However, several of his students became influential mathematicians, among them Richard Dedekind, Bernhard Riemann, and Friedrich Bessel.

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

Historically, the concept of fundamental group first emerged in the theory of Riemann surfaces, in the work of Bernhard Riemann, Henri Poincaré and Felix Klein, where it describes the monodromy properties of complex functions, as well as providing a complete topological classification of closed surfaces.

Heine proposed that Cantor solve an open problem that had eluded Dirichlet, Lipschitz, Bernhard Riemann, and Heine himself: the uniqueness of the representation of a function by trigonometric series.

A rigorous mathematical definition of the integral was given by Bernhard Riemann.

Additional impetus to consider continuous groups came from ideas of Bernhard Riemann, on the foundations of geometry, and their further development in the hands of Klein.

* Bernhard Riemann

Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler, Carl Gauss, Johann Bernoulli, Jacob Bernoulli, Aryabhata, Brahmagupta, Bhaskara II, Nilakantha Somayaji, Omar Khayyám, Muhammad ibn Mūsā al-Khwārizmī, Bernhard Riemann, Gottfried Leibniz, Andrey Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Alan Turing, von Neumann, Kurt Gödel, Joseph-Louis Lagrange, Georg Cantor, William Rowan Hamilton, Carl Jacobi, Évariste Galois, Nikolay Lobachevsky, Rene Descartes, Joseph Fourier, Pierre-Simon Laplace, Alonzo Church, Nikolay Bogolyubov and Pierre de Fermat.

Bernhard Riemann in his memoir " On the Number of Primes Less Than a Given Magnitude " published in 1859 extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation and established a relation between its zeros and the distribution of prime numbers.

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.

In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180 ° and circles have a ratio of circumference-to-diameter that is less than pi.

Tensors were first conceived by Tullio Levi-Civita and Gregorio Ricci-Curbastro, who continued the earlier work of Bernhard Riemann and Elwin Bruno Christoffel and others, as part of the absolute differential calculus.

* September 17 – Bernhard Riemann, German mathematician ( d. 1866 )

* Bernhard Riemann formulates the Riemann hypothesis, one of the most important open problems of contemporary mathematics.

* July 20 – Bernhard Riemann, German mathematician ( b. 1826 )

In the 19th century, Augustin Cauchy finally developed a rigorous theory of limits, and Bernhard Riemann followed up on this by formalizing what is now called the Riemann integral.

In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as Augustin Louis Cauchy ( 1789 – 1857 ), Bernhard Riemann ( 1826 – 1866 ), and Karl Weierstrass ( 1815 – 1897 ).

Bernhard Riemann, in a famous lecture in 1854, founded the field of Riemannian geometry, discussing in particular the ideas now called manifolds, Riemannian metric, and curvature.

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 standard way to express curvature of Riemannian manifolds.

Bernhard ’ s focus on Jungian depth psychology proved to be the single greatest influence on Fellini ’ s mature style and marked the turning point in his work from neorealism to filmmaking that was “ primarily oneiric ”.

The following has been proved by Bernhard Neumann and Angus Macintyre:

Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper On the Number of Primes Less Than a Given Magnitude, in which he defined his zeta function and proved its basic properties.

The combined effort of Bernhard Eunom Philippi with Vicente Perez Rosales, made the colonisation a reality and proved to be a success, as the region later was very well developed in agricultural and forestry, with European technology.

In mathematics, the Riemann series theorem ( also called the Riemann rearrangement theorem ), named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series is conditionally convergent, then its terms can be arranged in a permutation so that the series converges to any given value, or even diverges.

* Bernhard Riemann, a German mathematician, submits his habilitation thesis Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe (" About the representability of a function by a trigonometric series "), in which he describes the Riemann integral.

This series also featured Sandra Bernhard as his girlfriend Ms. Gsptlsnz.

* Bernard de Neumann, ( aka Bernhard von Neumann ), British, (" The Mathematician " in a series of portraits by John Wonnacott ) – Mathematician, Software Engineer, Naval Historian

Among the accusations against Vesco were that he parked funds belonging to IOS investors in a series of dummy corporations, one of which had an Amsterdam address that was later linked to Prince Bernhard of the Netherlands, and that he broke into a Swiss bank vault to obtain shares.

Bernhard started the Collection of British and American Authors in 1841, a reprint series familiar to anglophone travellers on the continent of Europe.

Hosted by Rip Taylor, the series is a parody of beauty contests, and featured six female contestants ( including the occasional overweight ones, not-yet-famous Sandra Bernhard and actress Teresa Ganzel, and on at least one occasion a male dressed in drag ) competing for the title of "$ 1. 98 Beauty Queen ".

Halmstads BK won the Bernhard Aronssons vandringspris after defeating IS Halmia in 1922 ; the club also won a series of tournaments in Jönköping, Malmö and Ängelholm, however the district championship was lost to Varberg this year.

Producer Harvey Bernhard, who produced the last three films, felt there could be more done to the series.

Bernhard and Horn also prepared for battle, although this may not have been a mutual decision.

Of his later works may be mentioned Die Dresdner Gemäldegallerie ( 1844 ), and the tragedies Herzog Bernhard ( 1855 ) and Der Sohn des Fürsten ( 1858 ).

The precedent of Bernhard holds that CE may be used as defense against any party who has fully and fairly litigated an issue in a previous action.

It was invented by Bernhard Schmidt in 1931, although it may have been independently invented by Finnish astronomer Yrjö Väisälä in 1924 ( sometimes called the Schmidt-Väisälä camera ).

The Arnold Bernhard Library, Carl Hansen Student Center, university administration, and many of the student residences may be found on this campus.

They may have been taken by either Ernst Hoffmann or Bernhard Walter, two SS men responsible for fingerprinting and taking photo IDs of those prisoners who were not selected for extermination.

Therefore it may be concluded that a church tower or chapel existed since before the year 1500: Bernhard Holtmann mentions the year 1490.

The election was also notable for two non-politician semi-celebrities running on third-party tickets: Bernhard Goetz, who had achieved fame in 1984 as the " subway vigilante " for shooting four youths who may have tried to rob him, on the Fusion Party ticket, and Kenny Kramer, who was the inspiration for the character Cosmo Kramer on the TV show Seinfeld, on the Libertarian Party ticket.

In March 1832, one third of the group left the Society and some began following Bernhard Müller, who claimed to be the Lion of Judah.

In pieces such as the Bernhard Molique " Concerto No 1 in G for concertina and orchestra ", or Percy Grainger's " Shepherd's Hey ", four, five and six note chords are not uncommon, and would be difficult or impossible to play without using all the fingers.

Prince Bernhard, who had remained in London with Queen Wilhelmina and members of the exiled Dutch government, was able to visit his family in Canada and be there for Margriet's birth.

The Secretary for Foreign Affairs, Bernhard von Bülow, did not believe that Britain would be a reliable ally because any future Cabinet could reverse the diplomatic policy of its predecessors, and because Parliament and public opinion often made difficulties about Britain's alliance commitments.

They would continue to be friends for several years, with Bernhard even making an appearance in Madonna's movie Truth or Dare.

In September 2008, Bernhard created controversy during one of her one-woman shows by saying that Republican Vice Presidential candidate Sarah Palin would be " gang-raped by my big black brothers " if she entered Manhattan.

Bernhard has stated that Excuses for Bad Behavior ( Part One ) will be re-released in late 2007.

Rabbi Bernhard stated that the only way for a member of the Lemba tribe to be recognized as a Jew is to undergo the formal Halakhic conversion process, after which they " would be welcomed with open arms.

With only one match remaining to be completed, between Hale Irwin for the United States and Bernhard Langer for the Europeans, the United States team led by one point.

The holders of the puppet strings turn out to be a " psychotic American corporation ," Mayflower Industries, run by husband and wife Darwin ( Richard E. Grant ) and Minerva Mayflower ( Sandra Bernhard ) and a blade-slinging butler, Alfred ( Donald Burton ).

Bernhard felt that whatever the odds an attempt must be made to relieve Nordlingen.

" Authors Günter Grass, Thomas Bernhard, Peter Handke, Italo Calvino, John Fowles, Angela Carter, John Banville, Michel Tournier, Giannina Braschi, Willem Brakman and Louis Ferron are widely considered postmodernist, but might " just as easily be categorized ... magic realist.

Bernhard Riemann extended Gauss's theory to higher dimensional spaces called manifolds in a way that also allows distances and angles to be measured and the notion of curvature to be defined, again in a way that was intrinsic to the manifold and not dependent upon its embedding in higher-dimensional spaces.

Later in the 19th century, the German mathematician Bernhard Riemann developed Elliptic geometry, another non-Euclidean geometry where no parallel can be found and the sum of angles in a triangle is more than 180 °.

In 1937, Augsburg elected Bernhard Christensen, an erudite and scholarly teacher, to be president ( 1938-1962 ).

Various names were given to these positions ( Damiano, for example, called them " subtelties "); the first book which called them " studies " appears to be Chess Studiels, an 1851 publication by Josef Kling and Bernhard Horwitz, which is sometimes also regarded as the starting point for the modern endgame study.

Despite these attempts calculus continued to be developed using non-rigorous methods until around 1830 when Augustin Cauchy, and later Bernhard Riemann and Karl Weierstrass, redefined the derivative and integral using a rigorous definition of the concept of limit.

After the war he tried to go into business, but when his sterling notes were checked by the Bank of England they were found to be counterfeit ( see Operation Bernhard ).