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Appendix Temesvár Letter Non-Euclidean Geometry Abstract 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). This helps justify the learning of various integration techniques. Students will find Leibniz' proof of the fundamental theorem of calculus very natural, as it re-emphasizes that an integral is a sum of differences. This will lead toward a study of definite integrals and eventually Riemann sums. This is when the theory can be introduced. The author will make available materials to follow this approach. Submitted: Jan 23, 18:27 GMT Last update: Jan 23, 18:27 GMT Authors last first name email country organization Web page corresponding? name Robert Rogers [email protected] United States SUNY Fredonia ✔ Submission 4 Title: Figurate numbers. A Bridge between History and Learning of Mathematics Paper: (Jan 30, 19:46 GMT) Bruner’s representation theory Tobias Mayer’s Mathematischer Atlas Author keywords: figurate numbers space numbers mathematical problems for secondary school students It is necessary to rethink the main principles of the Hungarian mathematics teaching, to apply new methods and new contents, to renew the training of the teachers in the spirit of Tamás Varga. Nowadays the Hungarian mathematics teachers are uncertain in consequence of the bad PISA results. They want to teach better, but they need some help. In this presentation I want to share my teaching experiences and give a new approach to the practice of mathematics instruction, Abstract: connecting a problem of the history of mathematics with the modern learning of mathematics. We present some problems of Mayer’s Mathematischer Atlas (1745), and analyze his method in discussing figurate and space numbers. We deal with some other mathematical problems which were posed for secondary school students (AMC 10, Mason’s problem, KöMal problems, Viviani’s theorem). Submitted: Jan 30, 19:46 GMT Last update: Jan 30, 19:46 GMT Authors last Web first name email country organization corresponding? name page Institute of Mathematics, University of Debrecen, Tünde Kántor [email protected] Hungary ✔ Hungary Submission 5 Title: Serbian Mathematics Institutions 1841-1941 Mathematics Voivodina Serbia Author keywords: Norma Mathematical Seminar Belgrade University This lecture presents a historical review of the development of mathematics institutions in Voivodina and Serbia from the time around the middle of the 18th century until the first half of the 20th century, when the results of the work of several Serbian mathematicians were already well known and recognized in the mathematical world. The living and educational circumstances among the Serbs who lived north of the rivers Sava and Danube – within the Habsburg Monarchy – were significantly different from the circumstances on the south – within the Ottoman Empire. In 18th and 19th century Voivodina, a multinational and multicultural southern region of the Austro-Hungarian Monarchy and a part of the monarchy's defense zone towards the Ottoman Empire, was regarded as a province by all its citizens except the Serbs. The religious and national communities of Hungarians, Germans and Croats had their cultural and educational centers - Pest, Vienna and Zagreb - where they could obtain higher education and therefore did not feel the need for such institutions in Voivodina. During the late 18th and early 19th century Novi Sad (today the principal city in Voivodina) gradually emerged as a prospective cultural and educational hub of the Serbs, not only from Voivodina, but also for the Serbs living under the Ottoman rule. In the Habsburg Monarchy, and in Voivodina as its province, the school curricula, textbooks, and teaching methods were determined by the monarch's order and the teaching of mathematics was in a modest but systematic fashion included in the programs of the Serbian elementary schools. The first mathematics book written in Voivodina was the New Serbian Arithmetic by Vasilije Damjanović printed in Venice in 1767. Its content does not show particularly high mathematical standards but it had educational and enlightening significance. Similar books by Avram Mrazovič, Atanasije Demetrovič Sekereš and Jovan Došenović, written in Voivodina during the 18th and 19th century have the same importance. It was only after grammar schools were established in Novi Sad (1810) and the nearby Sremski Karlovci (1791) that the firm foundation was laid for the institutional development of mathematics in Voivodina. From the very beginning arithmetic and Abstract: 'mathezis' (algebra and geometry) were regular subjects in the grammar school curricula. These were mainly taught using the translated textbooks written by Franc Močnik, a Slovenian mathematician who, as a school counsellor and inspector, played an important role in the development of mathematics education in primary and secondary schools in the Austro-Hungarian Monarchy. At that time the institutions of great importance were the first teacher training school (Norma) founded in Sombor in 1778 by Avram Mrazovič and its higher form named Preparandija, founded in 1812 in Sent Andreja (Hungary) and moved to Sombor in 1816. On the other side, the complete illiteracy and educational backwardness were predominant among the Serbs under the Ottomans. After the first uprisings against the Turks in 1804 and 1815 and reestablishing Serbian state the organization of primary schools commenced immediately, although it was not until the Hatisherif of 1830 that the Serbs were allowed to form their own schools as well as other state institutions. During the next period, which can be considered very short in the overall history of any scientific discipline, Serbia, once an underdeveloped country in all aspects of education, succeeded in establishing a position in the world of mathematics which could be considered equal to the most developed European countries. Apart from the works and results on several prominent Serbian mathematicians (Mihailo Petrović (1868-1943), Jovan Karamata (1902-1967), Vojislav G. Avakumović (1910-1990)), the overall development of mathematics in Serbia has so far been little known to the general mathematical public. Institutional development of mathematics in Serbia rests on two national institutions: Lyceum, school of higher education founded in 1838 (after 1863 the Higher (Great) school and after 1905 the University of Belgrade) and the Society of Serbian Letters, founded in 1841 (after 1886 the Serbian Royal Academy of Sciences and today the Serbian Academy of Arts and Sciences). Dimitrije Nešić (1836-1904), professor of mathematics and rector of the Higher School, founded the first mathematics library in Serbia in 1871. In time, as a result of the collaboration between the Academy and the University the library had become the main place for mathematicians to gather and work in Belgrade and became known as the Mathematical Seminar of the University of Belgrade. The year 1896 is considered to be the year it was founded and when it began its activities as an institution. The period between the two world wars is the most significant period in the development and institutionalization of the activities of the Mathematics Seminar and Petrović's school of mathematics, which represent the root of the overall development of mathematics in Serbia. After World War II, the Mathematics Seminar developed into the most significant Serbian institution of mathematics under the name of Mathematical Institute. The Institute was founded in 1946 under the authority of Serbian Academy of Sciences. Submitted: Feb 04, 16:22 GMT Last update: Feb 04, 16:22 GMT Authors last first name email country organization Web page corresponding? name Faculty of Technical Sciences, University of Novi Aleksandar Nikolic [email protected] Serbia ✔ Sad Submission
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