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Georg Friedrich Bernhard Riemann

MAED 3475
by

Kate Fites

on 22 April 2013

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Transcript of Georg Friedrich Bernhard Riemann

Education Riemann Sums Riemann's dissertation, completed under Gauss's supervision in 1851, was on the foundations of complex analysis.

It introduced several ideas of fundamental importance, such as the definitions of conformal mapping and simple connectivity. These are necessary for one of his main results, the Riemann mapping theorem: "any simply connected domain of the the complex plane having at least two boundary points can be conformally mapped onto the unit disk." Riemann was born on September 17, 1826 in Breselenz, Kingdom of Hanover (which is in present-day Germany). At an early age, he showed interest in history and mathematics.

14 years old - He started at a prep school in Lüneburg (where he was noticed for his math skills). The director of the school gave him a textbook on number theory by Legendre and six days later he came back saying, "That was a wonderful book! I have mastered it."

20 years old - he enrolled at Göttingen University and began his studies in theology (per his father), but later switched to philosophy to study science and mathematics. http://www2.seminolestate.edu/lvosbury/CalculusI_Folder/RiemannSumDemo.htm In 1853 Gauss asked his student Riemann to prepare an essay on the foundations of geometry. Over many months, Riemann developed his theory of higher dimensions and delivered his lecture at Göttingen in 1854 entitled Über die Hypothesen welche der Geometrie zu Grunde liegen ("On the hypotheses which underlie geometry"). When it was finally published in 1868, two years after his death, the mathematical public received it with enthusiasm and it is now recognized as one of the most important works in geometry.
The subject founded by this work is Riemannian Geometry. Riemann found the correct way to extend into n dimensions the differential geometry of surfaces, which Gauss himself proved in his theorema egregium. The fundamental object is called the Riemann curvature tensor. For the surface case, this can be reduced to a number (scalar), positive, negative or zero; the non-zero and constant cases being models of the known non-Euclidean geometries. His father, Friedrich Bernhard Riemann, was a poor Lutheran pastor who fought in the Napoleonic Wars.
His mother, Charlotte Ebell, died before any of her children had reached adulthood.

Riemann was the second of 6 children, shy and suffering from numerous nervous breakdowns. He exhibited exceptional mathematical skills, such as calculation abilities, from an early age but suffered from timidity and a fear of speaking in public. Georg Friedrich
Bernhard Riemann a.k.a Bernhard Riemann 21 years old - Riemann moved to the University of Berlin to study under several mathematicians, but Dirichlet was his biggest influence (and later collaborator). He studied here for 2 years before returning to Göttingen to study under Gauss. Riemann held his first lectures in 1854, which founded the field of Riemannian geometry and thereby set the stage for Einstein's general theory of relativity.

In 1859, following Dirichlet's death, he was promoted to head the mathematics department at Göttingen. Kate Fites Riemann married in July of 1862 and later that year caught a serious cold which developed into tuberculosis. Riemann spent the last weeks of his life in the Italian village of Selasca with his wife and three-year-old daughter. Geometry Resources http://www.usna.edu/Users/math/meh/riemann.html

http://www2.seminolestate.edu/lvosbury/CalculusI_Folder/RiemannSumDemo.htm
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