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Bernhard Riemann

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Georg Friedrich Bernhard Riemann (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting and revolutionary contributions to analysis, number theory, and differential geometry. [1]

96 relations: Abelian variety, Adolf Hurwitz, Albert Einstein, Alfred Clebsch, Algebraic geometry, Analytic number theory, Arnold Sommerfeld, Bible, Carl Friedrich Gauss, Carl Gustav Jacob Jacobi, Carl Wolfgang Benjamin Goldschmidt, Cauchy–Riemann equations, Complex analysis, Complex manifold, Crelle's Journal, Dannenberg (Elbe), David Hilbert, Detlef Laugwitz, Differential geometry, Dimension, Dirichlet's principle, Elliptic integral, Felix Klein, Fourier series, Frederick William University, Frobenius, General relativity, Georg Cantor, Germany, Gotthold Eisenstein, Gustav Roch, Habilitation, Hanover, Harmonic function, HarperCollins, Henri Poincaré, Hermann Schwarz, Hypergeometric function, Injective function, Italy, Jacobian variety, Jakob Steiner, Jameln, Karl Weierstrass, Kingdom of Hanover, Kingdom of Italy, Lake Maggiore, Laplace's equation, Least squares, List of things named after Bernhard Riemann, ..., Logarithm, Lutheranism, Lyceum, Manifold, Marcus du Sautoy, Mathematical analysis, Mathematical physics, Mathematics, Monodromy matrix, Moritz Abraham Stern, Napoleonic Wars, Non-Euclidean geometry, Number theory, On the Number of Primes Less Than a Given Magnitude, Peter Gustav Lejeune Dirichlet, Philology, Physics, Prime number, Prime Obsession, Prime-counting function, Real analysis, Riemann curvature tensor, Riemann hypothesis, Riemann integral, Riemann mapping theorem, Riemann surface, Riemann zeta function, Riemann–Lebesgue lemma, Riemann–Roch theorem, Riemann–Stieltjes integral, Riemannian geometry, Riemannian manifold, Set theory, Solomon Lefschetz, Square root, Tensor, The Music of the Primes, Theology, Theorema Egregium, Theta function, Topology, Tuberculosis, Uniformization theorem, University of Göttingen, Verbania, William Kingdon Clifford. Expand index (46 more) »

Abelian variety

In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.

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Adolf Hurwitz

Adolf Hurwitz (26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory.

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Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist.

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Alfred Clebsch

Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Analytic number theory

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.

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Arnold Sommerfeld

Arnold Johannes Wilhelm Sommerfeld, (5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored a large number of students for the new era of theoretical physics.

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The Bible (from Koine Greek τὰ βιβλία, tà biblía, "the books") is a collection of texts sacred in Judaism and Christianity.

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß,; Carolus Fridericus Gauss) (30 April 177723 February 1855) was a German mathematician who contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, astronomy, matrix theory, and optics.

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Carl Gustav Jacob Jacobi

Carl Gustav Jacob Jacobi (10 December 1804 – 18 February 1851) was a German mathematician, who made fundamental contributions to elliptic functions, dynamics, differential equations, and number theory.

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Carl Wolfgang Benjamin Goldschmidt

Carl Wolfgang Benjamin Goldschmidt (1807–February 15, 1851) was a German astronomer, mathematician, and physicist of Jewish descent who was a professor of astronomy at the University of Göttingen.

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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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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 manifold

In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.

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Crelle's Journal

Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).

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Dannenberg (Elbe)

Dannenberg is a town in the district Lüchow-Dannenberg, in Lower Saxony, Germany.

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David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.

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Detlef Laugwitz

Detlef Laugwitz (1932–2000) was a German mathematician and historian, who worked in differential geometry, history of mathematics, functional analysis, and non-standard analysis.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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Dirichlet's principle

In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation.

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Elliptic integral

In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse.

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Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory.

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Fourier series

In mathematics, a Fourier series is a way to represent a (wave-like) function as the sum of simple sine waves.

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Frederick William University

The Frederick William University (Friedrich-Wilhelms-Universität, Alma Mater Berolinensis) was a university in Berlin, Germany.

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Frobenius is a surname.

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General relativity

General relativity, also known as the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.

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Germany (Deutschland), officially the Federal Republic of Germany (Bundesrepublik Deutschland), is a federal parliamentary republic in western-central Europe.

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Gotthold Eisenstein

Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician.

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Gustav Roch

Gustav Roch (December 9, 1839 – November 21, 1866) was a German mathematician who made significant contributions to the theory of Riemann surfaces in a career that was prematurely curtailed at the age of 26.

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Habilitation (from Latin habilis "fit, proper, skillful") is the highest academic qualification a scholar can achieve by his or her own pursuit in many countries in Europe, Central Asia, Egypt and the Caucasus.

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Hanover or Hannover (Hannover), on the River Leine, is the capital of the federal state of Lower Saxony (Niedersachsen), Germany and was once by personal union the family seat of the Hanoverian Kings of Great Britain, under their title as the dukes of Brunswick-Lüneburg (later described as the Elector of Hanover).

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Harmonic function

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R (where U is an open subset of Rn) which satisfies Laplace's equation, i.e. everywhere on U. This is usually written as or.

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HarperCollins Publishers LLC is one of the world's largest publishing companies and, alongside Hachette, Holtzbrinck/Macmillan, Penguin Random House, and Simon & Schuster, is part of the "Big Five" English-language publishing companies.

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Henri Poincaré

Jules Henri Poincaré (29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and a philosopher of science.

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Hermann Schwarz

Karl Hermann Amandus Schwarz (25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis.

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Hypergeometric function

In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.

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Injective function

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.

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Italy (Italia), officially the Italian Republic (Repubblica Italiana), is a unitary parliamentary republic in Europe.

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Jacobian variety

In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles.

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Jakob Steiner

Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry.

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Jameln is a municipality in the district Lüchow-Dannenberg, in Lower Saxony, Germany.

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Karl Weierstrass

Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".

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Kingdom of Hanover

The Kingdom of Hanover (Königreich Hannover) was established in October 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian territories after the Napoleonic era.

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Kingdom of Italy

The Kingdom of Italy (Regno d'Italia) was a state founded in 1861 when King Victor Emmanuel II of Sardinia was proclaimed King of Italy.

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Lake Maggiore

Lake Maggiore (Lago Maggiore, lit. 'Greater Lake') or Lago Verbano (Lacus Verbanus) is a large lake located on the south side of the Alps.

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Laplace's equation

In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.

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Least squares

The method of least squares is a standard approach in regression analysis to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.

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List of things named after Bernhard Riemann

The German mathematician Bernhard Riemann (1826–1866) is the eponym of many things.

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In mathematics, the logarithm is the inverse operation to exponentiation.

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Lutheranism is a major branch of Protestant Christianity that identifies with the theology of Martin Luther—a German friar, ecclesiastical reformer, and theologian.

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The lyceum is a category of educational institution defined within the education system of many countries, mainly in Europe.

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In mathematics, a manifold is a topological space that resembles Euclidean space near each point.

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Marcus du Sautoy

Marcus Peter Francis du Sautoy, OBE (born 26 August 1965) is the Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.

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Mathematical analysis

Mathematical analysis is a branch of mathematics that studies continuous change and includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions.

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Mathematical physics

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

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

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Monodromy matrix

In mathematics, and particularly ordinary differential equations, a monodromy matrix is the inverse of the fundamental matrix of a system of ODEs evaluated at the period of the coefficients of the system.

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Moritz Abraham Stern

Moritz Abraham Stern (29 June 1807 – 30 January 1894) was a German mathematician.

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Napoleonic Wars

The Napoleonic Wars (1803–1815) were a series of major conflicts pitting the French Empire led by Emperor Napoleon I against an array of European powers formed into various coalitions.

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Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

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Number theory

Number theory (or arithmeticEspecially in older sources; see two following notes.) is a branch of pure mathematics devoted primarily to the study of the integers.

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On the Number of Primes Less Than a Given Magnitude

" die Anzahl der Primzahlen unter einer gegebenen " (usual English translation: "On the Number of Primes Less Than a Given Magnitude") is a seminal 10-page paper by Bernhard Riemann published in the November 1859 edition of the Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin.

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Peter Gustav Lejeune Dirichlet

Johann Peter Gustav Lejeune Dirichlet (or; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function.

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Philology is the study of language in written historical sources; it is a combination of literary criticism, history, and linguistics.

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Physics (from knowledge of nature, from φύσις phúsis "nature") is the natural science that involves the study of 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 through space and time, along with related concepts such as 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." More broadly, it is the general analysis of nature, conducted in order 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, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the scientific revolution in the 17th century, the natural sciences emerged as unique research programs 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 of other sciences while opening new avenues of research in areas such as mathematics and philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or 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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Prime number

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

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Prime Obsession

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications.

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Prime-counting function

In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by \scriptstyle\pi(x) (unrelated to the number pi).

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Real analysis

Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable.

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Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.

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Riemann hypothesis

In mathematics, the Riemann hypothesis, proposed by, is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2.

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Riemann integral

In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.

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Riemann mapping theorem

In complex analysis, the Riemann mapping theorem states that if U is a non-empty simply connected open subset of the complex number plane C which is not all of C, then there exists a biholomorphic mapping f (i.e. a bijective holomorphic mapping whose inverse is also holomorphic) from U onto the open unit disk This mapping is known as a Riemann mapping.

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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold.

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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function, ζ(s), is a function of a complex variable s that analytically continues the sum of the infinite series which converges when the real part of s is greater than 1.

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Riemann–Lebesgue lemma

In mathematics, the Riemann–Lebesgue lemma, named after Bernhard Riemann and Henri Lebesgue, is of importance in harmonic analysis and asymptotic analysis.

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Riemann–Roch theorem

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles.

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Riemann–Stieltjes integral

In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.

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Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.

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Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

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Set theory

Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects.

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Solomon Lefschetz

Solomon Lefschetz (Соломо́н Ле́фшец; 3 September 1884 – 5 October 1972) was an American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.

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Square root

In mathematics, a square root of a number a is a number y such that, in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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Tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

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The Music of the Primes

The Music of the Primes (British subtitle: Why an Unsolved Problem in Mathematics Matters; American subtitle: Searching to Solve the Greatest Mystery in Mathematics) is a 2003 book by Marcus du Sautoy, a professor in mathematics at the University of Oxford, on the history of prime number theory.

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Theology is the systematic and rational study of concepts of God and of the nature of religious ideas, but can also mean the learned profession acquired by completing specialized training in religious studies, usually at a university, seminary, or school of divinity.

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Theorema Egregium

Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a foundational result in differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces.

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Theta function

Jacobi's original theta function \theta_1 with u.

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In mathematics, topology (from the Greek τόπος, place, and λόγος, study), is the study of topological spaces.

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Tuberculosis, MTB, or TB (short for tubercle bacillus), in the past also called phthisis, phthisis pulmonalis, or consumption, is a widespread, infectious disease caused by various strains of mycobacteria, usually Mycobacterium tuberculosis.

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Uniformization theorem

In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of the three domains: the open unit disk, the complex plane, or the Riemann sphere.

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University of Göttingen

The University of Göttingen (Georg-August-Universität Göttingen, GAU), known informally as Georgia Augusta, is a public comprehensive research university in the city of Göttingen, Germany.

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Verbania (Verbania, Verbania) is the most populous comune (municipality) and the capital city of the province of Verbano-Cusio-Ossola in the Piedmont region of northwest Italy.

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William Kingdon Clifford

William Kingdon Clifford FRS (4 May 1845 – 3 March 1879) was an English mathematician and philosopher.

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[1] https://en.wikipedia.org/wiki/Bernhard_Riemann

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