these operations must follow. The scope of algebra thus grew to include the study of algebraic structures.
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Wikipedia - Mathematics - Areas of mathematics > Algebra
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The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether, and popularized by Van der Waerden's book Moderne Algebra. Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: group theory field theory vector spaces, whose study is essentially the same as linear algebra ring theory commutative algebra, which is the study of commutative rings, includes the study of polynomials, and is a foundational part of algebraic geometry homological algebra Lie algebra and Lie group theory Boolean algebra, which is widely used for the study of the logical structure of computers The study of types of algebraic structures as mathematical objects is the purpose of universal algebra and category theory. The latter applies to every mathematical structure (not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects such as topological spaces; this particular area of application is called algebraic topology.
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Wikipedia - Mathematics - Areas of mathematics > Algebra
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Section: Areas of mathematics > Calculus and analysis. Calculus, formerly called infinitesimal calculus, was introduced independently and simultaneously by 17th-century mathematicians Newton and Leibniz. It is fundamentally the study of the relationship of variables that depend on each other. Calculus was expanded in the 18th century by Euler with the introduction of the concept of a function and many other results. Presently, "calculus" refers mainly to the elementary part of this theory, and "analysis" is commonly used for advanced parts. Analysis is further subdivided into real analysis, where variables represent real numbers, and complex analysis, where variables represent complex numbers. Analysis includes many subareas shared by other areas of mathematics which include: Multivariable calculus Functional analysis, where variables represent varying functions Integration, measure theory and potential theory, all strongly related with probability theory on a continuum Ordinary differential equations Partial differential equations Numerical analysis, mainly devoted to the computation on computers of solutions of ordinary and partial differential equations that arise in many applications
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Wikipedia - Mathematics - Areas of mathematics > Calculus and analysis
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Section: Areas of mathematics > Discrete mathematics. Discrete mathematics, broadly speaking, is the study of individual, countable mathematical objects. An example is the set of all integers. Because the objects of study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms—especially their implementation and computational complexity—play a major role in discrete mathematics. The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems. Discrete mathematics includes: Combinatorics, the art of enumerating mathematical objects that satisfy some given constraints. Originally, these objects were elements or subsets of a given set; this has been extended to various objects, which establishes a strong link between combinatorics and other parts of discrete mathematics. For example, discrete geometry includes counting configurations of geometric shapes. Graph theory and hypergraphs Coding theory, including error correcting codes and a part of cryptography Matroid theory Discrete geometry Discrete probability distributions Game theory (although continuous games are also studied, most common games, such as chess and poker are discrete) Discrete optimization, including combinatorial optimization, integer programming, constraint programming
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Wikipedia - Mathematics - Areas of mathematics > Discrete mathematics
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Section: Areas of mathematics > Mathematical logic and set theory. The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. Before this period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically studied by mathematicians. Before Cantor's study of infinite sets, mathematicians were reluctant to consider actually infinite collections, and considered infinity to be the result of endless enumeration. Cantor's work offended many mathematicians not only by considering actually infinite sets but by showing that this implies different sizes of infinity, per Cantor's diagonal argument. This led to the controversy over Cantor's set theory. In the same period, various areas of mathematics concluded the former intuitive definitions of the basic mathematical objects were insufficient for ensuring mathematical rigour. This became the foundational crisis of mathematics. It was eventually solved in mainstream mathematics by systematizing the axiomatic method inside a formalized set theory. Roughly speaking, each mathematical object is defined by the set of all similar objects and the properties that these objects must have. For example, in Peano arithmetic, the natural numbers are defined by "zero is a number", "each number has a unique successor", "each number but zero has a unique predecessor", and some rules of reasoning. This mathematical abstraction from reality is embodied in the modern philosophy of formalism, as founded by David Hilbert around 1910. The "nature" of the objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinion—sometimes called "intuition"—to guide their study and proofs.
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Wikipedia - Mathematics - Areas of mathematics > Mathematical logic and set theory
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The "nature" of the objects defined this way is a philosophical problem that mathematicians leave to philosophers, even if many mathematicians have opinions on this nature, and use their opinion—sometimes called "intuition"—to guide their study and proofs. The approach allows considering "logics" (that is, sets of allowed deducing rules), theorems, proofs, etc. as mathematical objects, and to prove theorems about them. For example, Gödel's incompleteness theorems assert, roughly speaking that, in every consistent formal system that contains the natural numbers, there are theorems that are true (that is provable in a stronger system), but not provable inside the system. This approach to the foundations of mathematics was challenged during the first half of the 20th century by mathematicians led by Brouwer, who promoted intuitionistic logic, which explicitly lacks the law of excluded middle. These problems and debates led to a wide expansion of mathematical logic, with subareas such as model theory (modeling some logical theories inside other theories), proof theory, type theory, computability theory and computational complexity theory. Although these aspects of mathematical logic were introduced before the rise of computers, their use in compiler design, formal verification, program analysis, proof assistants and other aspects of computer science, contributed in turn to the expansion of these logical theories.
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Wikipedia - Mathematics - Areas of mathematics > Mathematical logic and set theory
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Section: Areas of mathematics > Statistics and other decision sciences. The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory. Statisticians generate data with random sampling or randomized experiments. Statistical theory studies decision problems such as minimizing the risk (expected loss) of a statistical action, such as using a procedure in, for example, parameter estimation, hypothesis testing, and selecting the best. In these traditional areas of mathematical statistics, a statistical-decision problem is formulated by minimizing an objective function, like expected loss or cost, under specific constraints. For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence. Because of its use of optimization, the mathematical theory of statistics overlaps with other decision sciences, such as operations research, control theory, and mathematical economics.
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Wikipedia - Mathematics - Areas of mathematics > Statistics and other decision sciences
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Section: History > Etymology. The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning 'something learned, knowledge, mathematics', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning 'mathematical science'. It entered the English language during the Late Middle English period through French and Latin. Similarly, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant "learners" rather than "mathematicians" in the modern sense. The Pythagoreans were likely the first to constrain the use of the word to just the study of arithmetic and geometry. By the time of Aristotle (384–322 BC) this meaning was fully established. In Latin and English, until around 1700, the term mathematics more commonly meant "astrology" (or sometimes "astronomy") rather than "mathematics"; the meaning gradually changed to its present one from about 1500 to 1800. This change has resulted in several mistranslations: For example, Saint Augustine's warning that Christians should beware of mathematici, meaning "astrologers", is sometimes mistranslated as a condemnation of mathematicians.
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Wikipedia - Mathematics - History > Etymology
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This change has resulted in several mistranslations: For example, Saint Augustine's warning that Christians should beware of mathematici, meaning "astrologers", is sometimes mistranslated as a condemnation of mathematicians. The apparent plural form in English goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of physics and metaphysics, inherited from Greek. In English, the noun mathematics takes a singular verb. It is often shortened to maths or, in North America, math.
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Wikipedia - Mathematics - History > Etymology
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Section: History > Ancient. In addition to recognizing how to count physical objects, prehistoric peoples may have also known how to count abstract quantities, like time—days, seasons, or years. Evidence for more complex mathematics does 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. The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to 1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical concept after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication, and division) first appear in the archaeological record. The Babylonians also possessed a place-value system and used a sexagesimal numeral system which is still in use today for measuring angles and time. In the 6th century BC, Greek mathematics began to emerge as a distinct discipline and some Ancient Greeks such as the Pythagoreans appeared to have considered it a subject in its own right. Around 300 BC, Euclid organized mathematical knowledge by way of postulates and first principles, which evolved into the axiomatic method that is used in mathematics today, consisting of definition, axiom, theorem, and proof. His book, Elements, is widely considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is often held to be Archimedes (c. 287 – c. 212 BC) of Syracuse.
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Wikipedia - Mathematics - History > Ancient
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287 – c. 212 BC) of Syracuse. He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic sections (Apollonius of Perga, 3rd century BC), trigonometry (Hipparchus of Nicaea, 2nd century BC), and the beginnings of algebra (Diophantus, 3rd century AD). The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition and approximation of sine and cosine, and an early form of infinite series.
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Wikipedia - Mathematics - History > Ancient
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Section: History > Medieval and later. During the Golden Age of Islam, especially during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics. The most notable achievement of Islamic mathematics was the development of algebra. Other achievements of the Islamic period include advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarizmi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. The Greek and Arabic mathematical texts were in turn translated to Latin during the Middle Ages and made available in Europe. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe, with innovations that revolutionized mathematics, such as the introduction of variables and symbolic notation by François Viète (1540–1603), the introduction of logarithms by John Napier in 1614, which greatly simplified numerical calculations, especially for astronomy and marine navigation, the introduction of coordinates by René Descartes (1596–1650) for reducing geometry to algebra, and the development of calculus by Isaac Newton (1643–1727) and Gottfried Leibniz (1646–1716). Leonhard Euler (1707–1783), the most notable mathematician of the 18th century, unified these innovations into a single corpus with a standardized terminology, and completed them with the discovery and the proof of numerous theorems. Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory, number theory, and statistics.
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Wikipedia - Mathematics - History > Medieval and later
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Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory, number theory, and statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show in part that any consistent axiomatic system—if powerful enough to describe arithmetic—will contain true propositions that cannot be proved. 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 to this very day. 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 (MR) 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 overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."
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Wikipedia - Mathematics - History > Medieval and later
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Section: Symbolic notation and terminology. Mathematical notation is widely used in science and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. This notation consists of symbols used for representing operations, unspecified numbers, relations and any other mathematical objects, and then assembling them into expressions and formulas. More precisely, numbers and other mathematical objects are represented by symbols called variables, which are generally Latin or Greek letters, and often include subscripts. Operation and relations are generally represented by specific symbols or glyphs, such as + (plus), × (multiplication), ∫ {\textstyle \int } (integral), = (equal), and < (less than). All these symbols are generally grouped according to specific rules to form expressions and formulas. Normally, expressions and formulas do not appear alone, but are included in sentences of the current language, where expressions play the role of noun phrases and formulas play the role of clauses. Mathematics has developed a rich terminology covering a broad range of fields that study the properties of various abstract, idealized objects and how they interact. It is based on rigorous definitions that provide a standard foundation for communication. An axiom or postulate is a mathematical statement that is taken to be true without need of proof. If a mathematical statement has yet to be proven (or disproven), it is termed a conjecture. Through a series of rigorous arguments employing deductive reasoning, a statement that is proven to be true becomes a theorem. A specialized theorem that is mainly used to prove another theorem is called a lemma. A proven instance that forms part of a more general finding is termed a corollary.
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Wikipedia - Mathematics - Symbolic notation and terminology
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A proven instance that forms part of a more general finding is termed a corollary. Numerous technical terms used in mathematics are neologisms, such as polynomial and homeomorphism. Other technical terms are words of the common language that are used in an accurate meaning that may differ slightly from their common meaning. For example, in mathematics, "or" means "one, the other or both", while, in common language, it is either ambiguous or means "one or the other but not both" (in mathematics, the latter is called "exclusive or"). Finally, many mathematical terms are common words that are used with a completely different meaning. This may lead to sentences that are correct and true mathematical assertions, but appear to be nonsense to people who do not have the required background. For example, "every free module is flat" and "a field is always a ring".
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Section: Relationship with sciences. Mathematics is used in most sciences for modeling phenomena, which then allows predictions to be made from experimental laws. The independence of mathematical truth from any experimentation implies that the accuracy of such predictions depends only on the adequacy of the model. Inaccurate predictions, rather than being caused by invalid mathematical concepts, imply the need to change the mathematical model used. For example, the perihelion precession of Mercury could only be explained after the emergence of Einstein's general relativity, which replaced Newton's law of gravitation as a better mathematical model. There is still a philosophical debate whether mathematics is a science. However, in practice, mathematicians are typically grouped with scientists, and mathematics shares much in common with the physical sciences. Like them, it is falsifiable, which means in mathematics that, if a result or a theory is wrong, this can be proved by providing a counterexample. Similarly as in science, theories and results (theorems) are often obtained from experimentation. In mathematics, the experimentation may consist of computation on selected examples or of the study of figures or other representations of mathematical objects (often mind representations without physical support). For example, when asked how he came about his theorems, Gauss once replied "durch planmässiges Tattonieren" (through systematic experimentation). However, some authors emphasize that mathematics differs from the modern notion of science by not relying on empirical evidence.
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Wikipedia - Mathematics - Relationship with sciences
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Section: Relationship with sciences > Pure and applied mathematics. Until the 19th century, the development of mathematics in the West was mainly motivated by the needs of technology and science, and there was no clear distinction between pure and applied mathematics. For example, the natural numbers and arithmetic were introduced for the need of counting, and geometry was motivated by surveying, architecture and astronomy. Later, Isaac Newton introduced infinitesimal calculus for explaining the movement of the planets with his law of gravitation. Moreover, most mathematicians were also scientists, and many scientists were also mathematicians. However, a notable exception occurred with the tradition of pure mathematics in Ancient Greece. The problem of integer factorization, for example, which goes back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem, now widely used for the security of computer networks. In the 19th century, mathematicians such as Karl Weierstrass and Richard Dedekind increasingly focused their research on internal problems, that is, pure mathematics. This led to split mathematics into pure mathematics and applied mathematics, the latter being often considered as having a lower value among mathematical purists. However, the lines between the two are frequently blurred. The aftermath of World War II led to a surge in the development of applied mathematics in the US and elsewhere. Many of the theories developed for applications were found interesting from the point of view of pure mathematics, and many results of pure mathematics were shown to have applications outside mathematics; in turn, the study of these applications may give new insights on the "pure theory".
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Wikipedia - Mathematics - Relationship with sciences > Pure and applied mathematics
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Many of the theories developed for applications were found interesting from the point of view of pure mathematics, and many results of pure mathematics were shown to have applications outside mathematics; in turn, the study of these applications may give new insights on the "pure theory". An example of the first case is the theory of distributions, introduced by Laurent Schwartz for validating computations done in quantum mechanics, which became immediately an important tool of (pure) mathematical analysis. An example of the second case is the decidability of the first-order theory of the real numbers, a problem of pure mathematics that was proved true by Alfred Tarski, with an algorithm that is impossible to implement because of a computational complexity that is much too high. For getting an algorithm that can be implemented and can solve systems of polynomial equations and inequalities, George Collins introduced the cylindrical algebraic decomposition that became a fundamental tool in real algebraic geometry. In the present day, the distinction between pure and applied mathematics is more a question of personal research aim of mathematicians than a division of mathematics into broad areas. The Mathematics Subject Classification has a section for "general applied mathematics" but does not mention "pure mathematics". However, these terms are still used in names of some university departments, such as at the Faculty of Mathematics at the University of Cambridge.
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Wikipedia - Mathematics - Relationship with sciences > Pure and applied mathematics
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Section: Relationship with sciences > Unreasonable effectiveness. The unreasonable effectiveness of mathematics is a phenomenon that was named and first made explicit by physicist Eugene Wigner. It is the fact that many mathematical theories (even the "purest") have applications outside their initial object. These applications may be completely outside their initial area of mathematics, and may concern physical phenomena that were completely unknown when the mathematical theory was introduced. Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. A second historical example is the theory of ellipses. They were studied by the ancient Greek mathematicians as conic sections (that is, intersections of cones with planes). It was almost 2,000 years later that Johannes Kepler discovered that the trajectories of the planets are ellipses. In the 19th century, the internal development of geometry (pure mathematics) led to definition and study of non-Euclidean geometries, spaces of dimension higher than three and manifolds. At this time, these concepts seemed totally disconnected from the physical reality, but at the beginning of the 20th century, Albert Einstein developed the theory of relativity that uses fundamentally these concepts. In particular, spacetime of special relativity is a non-Euclidean space of dimension four, and spacetime of general relativity is a (curved) manifold of dimension four. A striking aspect of the interaction between mathematics and physics is when mathematics drives research in physics. This is illustrated by the discoveries of the positron and the baryon Ω − .
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Section: Relationship with sciences > Specific sciences > Social sciences. Areas of mathematics used in the social sciences include probability/statistics and differential equations. These are used in linguistics, economics, sociology, and psychology. Often the fundamental postulate of mathematical economics is that of the rational individual actor – Homo economicus (lit. 'economic man'). In this model, the individual seeks to maximize their self-interest, and always makes optimal choices using perfect information. This atomistic view of economics allows it to relatively easily mathematize its thinking, because individual calculations are transposed into mathematical calculations. Such mathematical modeling allows one to probe economic mechanisms. Some reject or criticise the concept of Homo economicus. Economists note that real people have limited information, make poor choices, and care about fairness and altruism, not just personal gain. Without mathematical modeling, it is hard to go beyond statistical observations or untestable speculation. Mathematical modeling allows economists to create structured frameworks to test hypotheses and analyze complex interactions. Models provide clarity and precision, enabling the translation of theoretical concepts into quantifiable predictions that can be tested against real-world data. At the start of the 20th century, there was a development to express historical movements in formulas. In 1922, Nikolai Kondratiev discerned the ~50-year-long Kondratiev cycle, which explains phases of economic growth or crisis. Towards the end of the 19th century, mathematicians extended their analysis into geopolitics. Peter Turchin developed cliodynamics in the 1990s. Mathematization of the social sciences is not without risk.
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Wikipedia - Mathematics - Relationship with sciences > Specific sciences > Social sciences
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Section: Philosophy > Reality. The connection between mathematics and material reality has led to philosophical debates since at least the time of Pythagoras. The ancient philosopher Plato argued that abstractions that reflect material reality have themselves a reality that exists outside space and time. As a result, the philosophical view that mathematical objects somehow exist on their own in abstraction is often referred to as Platonism. Independently of their possible philosophical opinions, modern mathematicians may be generally considered as Platonists, since they think of and talk of their objects of study as real objects. Armand Borel summarized this view of mathematics reality as follows, and provided quotations of G. H. Hardy, Charles Hermite, Henri Poincaré and Albert Einstein that support his views. Something becomes objective (as opposed to "subjective") as soon as we are convinced that it exists in the minds of others in the same form as it does in ours and that we can think about it and discuss it together. Because the language of mathematics is so precise, it is ideally suited to defining concepts for which such a consensus exists. In my opinion, that is sufficient to provide us with a feeling of an objective existence, of a reality of mathematics ... Nevertheless, Platonism and the concurrent views on abstraction do not explain the unreasonable effectiveness of mathematics (as Platonism assumes mathematics exists independently, but does not explain why it matches reality).
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Wikipedia - Mathematics - Philosophy > Reality
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Section: Philosophy > Proposed definitions. There is no general consensus about the definition of mathematics or its epistemological status—that is, its place inside knowledge. A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science. Some just say, "mathematics is what mathematicians do". A common approach is to define mathematics by its object of study. Aristotle defined mathematics as "the science of quantity" and this definition prevailed until the 18th century. However, Aristotle also noted a focus on quantity alone may not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart. In the 19th century, when mathematicians began to address topics—such as infinite sets—which have no clear-cut relation to physical reality, a variety of new definitions were given. With the large number of new areas of mathematics that have appeared since the beginning of the 20th century, defining mathematics by its object of study has become increasingly difficult. For example, in lieu of a definition, Saunders Mac Lane in Mathematics, form and function summarizes the basics of several areas of mathematics, emphasizing their inter-connectedness, and observes: the development of Mathematics provides a tightly connected network of formal rules, concepts, and systems. Nodes of this network are closely bound to procedures useful in human activities and to questions arising in science. The transition from activities to the formal Mathematical systems is guided by a variety of general insights and ideas. Another approach for defining mathematics is to use its methods.
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Wikipedia - Mathematics - Philosophy > Proposed definitions
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Section: Philosophy > Rigor. Mathematical reasoning requires rigor. This means that the definitions must be absolutely unambiguous and the proofs must be reducible to a succession of applications of inference rules, without any use of empirical evidence and intuition. Rigorous reasoning is not specific to mathematics, but, in mathematics, the standard of rigor is much higher than elsewhere. Despite mathematics' concision, rigorous proofs can require hundreds of pages to express, such as the 255-page Feit–Thompson theorem. The emergence of computer-assisted proofs has allowed proof lengths to further expand. The result of this trend is a philosophy of the quasi-empiricist proof that can not be considered infallible, but has a probability attached to it. The concept of rigor in mathematics dates back to ancient Greece, where their society encouraged logical, deductive reasoning. However, this rigorous approach would tend to discourage exploration of new approaches, such as irrational numbers and concepts of infinity. The method of demonstrating rigorous proof was enhanced in the sixteenth century through the use of symbolic notation. In the 18th century, social transition led to mathematicians earning their keep through teaching, which led to more careful thinking about the underlying concepts of mathematics. This produced more rigorous approaches, while transitioning from geometric methods to algebraic and then arithmetic proofs. At the end of the 19th century, it appeared that the definitions of the basic concepts of mathematics were not accurate enough for avoiding paradoxes (non-Euclidean geometries and Weierstrass function) and contradictions (Russell's paradox).
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Wikipedia - Mathematics - Philosophy > Rigor
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At the end of the 19th century, it appeared that the definitions of the basic concepts of mathematics were not accurate enough for avoiding paradoxes (non-Euclidean geometries and Weierstrass function) and contradictions (Russell's paradox). This was solved by the inclusion of axioms with the apodictic inference rules of mathematical theories; the re-introduction of axiomatic method pioneered by the ancient Greeks. It results that "rigor" is no more a relevant concept in mathematics, as a proof is either correct or erroneous, and a "rigorous proof" is simply a pleonasm. Where a special concept of rigor comes into play is in the socialized aspects of a proof, wherein it may be demonstrably refuted by other mathematicians. After a proof has been accepted for many years or even decades, it can then be considered as reliable. Nevertheless, the concept of "rigor" may remain useful for teaching to beginners what is a mathematical proof.
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Wikipedia - Mathematics - Philosophy > Rigor
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Section: Training and practice > Education. Mathematics has a remarkable ability to cross cultural boundaries and time periods. As a human activity, the practice of mathematics has a social side, which includes education, careers, recognition, popularization, and so on. In education, mathematics is a core part of the curriculum and forms an important element of the STEM academic disciplines. Prominent careers for professional mathematicians include mathematics teacher or professor, statistician, actuary, financial analyst, economist, accountant, commodity trader, or computer consultant. Archaeological evidence shows that instruction in mathematics occurred as early as the second millennium BCE in ancient Babylonia. Comparable evidence has been unearthed for scribal mathematics training in the ancient Near East and then for the Greco-Roman world starting around 300 BCE. The oldest known mathematics textbook is the Rhind papyrus, dated from c. 1650 BCE in Egypt. Due to a scarcity of books, mathematical teachings in ancient India were communicated using memorized oral tradition since the Vedic period (c. 1500 – c. 500 BCE). In Imperial China during the Tang dynasty (618–907 CE), a mathematics curriculum was adopted for the civil service exam to join the state bureaucracy. Following the Dark Ages, mathematics education in Europe was provided by religious schools as part of the Quadrivium. Formal instruction in pedagogy began with Jesuit schools in the 16th and 17th century. Most mathematical curricula remained at a basic and practical level until the nineteenth century, when it began to flourish in France and Germany. The oldest journal addressing instruction in mathematics was L'Enseignement Mathématique, which began publication in 1899.
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Wikipedia - Mathematics - Training and practice > Education
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The oldest journal addressing instruction in mathematics was L'Enseignement Mathématique, which began publication in 1899. The Western advancements in science and technology led to the establishment of centralized education systems in many nation-states, with mathematics as a core component—initially for its military applications. While the content of courses varies, in the present day nearly all countries teach mathematics to students for significant amounts of time. During school, mathematical capabilities and positive expectations have a strong association with career interest in the field. Extrinsic factors such as feedback motivation by teachers, parents, and peer groups can influence the level of interest in mathematics. Some students studying mathematics may develop an apprehension or fear about their performance in the subject. This is known as mathematical anxiety, and is considered the most prominent of the disorders impacting academic performance. Mathematical anxiety can develop due to various factors such as parental and teacher attitudes, social stereotypes, and personal traits. Help to counteract the anxiety can come from changes in instructional approaches, by interactions with parents and teachers, and by tailored treatments for the individual.
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Wikipedia - Mathematics - Training and practice > Education
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Section: Training and practice > Psychology (aesthetic, creativity and intuition). The validity of a mathematical theorem relies only on the rigor of its proof, which could theoretically be done automatically by a computer program. This does not mean that there is no place for creativity in a mathematical work. On the contrary, many important mathematical results (theorems) are solutions of problems that other mathematicians failed to solve, and the invention of a way for solving them may be a fundamental way of the solving process. An extreme example is Apery's theorem: Roger Apery provided only the ideas for a proof, and the formal proof was given only several months later by three other mathematicians. Creativity and rigor are not the only psychological aspects of the activity of mathematicians. Some mathematicians can see their activity as a game, more specifically as solving puzzles. This aspect of mathematical activity is emphasized in recreational mathematics. Mathematicians can find an aesthetic value to mathematics. Like beauty, it is hard to define, it is commonly related to elegance, which involves qualities like simplicity, symmetry, completeness, and generality. G. H. Hardy in A Mathematician's Apology expressed the belief that the aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. He also identified other criteria such as significance, unexpectedness, and inevitability, which contribute to mathematical aesthetics. Paul Erdős expressed this sentiment more ironically by speaking of "The Book", a supposed divine collection of the most beautiful proofs. The 1998 book Proofs from THE BOOK, inspired by Erdős, is a collection of particularly succinct and revelatory mathematical arguments.
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Wikipedia - Mathematics - Training and practice > Psychology (aesthetic, creativity and intuition)
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Section: Cultural impact > Artistic expression. Notes that sound well together to a Western ear are sounds whose fundamental frequencies of vibration are in simple ratios. For example, an octave doubles the frequency and a perfect fifth multiplies it by 3 2 {\displaystyle {\frac {3}{2}}} . Humans, as well as some other animals, find symmetric patterns to be more beautiful. Mathematically, the symmetries of an object form a group known as the symmetry group. For example, the group underlying mirror symmetry is the cyclic group of two elements, Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } . A Rorschach test is a figure invariant by this symmetry, as are butterfly and animal bodies more generally (at least on the surface). Waves on the sea surface possess translation symmetry: moving one's viewpoint by the distance between wave crests does not change one's view of the sea. Fractals possess self-similarity.
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Wikipedia - Mathematics - Cultural impact > Artistic expression
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Section: Cultural impact > Awards and prize problems. The most prestigious award in mathematics is the Fields Medal, established in 1936 and awarded every four years (except around World War II) to up to four individuals. It is considered the mathematical equivalent of the Nobel Prize. Other prestigious mathematics awards include: The Abel Prize, instituted in 2002 and first awarded in 2003 The Chern Medal for lifetime achievement, introduced in 2009 and first awarded in 2010 The AMS Leroy P. Steele Prize, awarded since 1970 The Wolf Prize in Mathematics, also for lifetime achievement, instituted in 1978 A famous list of 23 open problems, called "Hilbert's problems", was compiled in 1900 by German mathematician David Hilbert. This list has achieved great celebrity among mathematicians, and at least thirteen of the problems (depending how some are interpreted) have been solved. A new list of seven important problems, titled the "Millennium Prize Problems", was published in 2000. Only one of them, the Riemann hypothesis, duplicates one of Hilbert's problems. A solution to any of these problems carries a 1 million dollar reward. To date, only one of these problems, the Poincaré conjecture, has been solved by the Russian mathematician Grigori Perelman.
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Wikipedia - Mathematics - Cultural impact > Awards and prize problems
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Section: Features. The main features of the mathematical language are the following. Use of common words with a derived meaning, generally more specific and more precise. For example, "or" means "one, the other or both", while, in common language, "both" is sometimes included and sometimes not. Also, a "line" is straight and has zero width. Use of common words with a meaning that is completely different from their common meaning. For example, a mathematical ring is not related to any other meaning of "ring". Real numbers and imaginary numbers are two sorts of numbers, none being more real or more imaginary than the others. Use of neologisms. For example polynomial, homomorphism. Use of symbols as words or phrases. For example, A = B {\displaystyle A=B} and ∀ x {\displaystyle \forall x} are respectively read as " A {\displaystyle A} equals B {\displaystyle B} " and "for all x {\displaystyle x} ". Use of formulas as part of sentences. For example: " E = m c 2 {\displaystyle E=mc^{2}} represents quantitatively the mass–energy equivalence." A formula that is not included in a sentence is generally meaningless, since the meaning of the symbols may depend on the context: in " E = m c 2 {\displaystyle E=mc^{2}\,} ", this is the context that specifies that E is the energy of a physical body, m is its mass, and c is the speed of light. Use of phrases that cannot be decomposed into their components.
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Wikipedia - Language of mathematics - Features
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Section: Understanding mathematical text. The consequence of these features is that a mathematical text is generally not understandable without some prerequisite knowledge. For example, the sentence "a free module is a module that has a basis" is perfectly correct, although it appears only as a grammatically correct nonsense, when one does not know the definitions of basis, module, and free module. H. B. Williams, an electrophysiologist, wrote in 1927: Now mathematics is both a body of truth and a special language, a language more carefully defined and more highly abstracted than our ordinary medium of thought and expression. Also it differs from ordinary languages in this important particular: it is subject to rules of manipulation. Once a statement is cast into mathematical form it may be manipulated in accordance with these rules and every configuration of the symbols will represent facts in harmony with and dependent on those contained in the original statement. Now this comes very close to what we conceive the action of the brain structures to be in performing intellectual acts with the symbols of ordinary language. In a sense, therefore, the mathematician has been able to perfect a device through which a part of the labor of logical thought is carried on outside the central nervous system with only that supervision which is requisite to manipulate the symbols in accordance with the rules.: 291
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Wikipedia - Language of mathematics - Understanding mathematical text
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Section: Examinations and Olympiads > National Mathematics Talent Contest. AMTI conducts a National Mathematics Talent Contest or NMTC at Primary(Gauss Contest) (Standards 4 to 6), Sub-junior (Kaprekar Contest) (Standards 7 and 8), Junior (Bhaskara Contest) (Standards 9 and 10), Inter(Ramanujan Contest) (Standards 11 and 12) and Senior (Aryabhata Contest) (B.Sc.) levels. For students at the Junior and Inter levels from Tamil Nadu, the NMTC also plays the role of Regional Mathematical Olympiad. Although the question papers are different for Junior and Inter levels, students from both levels may be chosen to appear at INMO based on their performance. The NMTC is usually held around the last week of October. A preliminary examination is conducted earlier (in September) for all levels except B.Sc. students. Students (Junior and Inter) qualifying the preliminary examination are invited for an Orientation Camp one week before the NMTC, where Olympiad problems and theories are taught. This is also useful for those students qualifying further for INMO.
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Wikipedia - Association of Mathematics Teachers of India - Examinations and Olympiads > National Mathematics Talent Contest
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Article: Chennai Mathematical Institute. Chennai Mathematical Institute (CMI) is a higher education and research institute in Chennai, India. It was founded in 1989 by the SPIC Science Foundation, and offers undergraduate and postgraduate programmes in physics, mathematics and computer science. CMI is noted for its research in algebraic geometry, in particular in the area of moduli of bundles. CMI was at first located in T. Nagar in the heart of Chennai in an office complex. It moved to a new 5-acre (20,000 m2) campus in Siruseri in October 2005. In December 2006, CMI was recognized as a university under Section 3 of the University Grants Commission (UGC) Act 1956, making it a deemed university. Until then, the teaching program was offered in association with Bhoj Open University, as it offered more flexibility.
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Wikipedia - Chennai Mathematical Institute - Summary
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Section: History. CMI began as the School of Mathematics, SPIC Science Foundation, in 1989. The SPIC Science Foundation was set up in 1986 by Southern Petrochemical Industries Corporation (SPIC) Ltd., one of the major industrial houses in India, to foster the growth of science and technology in the country. In 1996, the School of Mathematics became an independent institution and changed its name to SPIC Mathematical Institute. In 1998, in order to better reflect the emerging role of the institute, it was renamed the Chennai Mathematical Institute (CMI). From its inception, the institute has had a Ph.D. programme in Mathematics and Computer Science. In the initial years, the Ph.D. programme was affiliated to the BITS, Pilani and the University of Madras. In December 2006, CMI was recognized as a university under Section 3 of the UGC Act 1956. In 1998, CMI took the initiative to bridge the gap between teaching and research by starting B.Sc.(Hons.) and M.Sc. programmes in Mathematics and allied subjects. In 2001, the B.Sc. programme was extended to incorporate two courses with research components, leading to an M.Sc. degree in mathematics and an M.Sc. degree in Computer Science. In 2003, a new undergraduate course was added, leading to a B.Sc. degree in physics. In 2010, CMI launched a summer fellowship programme whereby they invited about 30 students from all over India to work under the faculty at CMI on various research projects. Later, in 2012, the B.Sc. degree in Physics was restructured as an integrated B.Sc. degree in Mathematics and Physics.
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Wikipedia - Chennai Mathematical Institute - History
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Section: Campus. CMI moved into its new campus on 5 acres (20,000 m2) of land at the SIPCOT Information Technology Park in Siruseri in October, 2005. The campus is located along the Old Mahabalipuram Road, which is developing as the IT corridor to the south of the city. The library block and the student's hostel were completed in late 2006 and become operational from January 2007. In 2006, CMI implemented a grey water recycling system on its campus. The system was designed for CMI by Sultan Ahmed Ismail to treat waste water produced after cleaning, washing and bathing to be used for gardening or ground water recharge. Construction is underway for a new building that will house an auditorium, accommodation for guests, as well as additional academic space - faculty offices, library and lecture halls. This construction is funded by a grant from the Ministry of Human Resource Development through the University Grants Commission.
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Wikipedia - Chennai Mathematical Institute - Campus
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Section: Academics > Academic programmes. CMI has Ph.D. programmes in Computer Sciences, Mathematics and Physics. Recently, CMI has introduced the possibility of students pursuing a part-time Ph.D. at the institute. Since 1998, CMI has offered a B.Sc.(Hons) degree in Mathematics and Computer Science. This three-year program also includes courses in Humanities and Physics. Many students, after completion of the B.Sc. degree, have pursued higher studies in Mathematics and Computer Sciences from universities both in India and abroad. Some students also go into industry while others take up subjects such as finance. In 2001, CMI began separate M.Sc. programmes in Mathematics and in Computer Science. In 2009, CMI began to offer a new programme M.Sc. in Applied Mathematics, which is scheduled to be replaced with a new M.Sc. in Data Science programme in 2018 [1] Archived 1 November 2020 at the Wayback Machine. In 2003, CMI introduced a new three-year programme in the form of a B.Sc.(Hons) degree in physics. The course topics are largely in theoretical physics. CMI now has its own physics laboratory. From the academic year 2007–2008, the Physics students are having regular lab courses right from the first year. In the academic year 2005–2006, lab sessions for third-year students were conducted at IIT Madras based on an agreement. In the summer following their first year, physics students go to HBCSE (under TIFR) in Mumbai for practical sessions and in the second year, they go to IGCAR, Kalpakkam. However, in 2012, the B.Sc.
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Wikipedia - Chennai Mathematical Institute - Academics > Academic programmes
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However, in 2012, the B.Sc. degree in Physics was restructured as an integrated B.Sc. degree in Mathematics and Physics. Degrees for the B.Sc. and M.Sc. programmes were earlier offered by MPBOU, the Madhya Pradesh Bhoj Open University and doctoral degrees by Madras University. After CMI became a deemed university, it gives its own degrees. CMI awarded its first official degrees in August 2007. The batch sizes typically vary from 10 to 50 and the overall strength of CMI is about 150–200 students and 40–50 faculty members. Nearly all the CMI programmes are run in conjunction and coordination with programmes at IMSc, an institute for research in Mathematics, Theoretical Computer Science and Theoretical Physics, located in Chennai.
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Wikipedia - Chennai Mathematical Institute - Academics > Academic programmes
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Section: Academics > Admission criteria. The entrance to each of these courses is based on a nationwide entrance test. The advertisement for this entrance test appears around the end of February or the beginning of March. The entrance test is held in the end of May and is usually scheduled so as not to clash with major entrance examinations. Results are given to students by the end of June. Students who have passed the Indian National Mathematics Olympiad get direct admission to the programme B.Sc.(Hons.) in Mathematics and Computer Science, and those who have passed the Indian National Physics Olympiad are offered direct entry to the B.Sc.(Hons.) in Physics programme. However, these students are also advised to fill in and send the application form some time in March. Students who pass the Indian National Olympiad in Informatics may be granted admission to the B.Sc.(Hons.) Mathematics and Computer Science programme. Admission is not guaranteed but is decided on a case-by-case basis by the admissions committee.
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Wikipedia - Chennai Mathematical Institute - Academics > Admission criteria
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Section: Academics > Arrangements with other Institutes. Till 2006, students received their B.Sc. and M.Sc. degrees from MPBOU and their Ph.D. degrees from Madras University. CMI conducts its academic programmes in conjunction with IMSc, so students from either institute can take courses at the other. CMI has agreements with TIFR (Tata Institute of Fundamental Research) and with the Indian Statistical Institutes in Delhi, Bangalore, Chennai and Kolkata, for cooperation on the furtherance of mathematical sciences. The physics programmes are run in conjunction with IMSc and IGCAR. The physics students spend one summer in HBCSE (under TIFR) in Mumbai and another in IGCAR, Kalpakkam, garnering practical experience. CMI has a memorandum of understanding with the École Normale Supérieure in Paris. Under this memorandum, research scholars from the ENS spend a semester in CMI. In exchange, three B.Sc. Mathematics students, at the end of their third year, go to the ENS for two months. The institute has a similar arrangement with École Polytechnique in Paris, whereby top-ranking senior B.Sc. Physics students spend the summer in Paris working with the faculty at École Polytechnique. CMI has a memorandum of understanding with IFMR, the Institute of Financial Management and Research, located in Nungambakkam, Chennai. Students from CMI getting a CGPA of more than 8.50 are offered direct admission to IFMR's one-year programme in Financial Mathematics, which is sponsored by ICICI Bank. Faculty from CMI are involved in teaching this programme.
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Wikipedia - Chennai Mathematical Institute - Academics > Arrangements with other Institutes
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Section: Research. In mathematics, the main areas of research activity have been in algebraic geometry, representation theory, operator algebra, commutative algebra, harmonic analysis, control theory and game theory. Research work includes stratification of binary forms in representation theory, the Donaldson-Uhlenbeck compactification in algebraic geometry, stochastic games, inductive algebras of harmonic analysis, etc. The research activity in theoretical computer science at CMI has been primarily in computational complexity theory, specification and verification of timed and distributed systems and analysis of security protocols. A computer scientist at CMI extended the deterministic isolation technique for reachability in planar graphs to obtain better complexity upper bounds for planar bipartite matching. In theoretical physics, research is being carried out mainly in string theory, quantum field theory and mathematical physics. In mathematical physics, research included developing a path integral approach to quantum entanglement. CMI string theorists study problems such as Big Bang like cosmological singularities, embeddings of BKL cosmology, dyons in super-Yang–Mills theories etc.
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Wikipedia - Chennai Mathematical Institute - Research
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Section: History. Mathematics in Kerala, during the times of Madhava of Sangamagrama, majorly flourished in the Muziris region of Thrikkandiyur, Thirur, Alattiyur, and Tirunavaya in the Malabar region of Kerala. Kerala school of astronomy and mathematics flourished between the 14th and 16th centuries. Commemorating the rich heritage of Mathematics in the region, Kerala School of Mathematics was hence chosen to be set up in the scenic mountains of the Western Ghats in the city of Kozhikode. The nascent plan to set up Kerala School of Mathematics started forming shape in around 2004. The then DAE chairman Anil Kakodkar and the then executive vice president of KSCSTE, M. S. Valiathan were instrumental in setting up the institute with the guidance of M. S. Raghunathan, Rajeeva Karandikar and Alladi Sitaram. The foundation stone of KSoM was laid by the then Chief Minister A.K. Antony in 2004. The institute was later inaugurated in 2008 by the then Chief Minister V. S. Achuthanandan and finally set up in 2009 with Parameswaran A. J. as the founding director.
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Wikipedia - Kerala School of Mathematics, Kozhikode - History
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Section: Contests. MSF Challenge: An annual contest, first held in 2006, to encourage school students to use computers for mathematical problem solving. Recognizing Ramanujan: An annual contest, first held in 2019, to encourage school students in adapting to unique thinking ability in mathematical problem solving. This contest also encourages students to get to know about the great Indian Mathematician Srinivasa Ramanujan. Akshit Gupta from Delhi Public School Rohini topped the first edition of this contest with 75% marks which was almost 15% more than the next best student in the edition. He till date remains the only student to secure a perfect score in the mathematical problem solving section of the exam. Navvye Anand from Sanskriti School is to date the only student to win the distinction of "Budding Ramanujan" in all three of its editions.
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Wikipedia - Mathematical Sciences Foundation - Contests
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Section: History. The University of Madras was incorporated in 1857 and the Department of Mathematics was an integral part of the university from its beginning. The department developed from its early years to become a centre of research in mathematics with the appointment of R. Vaidyanathaswamy as a Reader in Mathematics in 1927. The seeds of the Ramanujan Institute for Advanced Study in Mathematics were sown when the "Ramanujan Institute of Mathematics" was established by Alagappa Chettiar on 26 January 1950 as a memorial to the mathematician Srinivasa Ramanujan. It was governed by the Asoka Charitable Trust, Karaikudi, and was located at Krishna Vilas, Vepery, Chennai. The Ramanujan Institute of Mathematics was inaugurated by A. Lakshmanaswamy Mudaliar, Vice Chancellor of University of Madras, with T. Vijayaraghavan, a student of G.H. Hardy, as Director of the Institute. The institute faced a financial crisis when, in 1956, Asoka Charitable Trust expressed its inability to run the institute. However, due to the request from Subrahmanyan Chandrasekhar Jawaharlal Nehru took an initiative in such a way the management of the institute came to be vested with the University of Madras and the institute was taken over by the university in May 1957. The Asoka charitable Trust Started Ramanujan Institute of Mathematics in January, 1950 and as the Institute found itself in financial difficulties, Government of India agreed in 1953-54 to meet the expenses of a chair for Mathematics at the Institute Object to the condition that the Trust Would continue to spend the amount Previously spent by it for the activity of the Institute.
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Wikipedia - Ramanujan Institute for Advanced Study in Mathematics - History
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The Asoka charitable Trust Started Ramanujan Institute of Mathematics in January, 1950 and as the Institute found itself in financial difficulties, Government of India agreed in 1953-54 to meet the expenses of a chair for Mathematics at the Institute Object to the condition that the Trust Would continue to spend the amount Previously spent by it for the activity of the Institute. Grants of 18,000 for each year were given the Institute for the years 1953-54 and 1994-55, but the audited accounts of the Institute revealed that the Trust was not fulfilling the condition of the Government grant and had instead built up a Reserve Fund. No Government grant was therefore paid in 1965-56 Towards the close of 1956, the Trust decided to close down the Institute, but as a result of discussions with the Government of India, Initiated by the founder of the Trust and the Vice-Chancellor of the Madras University, and later earned on by the Vice-Chancellor, it has been agreed that in view of the difficulty of manning an Institute with the limited number of available Professors of the requisite quality, the activities of the Institute may be continued in the Department of Mathematics in the University of Madras It has been decided to create a Ramanujam Professorship of Mathematics on a scale of Rs 1,000—1,500 with selection grade up to Rs 1,700 and attach the existing permanent research staff of the Institute to the said Professor The Government of India will give the necessary grants to the University to enable them to carry out this arrangement until such time as the University Grants Commission sanctions an appropriate grant. During the short period of existence, the institute had a string of prominent mathematicians as visitors, including S.S. Pillai, noted number theorist, V.
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Wikipedia - Ramanujan Institute for Advanced Study in Mathematics - History
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Pillai, noted number theorist, V. Ganapathy Iyer, analyst and Norbert Wiener. After the demise of T. Vijayaraghavan in 1955, C.T. Rajagopal took over as the Director of the Institute. From 1957 to 1966, the Department of Mathematics and the Ramanujan Institute of Mathematics functioned as independent bodies under the University of Madras. In 1967 the University Grants Commission (India) proposed to make the Department of Mathematics of the University of Madras into one of its Centres of Advanced Study. In the same year these two institutions were amalgamated to form a UGC Centre for Advanced Study in Mathematics and named the center as the "Ramanujan Institute for Advanced Study in Mathematics" (RIASM). C.T. Rajagopal was appointed the first Director of the Ramanujan Institute for Advanced Study in Mathematics, and when he retired in 1969, the reins were taken over by T.S. Bhanumurthy.
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Wikipedia - Ramanujan Institute for Advanced Study in Mathematics - History
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Section: Ramanujan Museum. Utilising a grant of Rs. 1 lakh received as UGC Special Assistance for Equipment and with the help of the Vikram A. Sarabhai Community Science Centre, Ahmedabad a Mathematical Laboratory was established in the institute. About 65 mathematical models were acquired under the scheme. These models were exhibited for the participants of several Refresher Courses conducted through the Academic Staff College of the University of Madras, at the Silver Jubilee conference of the Association of Mathematics Teachers of India held at Madras during 10–13 January 1991, in the Science Exhibition held at National Institute of Technology, Tiruchirapalli during 10–14 July 1991, and are being lent to be exhibited in several schools in and around Chennai. Later the institute received an amount of Rs. 2 lakh from the National Board for Higher Mathematics, Rs. 1 lakh from The Hindu newspaper and Rs. 9 lakh from the Ministry of Culture and Tourism, Government of India, and a matching grant of Rs. 9 lakh from the University of Madras. The amount was used to establish the Ramanujan Museum in the premises of the Ramanujan Institute for Advanced Study in Mathematics. A grant of rupees one crore was later sanctioned by the Ministry of Human Resource Development, Government of India, towards the establishment of Ramanujan Museum and Research Centre.
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Wikipedia - Ramanujan Institute for Advanced Study in Mathematics - Ramanujan Museum
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Section: History > 1960s. The Joint Mathematical Council was formed in 1963 to improve the teaching of mathematics in UK schools. The Ministry of Education had been created in 1944, which became the Department of Education and Science in 1964. The Schools Council was formed in 1964, which regulated the syllabus of exams in the UK, and existed until 1984. The exam body Mathematics in Education and Industry in Trowbridge was formed in 1963, formed by the Mathematical Association; the first exam Additional Mathematics was first set in 1965. The Institute of Mathematics and its Applications was formed in 1964, and is the UK's chartered body for mathematicians, being based in Essex. Before calculators, many calculations would be done by hand with slide rules and log tables. The Nuffield Mathematics Teaching Project started in September 1964, lasting until 1971, to look at primary education, under Edith Biggs, from the Schools Inspectorate. The Nuffield Foundation Primary Mathematics Project began, with the 'Mathematics for the Majority Project', for the years up to 16, for slow learners.
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Wikipedia - Mathematics education in the United Kingdom - History > 1960s
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Section: History > 1970s. Decimal Day, on 15 February 1971, allowed less time on numerical calculations at school. The Metric system has curtailed lengthy calculations as well; the US, conversely, largely does not have the metric system. At Ruskin College on Monday 18 October 1976 Labour Prime Minister Jim Callaghan made a radical speech decrying the lack of numeracy in school leavers, possibly prompted by the William Tyndale affair in 1975. The Prime Minister also questioned why so many girls gave up science before leaving secondary school. But the Labour Party, instead, took curriculum change slowly, merely setting up the Committee of Inquiry into the Teaching of Mathematics in Schools, under Sir Wilfred Cockcroft, with Hilary Shuard and Elizabeth Williams. The subsequent report Mathematics Counts, was published in 1982; it offered few radical changes. In March 1977 the government had a £3.9m scheme to recruit 1,200 more teachers. In England and Wales, there was a shortfall of 1,120 Maths teachers, 424 in physical sciences, and 525 in Design and Technology. It would be paid for by the Training Services Agency, and run by the Local Government Training Board. The scheme was open to people over 28, who had not attended a higher education course in the last five years.
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Section: History > 1980s. Electronic calculators began to be owned at school from the early 1980s, becoming widespread from the mid-1980s. Parents and teachers believed that calculators would diminish abilities of mental arithmetic. Scientific calculators came to the aid for those working out logarithms and trigonometric functions. The BBC2 'Horizon' documentary Twice Five Plus the Wings of a Bird on Monday 28 April 1986, narrated by Peter Jones, looked at why people disliked abstract Maths, notably in the teenage years. The Trends in International Mathematics and Science Study (TIMSS) showed that in some topics, the UK apparently had adequate Mathematics teaching, and from such reports Sir Keith Joseph merely implemented feasibility studies of national attainment standards, but the next education secretary, Kenneth Baker, Baron Baker of Dorking, wanted a lot more than mere feasibility studies. From hearing reports of national industrial failure being caused by insufficient mathematical abilities, he swiftly proposed a national curriculum in January 1987, to start in September 1988. Anita Straker and Hilary Shuard were part of the team that developed the primary national curriculum. Since 1988, exams in Mathematics at age sixteen, except Scotland, have been provided by the GCSE.
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Section: History > 1990s. From the 1990s, mainly the late 1990s, computers became integrated into mathematics education at primary and secondary levels in the UK. On Wednesday 18 November 1992 exam league tables were published for 108 local authorities, in England, under the Education Secretary John Patten, Baron Patten. The tables showed GCSE and A-levels for all 4,400 state secondary schools in England. Independent schools results were shown from 1993, and would include truancy rates. Left-wing parent groups, teachers' unions had opposed the move. Labour said it showed the government's simplistic approach to education standards, adding that raw results cannot reflect the real achievement of schools. The Liberal Democrats were not opposed, but thought that any information being provided was limited. Ofsted would be brought in the next year by Education Minister Emily Blatch, Baroness Blatch. The specialist schools programme was introduced in the mid-1990s in England. Fifteen new City Technology Colleges (CTCs) from the early 1990s often focussed on Maths. In 1996 the United Kingdom Mathematics Trust was formed to run the British Mathematical Olympiad, run by the British Mathematical Olympiad Subtrust. The United Kingdom Mathematics Trust summer school is held at The Queen's Foundation in Birmingham each year. The National Numeracy Strategy, costing £60m, was devised by Anita Straker, for the government's Numeracy Task Force, for primary schools, for implementation in autumn 1999. Prof David Reynolds, of Newcastle University, was the chairman. He had appeared in a Panorama documentary on Maths education on 3 June 1996. The 60-page report in January 1998 recommended that children under the age of 8 should not have calculators.
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Wikipedia - Mathematics education in the United Kingdom - History > 1990s
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Section: History > 2000s. Mathematics and Computing Colleges were introduced in 2002 as part of the widened specialist schools programme; by 2007 there were 222 of these in England. The Excellence in Cities report was launched in March 1999, which led to the Advanced Extension Award in 2002, replacing the S-level for the top 10% of A-level candidates. Since 2008, the AEA is only available for Maths, provided by Edexcel; the scheme was introduced when the A* grade was introduced; the scheme was provided until 2018. In February 2004, the Smith Report, by the Principal of Queen Mary College, looked at how good exams were. People could pass at grade B at GCSE, but had taken much different type of exams. The report concluded that people could pass such exams, but lacked scant real-life proficiency at Maths. A-level Maths entries dropped from 67,000 in 2000 to 53,000 in 2004. The IGCSE, a more rigorous exam, was introduced in 2004, but the Labour government banned state secondary schools from being allowed to set the exam. It was viewed as 'elitist'. In a 2006 House of Lords report on science education, the Lib Dem chair Baroness Sharp, took an interest in the reduced participation in Maths in schools; she had worked with the Science Policy Research Unit at the University of Sussex. The 2001 report by the Lords Science and Technology Committee led to the National Science Learning Centre (Science Learning Centres) at National STEM Centre, with the University of York in 2006, with a Maths centre at University of Southampton. The National Centre for Excellence in the Teaching of Mathematics was founded 2006, after the Smith Report, being now in Sheffield.
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Wikipedia - Mathematics education in the United Kingdom - History > 2000s
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Section: History > 2010s. The HEA subject centres closed in August 2011. In September 2012 Prof Jeremy Hodgen, the chairman of the British Society for Research into Learning Mathematics, produced a report made by Durham University and KCL, where 7,000 children at secondary school took 1970s Maths exams. Maths exams results over the same time scale had doubled in grades, but the researchers did not find much improvement. Proficiency in routine Maths was better, but proficiency with difficult Maths was not as good. Mathematics free schools were opened in 2014 - the King's College London Mathematics School in Lambeth, and Exeter Mathematics School in Devon; both were selective sixth form colleges; others opened at Liverpool and Lancaster; more selective sixth form maths schools are to open in Cambridge, Surrey, and Durham. A newer curriculum for Maths GCSE (and English) was introduced in September 2015, with a new grading scale of 1–9. In August 2015 the ACME claimed that there was a shortfall of 5,500 secondary school Maths teachers, in England. But this shortfall was hugely uneven. Comprehensive schools in wealthy areas or state grammar schools were not commonly short of Maths teachers, but secondary schools in less-salubrious places were often hideously short of Maths teachers.
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Wikipedia - Mathematics education in the United Kingdom - History > 2010s
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Section: Nations > England. Mathematics education in England up to the age of 19 is provided in the National Curriculum by the Department for Education, which was established in 2010. Early years education is called the Early Years Foundation Stage in England, which includes arithmetic. In England there are 24,300 schools, of which 3,400 are secondary. The National Curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language. can solve problems by applying their mathematics to various routine and non-routine problems with increasing sophistication, including breaking down problems into a series of more straightforward steps and persevering in seeking solutions. Mathematics is a related subject in which pupils must be able to move fluently between representations of mathematical ideas. It is essential to everyday life, critical to science, technology and engineering, an appreciation of the beauty and power of mathematics, and a sense of and necessary for financial literacy and most forms of employment. A high-quality mathematics education, therefore, provides a foundation for understanding the world, the ability to reason mathematically, and curiosity about the subject. Pupils should build connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge in science, geography, computing and other subjects.
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Wikipedia - Mathematics education in the United Kingdom - Nations > England
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Section: Relation to other countries. In the 1980s the education researcher Sig Prais looked at mathematics education in Germany and the UK. He found that the teaching of mathematics of an appropriate level, in Germany, worked much better than to bludgeon all levels of mathematics onto all abilities in British comprehensive schools. In preparation for the new national curriculum in 1988, Sig Prais said 'There is an enormous burden on the teacher facing a mixed ability class. At age five, mixed ability classes are not such a problem. You can assume that nobody knows anything, but as the children process through the school, some will not have grasped all that they should, and they never catch up. In some countries, children are not allowed to move into the secondary schools until they are ready for it. They retake the lessons until they are.'
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Section: Secondary level > Mathematics teachers. Qualifications vary by region; the East Midlands and London have the most degree-qualified Maths teachers and North East England the least. For England about 40% mostly have a maths degree and around 20% have a BSc degree with QTS or a BEd degree. Around 20% have a PGCE, and around 10% have no higher qualification than A level Maths. For schools without sixth forms, only around 30% of Maths teachers have a degree, but for schools with sixth forms and sixth form colleges around 50% have a Maths degree. There are around 27,500 Maths teachers in England, of whom around 21,000 are Maths specialists; there are around 31,000 science teachers in England.
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Wikipedia - Mathematics education in the United Kingdom - Secondary level > Mathematics teachers
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Section: Sixth-form level. You will need at least grade 6 at GCSE to study Maths in the sixth form, and many sixth forms will only accept people with a grade 7 at GCSE. At A-level, participation by gender is broadly mixed; about 60% of A-level entrants are male, and around 40% are female. Further Mathematics is an additional course available at A-level. A greater proportion of females take Further Maths (30%) than take Physics (15%), which at A-level is overwhelmingly a male subject. From the UPMAP project (Understanding Participation rates in post-16 Mathematics and Physics) of the ESRC Targeted Initiative on Science and Mathematics Education (TISME), in conjunction with the Institute of Physics, it was found that uptake of Maths A-level was linked to the grade at GCSE. From 2012 figures, 79% with A*, 48% of A, 15% of B and 1% of grade C chose Maths in the 6th form. For English, History and Geography, 30% with grade B, and 10% with grade C chose the course in the 6th form. The House of Lords July 2012 report Higher Education in STEM Subjects recommended that everyone study some type of Maths after 16. For less-able sixth formers, there was the AS level titled 'Use of Mathematics'. Professor Robert Coe, Director of the Centre for Evaluation and Monitoring (CEM) at Durham University conducted research on grade inflation.
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Wikipedia - Mathematics education in the United Kingdom - Sixth-form level
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Section: Sixth-form level > Core Maths. People not taking Maths A-level can take the Core Mathematics Level 3 Certificate, developed by Mathematics in Education and Industry in Wiltshire. It was introduced by education minister Liz Truss from September 2015; her father was a university Maths lecturer. From 2014 it had been trialled in 170 schools. It was hoped that 200,000 sixth formers could study the course for three hours per week, but would possibly require 1,000 extra Maths teachers. 20% of sixth formers studied some kind of Mathematics in 2015. The Advisory Committee on Mathematics Education wanted the Core Maths introduction. In August 2016, there were 3,000 entries for the first Core Maths Level 3 exam. Consequently, the Conservative government was looking at making Maths education up to 18 compulsory.
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Wikipedia - Mathematics education in the United Kingdom - Sixth-form level > Core Maths
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Section: Broadcasting > Television. Educational series on television have included Mathematics and Life, BBC TV 18 September 1961 on Mondays at 11am, repeated on Fridays at 2pm, presented by Hugh David, produced by Donald Grattan Pure Mathematics, BBC TV 17 September 1962 on Mondays and Wednesdays at 10am, repeated on Wednesday and Fridays at 9.30am, for the fifth form and sixth-form, presented by Norman Hyland, produced by Donald Grattan; repeated in September 1963 Pure Mathematics Year II, BBC TV 16 September 1963 on Mondays and Wednesdays at 10am, for the age of 14, presented by Alan Tammadge (9 July 1921 - 25 February 2016, educated at Dulwich College and Emmanuel College, Cambridge); the series was the first of its kind on the BBC, to teach in such a formal way, known as 'chalk and talk'; the series was developed in response to an increasing lack of teachers for the sixth-form; in 1965, 38-year old Donald Grattan, a former grammar school Maths teacher, set up a new further education department at the BBC, with twenty producers; a new 'University of the Air' was being planned by Jennie Lee, Baroness Lee of Asheridge; in March 1968 through BBC Education, under Mr Grattan, this proposal turned largely into adult education courses, and from 1974 towards adult illiteracy; in July 1971 44-year-old Mr Grattan took over as Controller of Educational Broadcasting at the BBC, staying until July 1984; he died aged 93 on 21 August 2019.
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Wikipedia - Mathematics education in the United Kingdom - Broadcasting > Television
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Educational series on television have included Mathematics and Life, BBC TV 18 September 1961 on Mondays at 11am, repeated on Fridays at 2pm, presented by Hugh David, produced by Donald Grattan Pure Mathematics, BBC TV 17 September 1962 on Mondays and Wednesdays at 10am, repeated on Wednesday and Fridays at 9.30am, for the fifth form and sixth-form, presented by Norman Hyland, produced by Donald Grattan; repeated in September 1963 Pure Mathematics Year II, BBC TV 16 September 1963 on Mondays and Wednesdays at 10am, for the age of 14, presented by Alan Tammadge (9 July 1921 - 25 February 2016, educated at Dulwich College and Emmanuel College, Cambridge); the series was the first of its kind on the BBC, to teach in such a formal way, known as 'chalk and talk'; the series was developed in response to an increasing lack of teachers for the sixth-form; in 1965, 38-year old Donald Grattan, a former grammar school Maths teacher, set up a new further education department at the BBC, with twenty producers; a new 'University of the Air' was being planned by Jennie Lee, Baroness Lee of Asheridge; in March 1968 through BBC Education, under Mr Grattan, this proposal turned largely into adult education courses, and from 1974 towards adult illiteracy; in July 1971 44-year-old Mr Grattan took over as Controller of Educational Broadcasting at the BBC, staying until July 1984; he died aged 93 on 21 August 2019. Middle School Mathematics, BBC TV 16 September 1963 on Mondays at 3pm, a 28-part series presented by Dikran Tahta, Alan Tammadge, the President of the Mathematical Association in 1978, David Morris, Stewart Gartside, Gerald Leach (4 January 1933 - 10 January 2004, the husband of child psychologist Penelope Leach), and Maurice Meredith, produced by Donald Grattan, and John Cain; repeated in September 1964, September 1965, September 1966.
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Mathematics '64, BBC2 on Tuesdays at 7.30pm a 20-part series presented by Alan Tammadge, Raymond Cuninghame-Green, Frank Yates, Stuart Hollingdale, Peter Coaker and Geoffrey Matthews, of 'Tuesday Term', with Wilfred Cockcroft, produced by David Roseveare Mathematics in Action: A Course in Statistics, BBC2 16 September 1965 on Thursdays at 7.30pm, repeated on BBC1 on Mondays at 9.30am and Thursdays at 12pm; a 12-part series presented by Stewart Gartside, Peter Sprent (a statistician and the husband of Janet Sprent and head of the Department of Mathematics at the University of Dundee in the late 1960s), and Bill Coleman, with Peter Armitage (statistician), produced by Edward Goldwyn; repeated September 1966, September 1967, September 1968, September 1969 and September 1970 Mathematics in Action: Logic and the Computer, BBC2 13 January 1966 on Thursdays at 7.30pm, a ten-part series presented by Raymond Cuninghame-Green, Frank Lovis, Philip Woodward and Benedict Nixon, produced by Edward Goldwyn; repeated January 1967, January 1968, January 1969, January 1970 and January 1971 Mathematics in Action: Mathematics Applied, BBC2 21 April 1966 on Thursdays at 7.30pm, presented by Prof John Crank, Kenneth Wigley, Noel Williams, Malcolm Bevan and Sydney Urry (originally from Highcliffe in Dorset, and taught Mechanical Engineering at Wandsworth Technical College, he later helped to set up Brunel University in 1966 and the sandwich course schemes, he had a heart attack aged 74 on 12 June 1999), produced by John
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Wikipedia - Mathematics education in the United Kingdom - Broadcasting > Television
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Cain (attended Emanuel School and UCL) and Harry Levinson; repeated April 1967, April 1968, April 1969, April 1970, and April 1971 Maths Today, BBC1 21 September 1967 on Thursdays at 10.30am with repeats on Fridays at 10am, Mondays at 10.30am, and Wednesdays at 11.30am, a two-year series for the first and second years at secondary school, with an associated fortnightly series of six programmes for teachers called 'Teaching Maths Today' from Monday 18 September 1967 with Don Mansfield; presented by David Sturgess, Derick Last and Brenda Briggs, the wife of Trevor Jack Cole, produced by John Cain and Peter Weiss; Year 2 was from 23 September 1968; both series were repeated each year until 26 June 1973; Mr Sturgess lived at 8 Cobthorne Drive in Allestree, in Derbyshire, and was a Maths lecturer at the University of Nottingham, previously the head of the Mathematics Department at Bishop Lonsdale College of Education in Mickleover; Derick Last appeared in the 1967 film 'Mathematics and the Village' about the Cambridgeshire school Cottenham Village College, where he was head of Maths from 1963, and attended Eye Grammar School and Loughborough College, who lived at Wickham Skeith and Ditchingham. There was a later radio series on Radio 3.
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Square Two, BBC2 14 January 1970 on Wednesdays at 7pm, repeated on Saturdays on BBC1 at 9.30am, a 30-part series for people who have left school, presented by Stewart Gartside, Bill Coleman and Alan Tammadge, produced by David Roseveare, written by Hilary Shuard, Douglas Quadling, Ronald Thompson, Leslie Williams and Albert Lawrance; repeated in January 1971 Maths Workshop on BBC1 in the early 1970s with Jim Boucher and Michael Holt (author) Maths Topics, BBC1 17 September 1979 on Mondays at 10.30am, an O-level and CSE course, written by Ian Harris and Colin Banwell (of Bodmin School, and head boy of Sexey's Grammar School in Blackford, Somerset in 1953, who wrote 'Starting Points: For Teaching Mathematics in Middle and Secondary Schools' in 1972 with Ken Saunders ISBN 0906212510), produced by David Roseveare and Peter Bratt, repeated in September 1980, September 1981, September 1982, September 1983, September 1984, September 1985, September 1986, September 1987, and September 1988 Maths Help, BBC1 10 January 1982 on Sundays at 12pm, repeated on Mondays at 2.30pm on BBC2, 12-part series for O-level, but was much more for primary-school level abilities than 16 year olds, presented by Laurie Buxton of ILEA, and partly by Norman Gowar of the Open University, produced by Robert Clamp (attended Coalville Grammar School, and taught Maths at Latymer Upper School); repeated in October 1982, with another series in January 1983, that was more O-level standard Using Mathematics,
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Wikipedia - Mathematics education in the United Kingdom - Broadcasting > Television
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Section: Broadcasting > Radio. How Mathematicians Think, Third Programme 16 March 1950 on Thursdays at 7.30pm, with George Temple (mathematician) of KCL, Gerald James Whitrow of Imperial College, and Charles Coulson of KCL New Paths in Pure Mathematics, Third Programme 28 November 1950 on Wednesdays at 6.20pm, with parts 1 What Is a Curve? 2 Numbers and Axioms, with Max Newman, Professor of Mathematics at the University of Manchester 3 The Mathematics of Counting, 4 The Mathematics of Measuring, with Richard Rado of KCL 5 The Evolution of Geometrical Ideas, with John Greenlees Semple, Professor of Geometry at KCL Thinking in Numbers, Network Three 4 November 1959 on Wednesdays at 7.30pm, presented and written by statistician Maurice Kendall, with parts 1 Louis Rosenhead of the University of Liverpool, and Alexander Aitken of the University of Edinburgh 2 Staff of the National Physical Laboratory, and Reg Revans of the University of Manchester 3 Richard van der Riet Woolley, Michael Abercrombie of UCL, and Otto Robert Frisch of the University of Cambridge 4 Kenneth Mather Mathematics, part of For Schools, Home Service 6 May 1965 Thursdays at 9.30am, 10-part series presented by James Hawthorne; repeated in April 1966, April 1967, September 1967, and on Radio 4 in September 1968, and September 1969 Developing Maths Today, Radio 3 9 October 1969 on Fridays at 7.30pm, it was a radio version of the BBC2 'Teaching Maths Today', produced by John Turtle
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Section: Results by region in England. Of all A-level entrants at Key Stage 5, 23% take Maths A-level, with 16% of all female entrants and 30% of all male entrants; 4% of all entrants take Further Maths, with 2% of female entrants and 6% of male entrants. By number of A-level entries, 11.0% were Maths A-levels with 7.7% female and 15.0% male. In England in 2016 there were 81,533 entries for Maths A-level, with 65,474 from the state sector; there were 14,848 entries for Further Maths with 10,376 from the state sector Entries for Further Maths in 2016 by region - South East 2987 East of England 1270 North West 1111 South West 1070 West Midlands 868 East Midlands 774 Yorkshire and the Humber 749 North East 414
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Section: Further Maths IGCSE and Additional Maths FSMQ in England. Starting from 2012, Edexcel and AQA have started a new course which is an IGCSE in Further Maths. Edexcel and AQA both offer completely different courses, with Edexcel including the calculation of solids formed through integration, and AQA not including integration. AQA's syllabus mainly offers further algebra, with the factor theorem and the more complex algebra such as algebraic fractions. It also offers differentiation up to—and including—the calculation of normals to a curve. AQA's syllabus also includes a wide selection of matrices work, which is an AS Further Mathematics topic. AQA's syllabus is much more famous than Edexcel's, mainly for its controversial decision to award an A* with Distinction (A^), a grade higher than the maximum possible grade in any Level 2 qualification; it is known colloquially as a Super A* or A**. A new Additional Maths course from 2018 is OCR Level 3 FSMQ: Additional Maths (6993).
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Wikipedia - Additional Mathematics - Further Maths IGCSE and Additional Maths FSMQ in England
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Section: Additional Mathematics in Malaysia. In Malaysia, Additional Mathematics is offered as an elective to upper secondary students within the public education system. This subject is included in the Sijil Pelajaran Malaysia examination. Science stream students are required to apply for Additional Mathematics as one of the subjects in the Sijil Pelajaran Malaysia examination, while Additional Mathematics is an optional subject for students who are from arts or commerce streams. Additional Mathematics in Malaysia—also commonly known as Add Maths—can be organized into two learning packages: the Core Package, which includes geometry, algebra, calculus, trigonometry and statistics, and the Elective Package, which includes science and technology application and social science application. It covers various topics including: Format for Additional Mathematics Exam based on the Malaysia Certificate of Education is as follows: Paper 1 (Duration: 2 Hours): Questions are categorised into Sections A and B and are tested based on the student's knowledge to grasp the concepts and formulae learned during their 2 years of learning. Section A consists of 12 questions in which all must all be answered, whereas Section B consists of 3 questions and students are given the choice to answer 2 of the three questions only. Each question may contain from zero to three subsets of questions with marks ranging from 2 to 8 marks. The total weighting of the paper is 80 marks and constitutes 44% of the grade. Paper 2 (Duration: 2 hours 30 minutes): Questions are categorised into 3 sections: A, B and C. Section A contains 7 questions which must all be answered. Section B contains 4 questions where students are given the choice to answer 3 out of 4 of them.
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Section B contains 4 questions where students are given the choice to answer 3 out of 4 of them. Section C contains 4 questions where students are only required to answer 2 out of 4 of the given questions. All Section C questions are based on the same chapters every year and are thus predictable. A question in Section C carries 10 marks with at 3 to 4 subquestions per question. This paper tests the student's ability to apply various concepts and formulae in real-life situations. The total weighting of the paper is 100 marks and constitutes 56% of the grade. In 2020, the first batch of students learning the new syllabus, KSSM, will receive new Form 4 textbooks with new chapters which contain certain topics from A-levels.
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Section: Additional Mathematics in Hong Kong. In Hong Kong, the syllabus of HKCEE additional mathematics covered three main topics, algebra, calculus and analytic geometry. In algebra, the topics covered include mathematical induction, binomial theorem, quadratic equations, trigonometry, inequalities, 2D-vectors and complex number, whereas in calculus, the topics covered include limit, differentiation and integration. In the HKDSE, additional mathematics has been replaced by two Mathematics Extend Modules, which include a majority of topics in the original additional mathematics, and a few topics, such as matrix and determinant, from the syllabus of HKALE pure mathematics and applied mathematics, while notably missing analytic geometry, inequalities involving absolute values and rational functions, and complex numbers (of which only the basic arithmetic is covered in the Mathematics Compulsory part).
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Article: Advanced Extension Award. The Advanced Extension Awards are a type of school-leaving qualification in England, Wales and Northern Ireland, usually taken in the final year of schooling (age 17/18), and designed to allow students to "demonstrate their knowledge, understanding and skills to the full". Currently, it is only available for Mathematics and offered by the exam board Edexcel. They were introduced in 2002, in response to the UK Government's Excellence in Cities report, as a successor to the S-level examination, and aimed at the top 10% of students in A level tests. They are assessed entirely by external examinations. Due to introduction of the A* grade for A level courses starting September 2008 (first certification 2010), they have since been phased out, with the exception of the Advanced Extension Award in Mathematics which continues to be available to students.
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Wikipedia - Advanced Extension Award - Summary
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Section: Results. According to EducationGuardian.co.uk, in 2004, 50.4% of the 7246 entrants failed to achieve a grade at all (fail), indicating that the awards are fulfilling their role in separating the elite. Only 18.3% of students attained the top of the two grades available, the Distinction, with the next 31.3% of students receiving the grade of Merit. Given that only the top students in the country sat these examinations, these results indicate that the AEAs were successful in rewarding only the 50-100 students that were most able in a particular subject. It was possible to obtain an AEA distinction in more than one subject; however, given the rarity of AEA distinctions, this was uncommon.
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Wikipedia - Advanced Extension Award - Results
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Section: Available subjects. Due to the small numbers of candidates for each subject, the exam boards divided the subjects offered amongst themselves, so that – unlike A-levels – each AEA was only offered by one board. Biology (including Human Biology) (AQA) Business (OCR) Chemistry (AQA) Critical Thinking (OCR) Economics (AQA) English (OCR) French (OCR) Geography (WJEC) German (CCEA) History (Edexcel) Irish (CCEA) Latin (OCR) Mathematics (Edexcel) Physics (CCEA) Psychology (AQA) Religious Studies (Edexcel) Spanish (Edexcel) Welsh (WJEC) Welsh as a second language (WJEC)
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Section: Partial withdrawal. The last AEA examinations across the full range of subjects took place in June 2009, with results issued in August 2009. The Advanced Extension Award was then withdrawn for all subjects except mathematics. This came after the Joint Council for Qualifications (JCQ) decided that the new A* grade being offered at A level would overlap with the purpose of the AEA, rendering them unnecessary. However, the AEA in mathematics was extended until June 2012, as confirmed by Edexcel and the QCA. This was because it met a "definite need", since the A* grade was still not viewed as being challenging enough. In June 2011 Edexcel announced that the AEA was being extended further for mathematics, until June 2015, which was later extended until 2018. In 2018, Edexcel introduced a new specification, meaning the Advanced Extension Award in mathematics would continue to be available to students in 2019 and beyond, as a qualification aimed at the top 10% of students at A level. All other subjects remain withdrawn, though opportunity exists for examination boards to offer AEAs in other subjects should they choose to in the future, subject to certain expectations.
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Article: Advanced level mathematics. Advanced Level (A-Level) Mathematics is a qualification of further education taken in the United Kingdom (and occasionally other countries as well). In the UK, A-Level exams are traditionally taken by 17-18 year-olds after a two-year course at a sixth form or college. Advanced Level Further Mathematics is often taken by students who wish to study a mathematics-based degree at university, or related degree courses such as physics or computer science. Like other A-level subjects, mathematics has been assessed in a modular system since the introduction of Curriculum 2000, whereby each candidate must take six modules, with the best achieved score in each of these modules (after any retake) contributing to the final grade. Most students will complete three modules in one year, which will create an AS-level qualification in their own right and will complete the A-level course the following year—with three more modules. The system in which mathematics is assessed is changing for students starting courses in 2017 (as part of the A-level reforms first introduced in 2015), where the reformed specifications have reverted to a linear structure with exams taken only at the end of the course in a single sitting. In addition, while schools could choose freely between taking Statistics, Mechanics or Discrete Mathematics (also known as Decision Mathematics) modules with the ability to specialise in one branch of applied Mathematics in the older modular specification, in the new specifications, both Mechanics and Statistics were made compulsory, with Discrete Mathematics being made exclusive as an option to students pursuing a Further Mathematics course. The first assessment opportunity for the new specification is 2018 and 2019 for A-levels in Mathematics and Further Mathematics, respectively.
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Wikipedia - Advanced level mathematics - Summary
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Section: 2000s specification > Further mathematics. Students that were studying for (or had completed) an A-level in Mathematics had the opportunity to study an A-level in Further Mathematics, which required taking a further 6 modules to give a second qualification. The grades of the two A-levels will be independent of each other, with Further Mathematics requiring students to take a minimum of two Further Pure modules, one of which must be FP1, and the other either FP2 or FP3, which are simply extensions of the four Core modules from the normal Maths A-Level. Four more modules need to be taken; those available vary with different specifications. Not all schools are able to offer Further Mathematics, due to a low student number (meaning that the course is not financially viable) or a lack of suitably experienced teachers. To fulfil the demand, extra tutoring is available, with providers such as the Further Mathematics Support Programme. Some students had the opportunity to take a third maths qualification, "Additional Further Mathematics", which added more modules from those not used for Mathematics or Further Mathematics. Schools that offer this qualification usually only took this to AS-level, taking three modules, although some students went further, taking the extra six modules to gain another full A-Level qualification. Additional Further Mathematics is offered by Edexcel only, and a Pure Mathematics A-level is available for students who—on the Edexcel exam board—take the modules C1, C2, C3, C4, FP1 and either FP2 or FP3. No comparable qualification has been available since the 2017 reforms.
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Wikipedia - Advanced level mathematics - 2000s specification > Further mathematics
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Section: Grading. It was suggested by the Department for Education that the high proportion of candidates who obtain grade A makes it difficult for universities to distinguish between the most able candidates. As a result, the 2010 exam session introduced the grade A*—which serves to distinguish between the better candidates. Prior to the 2017 reforms, the A* grade in maths was awarded to candidates who achieve an A (480/600) in their overall A Level, as well as achieving a combined score of 180/200 in modules Core 3 and Core 4. For the reformed specification, the A* is given by a more traditional grade boundary based on the raw mark achieved by the candidate over their papers. The A* grade in further maths was awarded slightly differently. The same minimum score of 480/600 was required across all six modules. However, a 90% average (or a score of 270/300) had to be obtained across the candidate's best 'A2' modules. A2 modules included any modules other than those with a '1' (FP1, S1, M1 and D1 are not A2 modules, whereas FP2, FP3, FP4 (from AQA only), S2, S3, S4, M2, M3 and D2 are).
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Wikipedia - Advanced level mathematics - Grading
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Section: List of subjects. 1. Core Mathematics: Covers foundational topics like algebra, calculus, trigonometry, and coordinate geometry. 2. Further Mathematics: Expands upon Core Mathematics with additional areas such as complex numbers, matrices, differential equations, and numerical methods. 3. Pure Mathematics: Explores advanced topics in algebra, calculus, and mathematical proofs. 4. Applied Mathematics: Focuses on practical applications of mathematical concepts to solve real-world problems in various fields. 5. Mechanics: Focuses on the study of motion, forces, and vectors, particularly relevant for physics or engineering interests. 6. Statistics: Involves collecting, analysing, and interpreting data, including topics like probability, hypothesis testing, regression analysis, and sampling. 7. Discrete Mathematics: Deals with separate and distinct mathematical structures, including topics such as combinatorics, graph theory, and algorithms. 8. Decision Mathematics: Applies mathematical techniques to solve real-world problems related to optimisation, networks, and decision-making. 9. Financial Mathematics: Applies mathematical concepts to analyse financial markets, investments, and risk management.
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Wikipedia - Advanced level mathematics - List of subjects
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Article: The Archimedeans. The Archimedeans are the mathematical society of the University of Cambridge, founded in 1935. It currently has over 2000 active members, many of them alumni, making it one of the largest student societies in Cambridge. The society hosts regular talks at the Centre for Mathematical Sciences, including in the past by many well-known speakers in the field of mathematics. It publishes two magazines, Eureka and QARCH. One of several aims of the society, as laid down in its constitution, is to encourage co-operation between the existing mathematical societies of individual Cambridge colleges, which at present are just the Adams Society of St John's College, Queens' College Mathematics Society and the Trinity Mathematical Society, but in the past have included many more. The society is mentioned in G. H. Hardy's essay A Mathematician's Apology. Past presidents of The Archimedeans include Michael Atiyah and Richard Taylor.
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Wikipedia - The Archimedeans - Summary
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Section: Publications. Eureka is a mathematical journal that is published annually by The Archimedeans. It includes articles on a variety of topics in mathematics, written by students and academics from all over the world, as well as a short summary of the activities of the society, problem sets, puzzles, artwork and book reviews. The magazine has been published 65 times since 1939, and authors include many famous mathematicians and scientists such as Paul Erdős, Martin Gardner, Douglas Hofstadter, Godfrey Hardy, Béla Bollobás, John Conway, Stephen Hawking, Roger Penrose, Ian Stewart, Chris Budd, Fields Medallist Timothy Gowers and Nobel laureate Paul Dirac. The Archimedeans also publish QARCH, a magazine containing problem sets and solutions or partial solutions submitted by readers. It is published on an irregular basis and distributed free of charge. == References ==
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Wikipedia - The Archimedeans - Publications
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Section: Guiding principles. ATM lists as its guiding principles: The ability to operate mathematically is an aspect of human functioning which is as universal as language itself. Attention needs constantly to be drawn to this fact. Any possibility of intimidating with mathematical expertise is to be avoided. The power to learn rests with the learner. Teaching has a subordinate role. The teacher has a duty to seek out ways to engage the power of the learner. It is important to examine critically approaches to teaching and to explore new possibilities, whether deriving from research, from technological developments or from the imaginative and insightful ideas of others. Teaching and learning are cooperative activities. Encouraging a questioning approach and giving due attention to the ideas of others are attitudes to be encouraged. Influence is best sought by building networks of contacts in professional circles.
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Wikipedia - Association of Teachers of Mathematics - Guiding principles
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Section: Career. Bellos's first job was working for The Argus in Brighton before moving to The Guardian in London in 1994. From 1998 to 2003 he was South America correspondent of The Guardian, and wrote Futebol: the Brazilian Way of Life. The book was well received in the UK, where it was nominated for sports book of the year at the British Book Awards. In the US, it was included as one of Publishers Weekly's books of the year. They wrote: “Compelling...Alternately funny and dark...Bellos offers a cast of characters as colorful as a Carnival parade”. In 2006, he ghostwrote Pelé: The Autobiography, about the soccer player Pelé, which was a number one best-seller in the UK. Returning to live in the UK, Bellos decided to write about mathematics. The book Alex's Adventures in Numberland was published in 2010 and spent four months in The Sunday Times' top ten best-sellers' list. The Daily Telegraph described the book as a "mathematical wonder that will leave you hooked on numbers." The book was shortlisted for three awards in the UK, including the BBC Samuel Johnson Prize for Non-Fiction 2010. The Guardian reported that Bellos's book was narrowly beaten into second place. Chairman of the judges Evan Davis broke with protocol to discuss their deliberations: "[Bellos's] was a book everyone thought would be nice if it won, because it would be good for people to read a maths book. Some of us wished we'd read it when we were 14 years old.
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Wikipedia - Alex Bellos - Career
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Some of us wished we'd read it when we were 14 years old. If we'd taken the view that this is a book everyone ought to read, then it might have gone that way." Several translations of the book have been published. The Italian version, Il meraviglioso mondo dei numeri, won both the €10,000 Galileo Prize for science books and the 2011 Peano Prize for mathematics books. In the United States, the book was given the title Here's Looking at Euclid. Alex Through The Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life was published in 2014 and received positive reviews. The Daily Telegraph wrote: “If anything, Looking Glass is a better work than Numberland – it feels more immediate, more relevant and more fun.” Its US title was The Grapes of Math, about which The New York Times said Bellos was: “a charming and eloquent guide to math’s mysteries…There’s an interesting fact or mathematical obsessive on almost every page. And for its witty flourishes, it’s never shallow. Bellos doesn’t shrink from delving into equations, which should delight aficionados who relish those kinds of details.” Bellos presented the BBC TV series Inside Out Brazil (2003), and also authored the documentary Et Dieu créa…le foot, about football in the Amazon rainforest, which was shown on the National Geographic Channel. His short films on the Amazon have appeared on BBC, More4 and Al Jazeera. He also appears frequently on the BBC talking about mathematics.
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Wikipedia - Alex Bellos - Career
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Section: Publications > On mathematics. (2010) Alex's Adventures in Numberland/Here's Looking at Euclid ISBN 1526623994 (2014) Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life ISBN 1408817772 (2015) Snowflake Seashell Star: Colouring Adventures in Numberland with Edmund Harris ISBN 1782117881 (2016) Can You Solve My Problems?: Ingenious, Perplexing, and Totally Satisfying Math and Logic Puzzles ISBN 1783351144 (2016) Visions of Numberland/Patterns of the Universe with Edmund Harriss ISBN 9781408888988 (2017) Puzzle Ninja: Pit Your Wits Against the Japanese Puzzle Masters ISBN 145217105X (2019) So You Think You've Got Problems?: Puzzles to flex, stretch and sharpen your mind ISBN 178335190X (2020) The Language Lover’s Puzzle Book: Lexical perplexities and cracking conundrums from across the globe ISBN 1783352183
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Wikipedia - Alex Bellos - Publications > On mathematics
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Section: Publications > Awards and honours. 2019 Shortlisted for the Chalkdust Magazine Book of the Year for So You Think You've Got Problems? 2017 Shortlisted for the Blue Peter Book Award for Best Book with Facts for Football School: Where Football Explains the World 2012 Premio Letterario Galileo, winner, Il meraviglioso mondo dei numeri 2012 Peano Prize, winner, Il meraviglioso mondo dei numeri 2011 Shortlisted for the Royal Society Prizes for Science Books for Alex's Adventures in Numberland 2010 Amazon.com, Best Books of 2010: Science for Here's Looking at Euclid 2010 Shortlisted for the British Book Awards, Non-Fiction Book of the Year for Alex's Adventures in Numberland 2010 Shortlisted for the BBC Samuel Johnson Prize for Non-Fiction for Alex's Adventures in Numberland 2004 Shortlisted for British Book Awards, Sports Book of the Year for Futebol: The Brazilian Way of Life 2003 Shortlisted for National Sporting Club British Sports Book Awards Futebol: The Brazilian Way of Life
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Wikipedia - Alex Bellos - Publications > Awards and honours
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Article: Beyer Professor of Applied Mathematics. The Beyer Chair of Applied Mathematics is an endowed professorial position in the Department of Mathematics, University of Manchester, England. The endowment came from the will of the celebrated locomotive designer and founder of locomotive builder Beyer, Peacock & Company, Charles Frederick Beyer. He was the university's largest single donor. The first appointment in 1881 was of Arthur Schuster who held the position until 1888. After Schuster's departure, the chair of Mathematics to which Horace Lamb had been appointed in 1885 became the Beyer Professorship of Mathematics and remained so until Lamb's retirement in 1920. At this point an existing chair, of Mathematics and Natural Philosophy to which Sydney Chapman had been appointed in 1919, was renamed the Beyer Professorship of Mathematics and Natural Philosophy. After Chapman's resignation, the Beyer title was applied to the chair of Applied Mathematics. There was no incumbent between 1937 and 1945. Most of the holders of the post were elected as Fellows of the Royal Society, an honour bestowed on a small minority of UK mathematics professors. Lamb, Champman, Milne and Goldstein all received the Smith's Prize and indication of early career promise. The other endowed chairs in mathematics at the University of Manchester are the Richardson Chair of Applied Mathematics, and the Fielden Chair of Pure Mathematics as well as the named Sir Horace Lamb Chair.
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Wikipedia - Beyer Professor of Applied Mathematics - Summary
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Section: BMO Round 1. The first round of the BMO is held in November each year, and from 2006 is an open entry competition. The qualification to BMO Round 1 is through the Senior Mathematical Challenge or the Mathematical Olympiad for Girls. Students who do not make the qualification may be entered at the discretion of their school for a fee of £40. The paper lasts 3½ hours, and consists of six questions (from 2005), each worth 10 marks. The exam in the 2020-2021 cycle was adjusted to consist of two sections, first section with 4 questions each worth 5 marks (only answers required), and second section with 3 question each worth 10 marks (full solutions required). The duration of the exam had been reduced to 2½ hours, due to the difficulties of holding a 3½ hours exam under COVID-19. Candidates are required to write full proofs to the questions. An answer is marked on either a "0+" or a "10-" mark scheme, depending on whether the answer looks generally complete or not. An answer judged incomplete or unfinished is usually capped at 3 or 4, whereas for an answer judged as complete, marks may be deducted for minor errors or poor reasoning but it is likely to get a score of 7 or more. As a result, it is uncommon for an answer to score a middling mark between 4 and 6. While around 1000 gain automatic qualification to sit the BMO1 paper each year, the additional discretionary and international students means that since 2016, on average, around 1600 candidates have been entered for BMO1 each year.
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Wikipedia - British Mathematical Olympiad - BMO Round 1
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While around 1000 gain automatic qualification to sit the BMO1 paper each year, the additional discretionary and international students means that since 2016, on average, around 1600 candidates have been entered for BMO1 each year. Although these candidates represent the very best mathematicians in their age group, the difficulty level of the BMO papers mean that many of these attain a very low score. The scores were particularly low until 2004, for example, when the median score was approximately 5-6 (out of 50). In 2005, UKMT changed the system and added an extra easier question meaning the median is now raised. In 2008, 23 students scored more than 40/60 and around 50 got over 30/60. In addition to the British students, until 2018, there was a history of about 20 students from New Zealand being invited to take part. In recent years, entries to BMO have been made from schools in Ireland, Kazakhstan, India, China, South Korea, Hong Kong, Singapore, and Thailand. BMO1 paper for the cycle 2021-22 attracted 1857 entries. Only 5 candidates scored 90% or more. A score of 21/60 was enough to earn a Distinction, awarded to top 26% of the candidates. From the results of the BMO1, around 100 top scoring students are invited to sit the BMO2. For the 2021-22 cycle, the score needed for to qualify for BMO2 was 33 for a year 13 pupil and 29 for a pupil in year 10 and below. Students who did not take the BMO1, or who did not qualify for an invitation, may be entered into the next round at the discretion of their school through payment of a fee of £50.
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Wikipedia - British Mathematical Olympiad - BMO Round 1
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Section: BMO Round 2. BMO2 (known as the Further International Selection Test, FIST from 1972 to 1991) is normally held in late January or early February, and is significantly more difficult than BMO1. BMO2 also lasts 3½ hours, but consists of only four questions, each worth 10 marks. Like the BMO1 paper, it is not designed merely to test knowledge of advanced mathematics but rather to test the candidate's ability to apply the mathematical knowledge to solve unusual problems and is an entry point to training and selection for the international competitions. BMO2 paper for the cycle 2021-22 attracted over 200 entries. A score of 17/40 was enough to earn a Distinction, awarded to top 25% of the candidates. Only 4 candidates scored more than 30/40. Twenty-four of the top scorers from BMO2 are subsequently invited to the training camp at Trinity College, Cambridge for the first stage of the IMO UK team selection. The top 4 female scorers from BMO2 are selected to represent the UK at the European Girls' Mathematical Olympiad.
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Wikipedia - British Mathematical Olympiad - BMO Round 2
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Section: IMO Selection Papers. For more information about IMO selection in other countries, see International Mathematical Olympiad selection process Since 1985, further selection tests have been used after BMO2 to select the IMO team. (The team was selected following the single BMO paper from 1967 to 1971, then following the FIST paper for some years from 1972.) Initially these third-stage tests resulted in selection of both team and reserve; from 1993 a squad (team plus reserve) was selected following these tests with the team being separated from the reserve after further correspondence training, and after further selection tests from 2001 onwards. The third-stage tests have had names including FIST 2 (1985), Second International Selection Test (SIST), Reading Selection Test (1987), Final Selection Test (FST, 1992 to 2001) and First Selection Test (FST, from 2002); the fourth-stage tests have been Team Selection Test (TST, 2001) and Next Selection Test (NST, 2002 onwards). These tests have been held at training and selection camps in several locations, recently Trinity College, Cambridge and Oundle School. Since 2017, the tests are simply called Team Selection Tests (TSTs). Six TSTs were held in 2017 and 2018. Since 2019, the number of TSTs have been reduced to 4 or two rounds, the first round is held in late April and the second round in late May. The UK IMO squad of 10 is selected following the first round of tests with the final team of 6 to represent the UK at the International Mathematical Olympiad announced following the second round.
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Wikipedia - British Mathematical Olympiad - IMO Selection Papers
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Article: British Mathematical Olympiad Subtrust. The British Mathematical Olympiad Subtrust (BMOS) is a section of the United Kingdom Mathematics Trust which currently runs the British Mathematical Olympiad as well as the UK Mathematical Olympiad for Girls, several training camps throughout the year such as a winter camp in Hungary, an Easter camp at Trinity College, Cambridge, and other training and selection of the International Mathematical Olympiad team. Since 1999, it also organizes the UK National Mathematics Summer Schools. It was established alongside the British Mathematical Olympiad Committee (BMOC) in 1991 with the support of the Edinburgh Mathematical Society, Institute of Mathematics and its Applications, the London Mathematical Society, and the Mathematical Association, each nominated two members. The BMOS replaced some of the Mathematical Association's activities.
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Wikipedia - British Mathematical Olympiad Subtrust - Summary
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Article: Christopher Budd (mathematician). Christopher John Budd (born 15 February 1960) is a British mathematician known especially for his contribution to non-linear differential equations and their applications in industry. He is currently Professor of Applied Mathematics at the University of Bath, and was Professor of Geometry at Gresham College from 2016 to 2020. Budd gained his Bachelor's degree in mathematics at St John's College, Cambridge, where he was senior wrangler. He went on to be awarded a D.Phil. from Oxford University, studying numerical methods for nonlinear elliptic partial differential equations under the supervision of John Norbury. He spent three years as a fellow of St John's College, Oxford, working in numerical analysis at the Oxford University Computing Laboratory and as a fellow sponsored by the CEGB developing numerical methods for third-order partial differential equations. He went on to a permanent post as a lecturer in numerical analysis at the University of Bristol before gaining a position as Professor of Applied Mathematics at the University of Bath in 1995. He was appointed the Professor of Geometry at Gresham College in 2016, where he delivered a series of public lectures on Mathematics and the Making of the Modern World. His research interests involve the analysis, application and numerical analysis of the solution of nonlinear differential equations with a particular emphasis on problems which arise in industry. His recent work has been in geometric integration which aims to develop numerical methods which reproduce qualitative structures in differential equations. He is co-director of the interdisciplinary Centre for Nonlinear Mechanics at the University of Bath and is active in promoting interdisciplinary collaboration both nationally and internationally.
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Wikipedia - Christopher Budd (mathematician) - Summary
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He is co-director of the interdisciplinary Centre for Nonlinear Mechanics at the University of Bath and is active in promoting interdisciplinary collaboration both nationally and internationally. Budd is a passionate populariser of mathematics, reflected in his appointment as Chair of Mathematics of the Royal Institution of Great Britain in 2000. He works on a number of projects with schools and has written a book, "Mathematics Galore", based on his series of popular talks. He has also made numerous guest appearances on national radio and television, such as on the BBC's The One Show[1] and popular science panel comedy game show It's Only a Theory[2]. He won the Leslie Fox Prize for Numerical Analysis in 1991. In 1999 he was one of ten scientists awarded the title of "Scientist for the new century" by the Royal Institution. In 2001 he was one of 20 lecturers in the UK to be awarded an ILT Teaching Fellowship, and he was nominated the LMS popular lecturer in applied mathematics. He was awarded the Order of the British Empire (OBE) in the Queen's Birthday Honours List in 2015 for services to science and maths education. He has supervised at least 9 students for a PhD.
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Wikipedia - Christopher Budd (mathematician) - Summary
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Section: A - F. Rediet Abebe, graduate student at Pembroke College, Cambridge Frank Adams, fellow of Trinity College, Cambridge, Lowndean Professor of Astronomy and Geometry 1970-1989 John Couch Adams, fellow of St. John's College, Cambridge 1843–1852; fellow of Pembroke College, Cambridge 1853–1892; Lowndean Professor of Astronomy and Geometry 1859-1891 Michael Atiyah, fellow of Trinity College, Cambridge 1954–1957; fellow of Pembroke College, Cambridge 1958–1961; Master of Trinity College, Cambridge 1990-1997 Charles Babbage, Lucasian Professor of Mathematics 1828-1839 Christopher Budd, Gresham Professor of Geometry, student at St John's College 1979-1983 Alan Baker, fellow of Trinity College, Cambridge 1964- H. F. Baker, fellow of St. John's College, Cambridge Dennis Barden, fellow of Pembroke College, Cambridge Isaac Barrow, fellow of Trinity College, Cambridge 1649–1655, Lucasian Professor of Mathematics Arthur Berry, 1862-1929, Vice-Provost of King's College, Cambridge Bryan John Birch, undergraduate and research student at Trinity College, Cambridge, fellow of Churchill College, Cambridge Michael Boardman Béla Bollobás, fellow of Trinity College, Cambridge Richard Ewen Borcherds Henry Briggs, Fellow of St. John's College, Cambridge William Burnside, attended St John's College and Pembroke College, Cambridge. Appointed professor of mathematics at the Royal Naval College in Greenwich, at site of University of Greenwich Mathematics Department. Dame Mary Cartwright, fellow and Mistress of Girton College, Cambridge J. W. S.
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Wikipedia - List of Cambridge mathematicians - A - F
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W. S. Cassels, fellow of Trinity College, Cambridge 1949–1984; Sadleirian Professor of Pure Mathematics 1967-1986 Arthur Cayley, student at Trinity College, Cambridge D. G. Champernowne Sydney Chapman, student at and later lecturer and fellow (1914–1919) of Trinity College, Cambridge William Kingdon Clifford John Coates, fellow of Emmanuel College, Cambridge 1975–1977; Sadleirian Professor of Pure Mathematics 1986–2012 John Horton Conway, fellow of Sidney Sussex College, Cambridge 1964–1970; fellow of Gonville and Caius College, Cambridge 1970-1986 Roger Cotes Percy John Daniell Philip Dawid Harold Davenport James Davenport, undergraduate and research student at Trinity College, Cambridge Rollo Davidson, undergraduate and research fellow of Trinity College, Cambridge 1962–1970, fellow-elect of Churchill College, Cambridge Augustus De Morgan Paul Dirac, fellow of St. John's College, Cambridge 1927–1969; Lucasian Professor of Mathematics 1932-1969 Simon Donaldson, undergraduate at Pembroke College, Cambridge 1976-1979 Arthur Stanley Eddington Andrew Forsyth, fellow of Trinity College, Cambridge; Sadleirian Professor of Pure Mathematics
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Wikipedia - List of Cambridge mathematicians - A - F
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Section: G - M. Anil Kumar Gain, Fellow of the Royal Statistical Society James Glaisher Peter Goddard, Master of St John's College, Cambridge 1994-2004 William Timothy Gowers, fellow of Trinity College, Cambridge ?- ; Rouse Ball Professor of Mathematics 1998- Geoffrey Grimmett, fellow of Churchill College, Cambridge, Professor of Mathematical Statistics 1992- Ian Grojnowski, faculty member of DPMMS, 1999- G. H. Hardy, fellow of Trinity College, Cambridge 1900–1919, 1931–1942; Sadleirian Professor of Pure Mathematics 1931-1942 Stephen Hawking, fellow of Gonville and Caius College, Cambridge 1966–2018; Lucasian Professor of Mathematics 1979-2009 Nigel Hitchin, fellow of Gonville and Caius College, Cambridge, Rouse Ball Professor of Mathematics 1994-1997 E. W. Hobson James Jeans Harold Jeffreys, fellow of St John's College, Cambridge 1914–1989; Plumian Professor of Astronomy 1946-1958 Vinod Johri, Commonwealth fellow for post-doctorate work at Department of Applied Mathematics and Theoretical Physics, Cambridge University, 1967-1968 Thomas Jones, mathematician, fellow of Trinity College, Cambridge Richard Jozsa, holder of the Leigh Trapnell Chair in Quantum Physics Frank Kelly, fellow 1976-2006 and master 2006- of Christ's College, professor of the Mathematics of Systems David George Kendall, fellow of Churchill College, Cambridge, Professor of Mathematical Statistics 1962-1985 John Maynard Keynes, B.A.
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Wikipedia - List of Cambridge mathematicians - G - M
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