Submission 1 Title: Temesvár letter Appendix Author keywords: Temesvár letter Non-Euclidean Geometry The Temesvár letter (3 November 1823) is the first, written document of the discovery of the Non-euclidean Geometry by János Bolyai. The letter contains the famous sentence “semmiből egy ujj, más világot teremtettem” (from nothing I have created a new, Abstract: different word, translation made by the author), we consider the evidence of discovering the Non-Euclidean Geometry. Unfortunately, the first detailed version of his theory, presented to his superior, captain Johann Wolter Edler von Eckwehr (probably in 1825-26), has been lost. His notices however prove that his basic ideas were put on paper since 1820. Submitted: Jan 13, 22:23 GMT Last update: Jan 13, 22:23 GMT Authors first name last name email country organization Web page corresponding? Péter Körtesi
[email protected] Hungary university of Miskolc http://www.uni-miskolc.hu/~matkp ✔ Submission 2 Title: Riemann Sums Belong at the End of Integral Calculus, Not the Beginning. Teaching Integral Calculus Author keywords: History of Integration Differential Equations The typical integral calculus class starts with a lengthy definition of a definite integral utilizing Riemann sums. This occurs even though the integration of differentials, integral notation, and the fundamental theorem of calculus predate the birth of Riemann, who was more concerned with the representation of functions by trigonometric series. This talk proposes that it is pedagogically advantageous to follow history and that the topics of an integral calculus course can be rearranged to reflect this. Students will first Abstract: learn that integration (sum) is naturally the inverse operation of differentiation (difference) and will utilize this approach to solve various "inverse problems" (differential equations).