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Augustin-Louis Cauchy

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Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics. [1]

158 relations: Absolute convergence, Abstract algebra, Age of Enlightenment, American Academy of Arts and Sciences, Arcueil, Argument principle, Augustin-Jean Fresnel, Augustin-Louis Cauchy, École des ponts ParisTech, École Polytechnique, Baron, Bibliothèque nationale de France, Bureau des Longitudes, Burnside's lemma, Calculus, Cambridge University Press, Canal de l'Ourcq, Cauchy (crater), Cauchy boundary condition, Cauchy condensation test, Cauchy distribution, Cauchy formula for repeated integration, Cauchy horizon, Cauchy matrix, Cauchy momentum equation, Cauchy principal value, Cauchy problem, Cauchy product, Cauchy sequence, Cauchy stress tensor, Cauchy surface, Cauchy's convergence test, Cauchy's equation, Cauchy's functional equation, Cauchy's integral formula, Cauchy's integral theorem, Cauchy's theorem (geometry), Cauchy's theorem (group theory), Cauchy–Binet formula, Cauchy–Euler equation, Cauchy–Hadamard theorem, Cauchy–Kowalevski theorem, Cauchy–Rassias stability, Cauchy–Riemann equations, Cauchy–Schwarz inequality, Celestial mechanics, Charles Hermite, Charles X of France, Circle, Collège de France, ..., Complex analysis, Complex plane, Conic section, Dictionary of Scientific Biography, Dispersion (optics), Elasticity (physics), Euler characteristic, Feedback, Fellow of the Royal Society of Edinburgh, Fermat polygonal number theorem, Foundations of Science, France, Francesco Faà di Bruno, French Academy of Sciences, French Revolution, Fribourg, Gaspard Monge, Generality of algebra, Great Famine (Ireland), Guglielmo Libri Carucci dalla Sommaja, Hans Freudenthal, Henri, Count of Chambord, Holomorphic function, House of Orléans, Infinitesimal, Institut Catholique de Paris, Institut de France, Integral test for convergence, Jean-Marie Duhamel, Jean-Victor Poncelet, John Colson, Joseph Liouville, Joseph-Louis Lagrange, July Revolution, Kingdom of France, Last rites, Latitude, Laurent series, Lazare Carnot, Leonhard Euler, Limit of a function, Limit of a sequence, List of monarchs of Sardinia, List of the 72 names on the Eiffel Tower, List of things named after Augustin-Louis Cauchy, Longitude, Louis François Cauchy, Louis Philippe I, Louis Poinsot, Louis XVIII of France, Lycée Henri-IV, Mathematical analysis, Mathematical physics, Mathematician, Mathematics, Matrix (mathematics), Maximilien Robespierre, Mechanics, Napoleon, Napoleon III, Negative-feedback amplifier, Neighbourhood, Niels Henrik Abel, Non-standard analysis, Nyquist stability criterion, Operational calculus, Optics, Paris, Peano existence theorem, Permutation group, Physicist, Physics, Pierre Alphonse Laurent, Pierre de Fermat, Pierre-Simon Laplace, Polarization (waves), Polyhedron, Pont de Saint-Cloud, Potato starch, Prague, Problem of Apollonius, Q-Pochhammer symbol, Random House Webster's Unabridged Dictionary, Regular polyhedron, Reign of Terror, Residue (complex analysis), Residue theorem, Robin Hartshorne, Root test, Rouen, Royal Society, Royal Swedish Academy of Sciences, Sceaux, Hauts-de-Seine, Second French Empire, Signed-digit representation, Siméon Denis Poisson, Society of Jesus, Society of Saint Vincent de Paul, Springer Science+Business Media, Stress (mechanics), Symmetric function, Symmetric group, Taylor's theorem, Themistocles M. Rassias, Uniform continuity, Viktor Bunyakovsky, Wave, Zeros and poles. Expand index (108 more) »

Absolute convergence

In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.

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Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

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Age of Enlightenment

The Enlightenment (also known as the Age of Enlightenment or the Age of Reason; in lit in Aufklärung, "Enlightenment", in L’Illuminismo, “Enlightenment” and in Spanish: La Ilustración, "Enlightenment") was an intellectual and philosophical movement that dominated the world of ideas in Europe during the 18th century, "The Century of Philosophy".

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American Academy of Arts and Sciences

The American Academy of Arts and Sciences is one of the oldest learned societies in the United States of America.

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Arcueil

Arcueil is a commune in the Val-de-Marne department in the southern suburbs of Paris, France.

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Argument principle

In complex analysis, the argument principle (or Cauchy's argument principle) relates the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.

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Augustin-Jean Fresnel

Augustin-Jean Fresnel (10 May 178814 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s until the end of the 19th century.

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Augustin-Louis Cauchy

Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.

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École des ponts ParisTech

École des Ponts ParisTech (originally called École nationale des ponts et chaussées or ENPC, also nicknamed Ponts) is a university-level institution of higher education and research in the field of science, engineering and technology.

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École Polytechnique

École Polytechnique (also known as EP or X) is a French public institution of higher education and research in Palaiseau, a suburb southwest of Paris.

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Baron

Baron is a rank of nobility or title of honour, often hereditary.

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Bibliothèque nationale de France

The (BnF, English: National Library of France) is the national library of France, located in Paris.

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Bureau des Longitudes

The Bureau des Longitudes is a French scientific institution, founded by decree of 25 June 1795 and charged with the improvement of nautical navigation, standardisation of time-keeping, geodesy and astronomical observation.

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Burnside's lemma

Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma or the orbit-counting theorem, is a result in group theory which is often useful in taking account of symmetry when counting mathematical objects.

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Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Canal de l'Ourcq

The Canal de l'Ourcq is a 108.1 km (67.2 mi) long canal of in the Île-de-France region (greater Paris) with 10 locks.

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Cauchy (crater)

Cauchy is a small lunar impact crater on the eastern Mare Tranquillitatis.

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Cauchy boundary condition

In mathematics, a Cauchy boundary conditions augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so to ensure that a unique solution exists.

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Cauchy condensation test

In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series.

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Cauchy distribution

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.

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Cauchy formula for repeated integration

The Cauchy formula for repeated integration, named after Augustin Louis Cauchy, allows one to compress n antidifferentiations of a function into a single integral (cf. Cauchy's formula).

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Cauchy horizon

In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory of partial differential equations).

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Cauchy matrix

In mathematics, a Cauchy matrix, named after Augustin Louis Cauchy, is an m×n matrix with elements aij in the form a_.

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Cauchy momentum equation

The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum.

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Cauchy principal value

In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.

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Cauchy problem

A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain.

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Cauchy product

In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series.

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Cauchy sequence

In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.

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Cauchy stress tensor

In continuum mechanics, the Cauchy stress tensor \boldsymbol\sigma, true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy.

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Cauchy surface

Intuitively, a Cauchy surface is a plane in space-time which is like an instant of time; its significance is that giving the initial conditions on this plane determines the future (and the past) uniquely.

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Cauchy's convergence test

The Cauchy convergence test is a method used to test infinite series for convergence.

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Cauchy's equation

Cauchy's equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material.

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Cauchy's functional equation

Cauchy's functional equation is the functional equation Solutions to this are called additive functions.

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Cauchy's integral formula

In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis.

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Cauchy's integral theorem

In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane.

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Cauchy's theorem (geometry)

Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy.

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Cauchy's theorem (group theory)

Cauchy's theorem is a theorem in the mathematics of group theory, named after Augustin Louis Cauchy.

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Cauchy–Binet formula

In linear algebra, the Cauchy–Binet formula, named after Augustin-Louis Cauchy and Jacques Philippe Marie Binet, is an identity for the determinant of the product of two rectangular matrices of transpose shapes (so that the product is well-defined and square).

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Cauchy–Euler equation

In mathematics, a Cauchy-Euler equation (most known as the Euler-Cauchy equation, or simply Euler's equation) is a linear homogeneous ordinary differential equation with variable coefficients.

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Cauchy–Hadamard theorem

In mathematics, the Cauchy–Hadamard theorem is a result in complex analysis named after the French mathematicians Augustin Louis Cauchy and Jacques Hadamard, describing the radius of convergence of a power series.

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Cauchy–Kowalevski theorem

In mathematics, the Cauchy–Kowalevski theorem (also written as the Cauchy–Kovalevskaya theorem) is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems.

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Cauchy–Rassias stability

A classical problem of Stanislaw Ulam in the theory of functional equations is the following: When is it true that a function which approximately satisfies a functional equation E must be close to an exact solution of E? In 1941, Donald H. Hyers gave a partial affirmative answer to this question in the context of Banach spaces.

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Cauchy–Riemann equations

In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.

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Cauchy–Schwarz inequality

In mathematics, the Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas.

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Celestial mechanics

Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects.

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Charles Hermite

Prof Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

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Charles X of France

Charles X (Charles Philippe; 9 October 1757 – 6 November 1836) was King of France from 16 September 1824 until 2 August 1830.

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Circle

A circle is a simple closed shape.

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Collège de France

The Collège de France, founded in 1530, is a higher education and research establishment (grand établissement) in France and an affiliate college of PSL University.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Dictionary of Scientific Biography

The Dictionary of Scientific Biography is a scholarly reference work that was published from 1970 through 1980.

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Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

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Elasticity (physics)

In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.

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Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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Feedback

Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop.

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Fellow of the Royal Society of Edinburgh

Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland judges to be "eminently distinguished in their subject".

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Fermat polygonal number theorem

In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most -gonal numbers.

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Foundations of Science

Foundations of Science is a peer-reviewed interdisciplinary academic journal focussing on methodological and philosophical topics concerning the structure and the growth of science.

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France

France, officially the French Republic (République française), is a sovereign state whose territory consists of metropolitan France in Western Europe, as well as several overseas regions and territories.

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Francesco Faà di Bruno

The Blessed Francesco Faà di Bruno (29 March 1825 – 27 March 1888) was an Italian priest and advocate of the poor, a leading mathematician of his era and a noted religious musician.

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French Academy of Sciences

The French Academy of Sciences (French: Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research.

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French Revolution

The French Revolution (Révolution française) was a period of far-reaching social and political upheaval in France and its colonies that lasted from 1789 until 1799.

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Fribourg

Fribourg (Fribôrg or Friboua) or Freiburg (German, or Freiburg im Üechtland, Swiss German pronunciation:; Friborgo or Friburgo; Friburg) is the capital of the Swiss canton of Fribourg and the district La Sarine.

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Gaspard Monge

Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, the inventor of descriptive geometry (the mathematical basis of technical drawing), and the father of differential geometry.

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Generality of algebra

In the history of mathematics, the generality of algebra was a phrase used by Augustin-Louis Cauchy to describe a method of argument that was used in the 18th century by mathematicians such as Leonhard Euler and Joseph-Louis Lagrange,.

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Great Famine (Ireland)

The Great Famine (an Gorta Mór) or the Great Hunger was a period of mass starvation, disease, and emigration in Ireland between 1845 and 1849.

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Guglielmo Libri Carucci dalla Sommaja

Guglielmo Libri Carucci dalla Sommaja (January 1, 1803 – September 28, 1869) was an Italian count and mathematician, who became known for his love and subsequent theft of ancient and precious manuscripts.

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Hans Freudenthal

Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish-German-born Dutch mathematician.

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Henri, Count of Chambord

Henri, Count of Chambord (Henri Charles Ferdinand Marie Dieudonné d'Artois, duc de Bordeaux, comte de Chambord); 29 September 1820 – 24 August 1883) was disputedly King of France from 2 to 9 August 1830 as Henry V, although he was never officially proclaimed as such. Afterwards, he was the Legitimist pretender to the throne of France from 1844 to 1883. He was nearly received as King in 1871 and 1873. Henri was the posthumous son of Charles Ferdinand, Duke of Berry, younger son of Charles X of France, by his wife, Princess Carolina of Naples and Sicily, daughter of King Francis I of the Two Sicilies. As the grandson of the King Charles X of France, Henri was a Petit-Fils de France. He also was the last legitimate descendant in the male line of Louis XV of France (His grandfather Charles X was a grandson of Louis XV).

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Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.

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House of Orléans

The 4th House of Orléans, sometimes called House of Bourbon-Orléans (Maison de Bourbon-Orléans) to distinguish it, is the fourth holder of a surname previously used by several branches of the Royal House of France, all descended in the legitimate male line from the dynasty's founder, Hugh Capet.

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Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them.

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Institut Catholique de Paris

The Institut Catholique de Paris (ICP), known in English as the Catholic University of Paris (and in Latin as Universitas catholica Parisiensis), is a private university located in Paris, France.

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Institut de France

The Institut de France (Institute of France) is a French learned society, grouping five académies, the most famous of which is the Académie française.

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Integral test for convergence

In mathematics, the integral test for convergence is a method used to test infinite series of non-negative terms for convergence.

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Jean-Marie Duhamel

Jean-Marie Constant Duhamel (5 February 1797 – 29 April 1872) was a French mathematician and physicist.

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Jean-Victor Poncelet

Jean-Victor Poncelet (1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique.

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John Colson

John Colson (1680–1760) was an English clergyman and mathematician, Lucasian Professor of Mathematics at Cambridge University.

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Joseph Liouville

Joseph Liouville FRS FRSE FAS (24 March 1809 – 8 September 1882) was a French mathematician.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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July Revolution

The French Revolution of 1830, also known as the July Revolution (révolution de Juillet), Third French Revolution or Trois Glorieuses in French ("Three Glorious "), led to the overthrow of King Charles X, the French Bourbon monarch, and the ascent of his cousin Louis Philippe, Duke of Orléans, who himself, after 18 precarious years on the throne, would be overthrown in 1848.

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Kingdom of France

The Kingdom of France (Royaume de France) was a medieval and early modern monarchy in Western Europe.

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Last rites

The last rites, in Catholicism, are the last prayers and ministrations given to many Catholics when possible shortly before death.

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Latitude

In geography, latitude is a geographic coordinate that specifies the north–south position of a point on the Earth's surface.

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Laurent series

In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree.

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Lazare Carnot

Lazare Nicolas Marguerite, Count Carnot (13 May 1753 – 2 August 1823) was a French mathematician, physicist and politician.

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Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

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Limit of a function

Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

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Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

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List of monarchs of Sardinia

The following is a list of rulers of Sardinia, in particular, of the monarchs of the Kingdom of Sardinia and Corsica from 1323 and then of the Kingdom of Sardinia from 1479 to 1861.

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List of the 72 names on the Eiffel Tower

On the Eiffel Tower, seventy-two names of French scientists, engineers, and mathematicians are engraved in recognition of their contributions.

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List of things named after Augustin-Louis Cauchy

Many things are named after the 19th-century French mathematician Augustin-Louis Cauchy.

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Longitude

Longitude, is a geographic coordinate that specifies the east-west position of a point on the Earth's surface.

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Louis François Cauchy

Louis François Cauchy (27 May 1760 – 28 December 1848) was a senior French government official and the father of the mathematician Augustin-Louis Cauchy.

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Louis Philippe I

Louis Philippe I (6 October 1773 – 26 August 1850) was King of the French from 1830 to 1848 as the leader of the Orléanist party.

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Louis Poinsot

Louis Poinsot (3 January 1777 – 5 December 1859) was a French mathematician and physicist.

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Louis XVIII of France

Louis XVIII (Louis Stanislas Xavier; 17 November 1755 – 16 September 1824), known as "the Desired" (le Désiré), was a monarch of the House of Bourbon who ruled as King of France from 1814 to 1824, except for a period in 1815 known as the Hundred Days.

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Lycée Henri-IV

The Lycée Henri-IV is a public secondary school located in Paris.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematical physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Maximilien Robespierre

Maximilien François Marie Isidore de Robespierre (6 May 1758 – 28 July 1794) was a French lawyer and politician, as well as one of the best known and most influential figures associated with the French Revolution and the Reign of Terror.

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Mechanics

Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

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Napoleon

Napoléon Bonaparte (15 August 1769 – 5 May 1821) was a French statesman and military leader who rose to prominence during the French Revolution and led several successful campaigns during the French Revolutionary Wars.

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Napoleon III

Louis-Napoléon Bonaparte (born Charles-Louis Napoléon Bonaparte; 20 April 1808 – 9 January 1873) was the President of France from 1848 to 1852 and as Napoleon III the Emperor of the French from 1852 to 1870.

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Negative-feedback amplifier

A Negative-feedback amplifier (or feedback amplifier) is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal.

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Neighbourhood

A neighbourhood (British English), or neighborhood (American English; see spelling differences), is a geographically localised community within a larger city, town, suburb or rural area.

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Niels Henrik Abel

Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.

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Non-standard analysis

The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.

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Nyquist stability criterion

In control theory and stability theory, the Nyquist stability criterion, discovered by Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, on is a graphical technique for determining the stability of a dynamical system.

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Operational calculus

Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation.

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Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Paris

Paris is the capital and most populous city of France, with an area of and a population of 2,206,488.

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Peano existence theorem

In mathematics, specifically in the study of ordinary differential equations, the Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees the existence of solutions to certain initial value problems.

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Permutation group

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself).

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Physicist

A physicist is a scientist who has specialized knowledge in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.

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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Pierre Alphonse Laurent

Pierre Alphonse Laurent (18 July 1813 – 2 September 1854) was a French mathematician and Military Officer best known as the discoverer of the Laurent series, an expansion of a function into an infinite power series, generalizing the Taylor series expansion.

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Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace (23 March 1749 – 5 March 1827) was a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

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Polarization (waves)

Polarization (also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations.

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Polyhedron

In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.

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Pont de Saint-Cloud

The pont de Saint-Cloud (Saint-Cloud Bridge) is a French bridge constructed of metal which crosses the Seine between the communes of Boulogne-Billancourt and Saint-Cloud in the French department of Hauts-de-Seine.

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Potato starch

Potato starch is starch extracted from potatoes.

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Prague

Prague (Praha, Prag) is the capital and largest city in the Czech Republic, the 14th largest city in the European Union and also the historical capital of Bohemia.

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Problem of Apollonius

In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1).

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Q-Pochhammer symbol

In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a ''q''-analog of the Pochhammer symbol.

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Random House Webster's Unabridged Dictionary

Random House Webster's Unabridged Dictionary is a large American dictionary, first published in 1966 as The Random House Dictionary of the English Language: The Unabridged Edition.

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Regular polyhedron

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.

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Reign of Terror

The Reign of Terror, or The Terror (la Terreur), is the label given by some historians to a period during the French Revolution after the First French Republic was established.

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Residue (complex analysis)

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.

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Residue theorem

In complex analysis, a discipline within mathematics, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals as well.

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Robin Hartshorne

Robin Cope Hartshorne (born March 15, 1938) is an American mathematician.

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Root test

In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series.

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Rouen

Rouen (Frankish: Rodomo; Rotomagus, Rothomagus) is a city on the River Seine in the north of France.

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Royal Society

The President, Council and Fellows of the Royal Society of London for Improving Natural Knowledge, commonly known as the Royal Society, is a learned society.

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Royal Swedish Academy of Sciences

The Royal Swedish Academy of Sciences or Kungliga Vetenskapsakademien is one of the Royal Academies of Sweden.

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Sceaux, Hauts-de-Seine

Sceaux is a commune in the southern suburbs of Paris, France.

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Second French Empire

The French Second Empire (Second Empire) was the Imperial Bonapartist regime of Napoleon III from 1852 to 1870, between the Second Republic and the Third Republic, in France.

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Signed-digit representation

In mathematical notation for numbers, signed-digit representation is a positional system with signed digits; the representation may not be unique.

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Siméon Denis Poisson

Baron Siméon Denis Poisson FRS FRSE (21 June 1781 – 25 April 1840) was a French mathematician, engineer, and physicist, who made several scientific advances.

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Society of Jesus

The Society of Jesus (SJ – from Societas Iesu) is a scholarly religious congregation of the Catholic Church which originated in sixteenth-century Spain.

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Society of Saint Vincent de Paul

The Society of St Vincent de Paul (SVP or SVdP or SSVP) is an international voluntary organization in the Catholic Church, founded in 1833 for the sanctification of its members by personal service of the poor.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Stress (mechanics)

In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.

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Symmetric function

In mathematics, a symmetric function of n variables is one whose value given n arguments is the same no matter the order of the arguments.

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

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Taylor's theorem

In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.

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Themistocles M. Rassias

Themistocles M. Rassias (Θεμιστοκλής Μ. Ρασσιάς; born April 2, 1951) is a Greek mathematician, and a Professor at the National Technical University of Athens (Eθνικό Μετσόβιο Πολυτεχνείο), Greece.

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Uniform continuity

In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f(x) and f(y) be as close to each other as we please by requiring only that x and y are sufficiently close to each other; unlike ordinary continuity, the maximum distance between f(x) and f(y) cannot depend on x and y themselves.

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Viktor Bunyakovsky

Viktor Yakovlevich Bunyakovsky (Ви́ктор Я́ковлевич Буняко́вский, Ві́ктор Я́кович Буняко́вський;, Bar, Podolia Governorate, Russian Empire –, St. Petersburg, Russian Empire) was a Russian mathematician, member and later vice president of the Petersburg Academy of Sciences.

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Wave

In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport.

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Zeros and poles

In mathematics, a zero of a function is a value such that.

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A. L. Cauchy, A. L. de Cauchy, Augustin Cauchy, Augustin Louis Baron Cauchy, Augustin Louis Cauchy, Augustin Louis, Baron Cauchy, Augustin louis cauchy, Augustin-Louis, Baron Cauchy, Augustine Louis Cauchy, Baron Augustin-Louis Cauchy, Cauchy, Cauchy, Augustin Louis.

References

[1] https://en.wikipedia.org/wiki/Augustin-Louis_Cauchy

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