Auflistung Mathematical Sciences nach Titel
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Albijanić, Miloljub (Matematički fakultet , 2016)[more][less]
Zusammenfassung: Osnovni koncept rada jeste povezanost apstraktne teorije i primenjene matematiˇcke analize u univerzalnom matematiˇckom sistemu. Matematika je doˇzivela veliku praktiˇcnu primenu, na primer, primenu matematiˇcke statistike, numeriˇcke analize, primene u elektrotehnici, doprinos razvoju raˇcunarstva i dr. Istovremeno, u nauˇcnom pogledu, uzdigla se do neslu´cenih apstrakcija (topoloˇski prostori, vektorski prostori i drugo). Zbog ovih ˇcinjenica neophodno je unapredivati nastavu matematiˇcke analize na tehniˇckim fakultetima ali i same metode nastave. Rad sadrˇzi teorijsko i empirijsko istraˇzivanje. Teorijsko istraˇzivanje rasvetljava pojmove apstrakcije i primene i daje primere iz slede´cih nastavnih tema: Lagranˇzova teorema, konveksnost i posledice; Tejlorova formula; Hardijev pristup za izraˇcunavanje povrˇsine ravne figure; Furijeovi redovi i primene; Banahova teorema o fiksnoj taˇcki i primene. Empirijsko istraˇzivanje sastoji se iz dva dela: upitnika i testa. Ovo istraˇzivanje otkriva kako odnos teorije i primene doˇzivljavaju studenti, kako vide nastavu matematike i koja nastavna sredstva koriste. Istraˇzivanje otkriva i kako studenti reˇsavaju jednostavne probleme i koju vrstu zadataka uspeˇsnije reˇsavaju. Uzorak ˇcini 429 studenata elektrotehnike, gradevine i maˇsinstva za Upitnik i 450 studenata istih fakulteta za Test. Studenti koji su uˇcestvovali u istraˇzivanju pohadaju Univerzitet u Beogradu, Univerzitet u Novom Sadu i Univerzitet u Niˇsu. Rezultati istraˇzivanja su potvrdili da studenti tehniˇckih fakulteta imaju pozitivan odnos prema matematici i da njen znaˇcaj vide kroz primenu, odnosno njenu upotrebnu vrednost. Studenti imaju jasno definisane stavove o tome da je dobro predavanje nastavnika ono koje je razumljivo, razgovetno i koje motiviˇse studente da u njemu uˇcestvuju. Istiˇcu znaˇcaj primera koji imaju elemente primene. Vizuelna prezentacija pove´cava uspeˇsnost reˇsavanja zadataka. Istraˇzivanje pokazuje da studenti nisu stekli veˇstinu da znanje iz matematiˇcke analize primene u reˇsavanju zadataka i problema. Teorijskim rasvetljavanjem pojmova apstrakcije i primene, a zatim prikazom pet tema matemati ˇcke analize, potvrdeno je da su apstraktna teorija i primenjena matematiˇcka analiza medusobno povezane i objedinjene u univerzalnom matematiˇckom sistemu. Na osnovu nalaza formulisane su preporuke koje se odnose na inovativne pristupe u nastavi kao ˇsto su planiranje nastave i unapredivanje sadrˇzaja, postavljanje pitanja, inteligentni pogled, poboljˇsanje predavanja i koriˇs´cenje nastavnih sredstava. Na ovaj naˇcin potvrduje se da metodiˇcki dobro postavljena nastava pomaˇze boljem razumevanju odnosa izmedu apstrakcije i primene matematiˇcke analize. Kljuˇcne reˇci: Matematiˇcka analiza, nastava, apstrakcija, primena, Lagranˇzova teorema, konveksnost, Furijeovi redovi, fiksna taˇcka. URI: http://hdl.handle.net/123456789/4684 Dateien zu dieser Ressource: 1
doktorat_albijanic.pdf ( 4.985Mb ) -
Albijanić, Miroljub (Beograd , 2016)[more][less]
Zusammenfassung: The main concept of this thesis is the connection of abstract theory and applied mathematical analysis in the universal mathematical system. The Mathematics is being applied practically in great number of cases, for example, in the application of mathematical statistics, numerical analysis, application in electrical engineering, contribution to computer developing etc. At the same time, in scientific perspective, it reached the level of incredible abstractions (topological spaces, vector spaces et al.). Due to these facts, it has become necessary to advance the teaching of mathematical analysis in technological universities, but also the very methods of teaching as well. This thesis contains both a theoretical and an empirical research. The theoretical research sheds light onto the notions of abstraction and application and gives examples from next teaching subjects: Lagrange’s Theorem, Convexity and Consequences. Taylor’s Formula. Hardy’s Approach to Calculating Surfaces of Flat Shapes. Fourier’s Series and their Application. Banach Fixed-Point Theorem and its’ Application. The empirical research consists of two parts: a questionnaire and a test. This research shows how the relation between theory and application is seen by students, how they perceive the teaching of mathematics and which learning instruments they use. The research also shows how students solve simple problems and which type of problems they solve more sucessfully. The sample consists of 429 students of electrical engineering, construction and mechanical engineering for the Questionnaire and 450 students of the same universities for the Test. Students that participated in the research are studying at the University of Belgrade, University of Novi Sad and University of Niˇs. The results of the research confirmed that students from technological universities have a favourable attitude towards mathematics and that they see its significance in its application, i.e. in its use value. Students have clearly defined attitude on the idea that a good lecture by a professor is one which can be understood, which is well articulated, and which motivates students to take part in it. They point out the significance of examples that have elements of application. Visual presentations also enhance the success in solving problems. The research shows that students did not acquire the skill to apply their knowledge of mathematical analysis in solving tasks and problems. Theoretical clarification of notions of abstraction and application, followed by a displayfive topics of mathematical analysis confirm that abstract theory and applied mathematical analysis are interconnected and conjoint in the universal mathematical system. On the basis of results recommendations are defined concerning innovational approaches to teaching, such as planning the lectures and meliorating the contents, asking questions, and also an intelligent prospect, lecture improvement and learning instruments application. This way, it is confirmed that a methodically well organized lecture helps a better understanding of the relation between abstraction and application of mathematical analysis. URI: http://hdl.handle.net/123456789/4447 Dateien zu dieser Ressource: 1
doktorska_disertacija_MAlbijanic.pdf ( 4.920Mb ) -
Premović Aleksić, Dragica (Novi Pazar , 2014)[more][less]
URI: http://hdl.handle.net/123456789/4075 Dateien zu dieser Ressource: 1
Arh_Tutin_Sjenica.PDF ( 422.9Mb ) -
Лурје, С. Ј.; Лурье., С. Я.; Lurje, S.J. (Prosveta , 1952)[more][less]
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Radojević Todosijević, Milica (Beograd , 2020)[more][less]
URI: http://hdl.handle.net/123456789/5069 Dateien zu dieser Ressource: 1
Radojevic-TodosijevicMilica.pdf ( 6.961Mb ) -
Sofijanić, Goran (MATEMATIČKI FAKULTET UNIVERZITETA U BEOGRADU , 2011)[more][less]
URI: http://hdl.handle.net/123456789/1833 Dateien zu dieser Ressource: 1
Arhita iz Taranta (konacna verzija).pdf ( 1.938Mb ) -
Jovanović, Uroš (Beograd , 2017)[more][less]
URI: http://hdl.handle.net/123456789/4527 Dateien zu dieser Ressource: 1
masJovanovicUros.pdf ( 2.698Mb ) -
Zorić, Georgi (Beograd , 1837)[more][less]
URI: http://hdl.handle.net/123456789/3723 Dateien zu dieser Ressource: 1
UBSM_R_858_high_R.pdf ( 17.92Mb ) -
Stojković, Atanasije (Beograd , 1973)[more][less]
URI: http://hdl.handle.net/123456789/4166 Dateien zu dieser Ressource: 1
aristid_natalija.pdf ( 12.45Mb ) -
Vrećica, Ilija (Beograd , 2015)[more][less]
URI: http://hdl.handle.net/123456789/4247 Dateien zu dieser Ressource: 1
Vrecica_Ilija.pdf ( 801.6Kb ) -
Orlov, Konstantin (Belgrade , 1934)[more][less]
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Damjanović, Vasilije (, 1767)[more][less]
URI: http://hdl.handle.net/123456789/718 Dateien zu dieser Ressource: 1
VasilijeDamjanovicAritmetika.pdf ( 32.49Mb ) -
Đokić, Dragan (Beograd , 2016)[more][less]
URI: http://hdl.handle.net/123456789/4335 Dateien zu dieser Ressource: 1
Djokic_Dragan.pdf ( 6.123Mb ) -
Škreblin, Stjepan (Zagreb , 1935)[more][less]
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Močnik - Najman (Beograd , 1909)[more][less]
URI: http://hdl.handle.net/123456789/2172 Dateien zu dieser Ressource: 1
arm alg VRS.pdf ( 10.79Mb ) -
Stajić, Vlastimir (Beograd , 1942)[more][less]
URI: http://hdl.handle.net/123456789/5344 Dateien zu dieser Ressource: 1
Aritmetika_Algebra.pdf ( 53.55Mb ) -
Stajić, Vlastimir (BEOGRAD , 1933)[more][less]
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Stajić, Vlastimir (Beograd , 1940)[more][less]
URI: http://hdl.handle.net/123456789/5341 Dateien zu dieser Ressource: 1
Aritmetika_II.pdf ( 33.27Mb ) -
Stajić, Vlastimir (Beograd , 1933)[more][less]
URI: http://hdl.handle.net/123456789/2185 Dateien zu dieser Ressource: 1
Binder1 arit R.pdf ( 3.892Mb ) -
Latković, Nikola (BEOGRAD , 1935)[more][less]