Done ByST.ID - Hawra Jameel Jassim20121528 - Kawther Sayed Ahmad20113367 -Maria Mohammed20120982 - Masooma Aamer20122659 Instructor: Dr. Abdullah Eid University.

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Done ByST.ID - Hawra Jameel Jassim Kawther Sayed Ahmad Maria Mohammed Masooma Aamer Instructor: Dr. Abdullah Eid University of Bahrain Bahrain Teachers College

Name: Georg Friedrich Bernhard Riemann. Nationality : Germany. Born on: September 17, 1826 AD, Breselenz. Died: July 20,1866 AD in Italy Famous as : Mathematician fields in : mathematics and physics

-He made important contributions to the theory of functions, complex analysis, and numbers theory. - He introduced a way of generalizing the study of polynomial equations in two real variables to the case of two complex variables. x + iy(where i = √(−1)) - He made the first significant uses of Topology in mathematics.

Topology: The study of those properties of geometric forms that remain Invariant under certain transformations, as bending or stretching.

Genus: Genus: The maximal number of closed curves that can be drawn on the surface without splitting it into separate pieces. * Genus: ( The number of holes ) Genus used in: -Number theory -Areas - Topology -Complex analysis - Topology -Complex analysis

Genus = 0 Genus = 1 Genus = 2

Approximation of area upper and lower Riemann Sum

Approximate the area under the curve using “lower and upper Riemann sum”.

Do you have any questions?

Thank you for listening

  Riemann Center for Geometry and Physics (2013) Retrieved from Riemann Center for Geometry and Physics (2013) Retrieved from  NNDB(2014) Retrieved from:  Jeremy John Gray Encyclopedia Britannica. [ONLINE] Available at: [Accessed 28 March 15].  (2006). Retrieved from kuta software: %20Approximating%20Area%20Under%20Curve.pdf %20Approximating%20Area%20Under%20Curve.pdf  Online Dictionary Pictures from Friedrich E. P. Hirzebruch and Matthias Kreck On the Concept of Genus in Topology and Complex Analysis. [ONLINE] Available at: [Accessed 04 April 15].