APSTRAKCIJA I PRIMENA MATEMATIČKE ANALIZE U NASTAVI NA TEHNIČKIM FAKULTETIMA

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APSTRAKCIJA I PRIMENA MATEMATIČKE ANALIZE U NASTAVI NA TEHNIČKIM FAKULTETIMA

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dc.contributor.advisor Mateljević, Miodrag
dc.contributor.author Albijanić, Miroljub
dc.date.accessioned 2017-03-24T18:31:48Z
dc.date.available 2017-03-24T18:31:48Z
dc.date.issued 2016
dc.identifier.uri http://hdl.handle.net/123456789/4447
dc.description.abstract 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. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2017-03-24T18:31:48Z No. of bitstreams: 1 doktorska_disertacija_MAlbijanic.pdf: 4920936 bytes, checksum: 7147bd9b7ea79697f96930bd3f3e51fa (MD5) en
dc.description.provenance Made available in DSpace on 2017-03-24T18:31:48Z (GMT). No. of bitstreams: 1 doktorska_disertacija_MAlbijanic.pdf: 4920936 bytes, checksum: 7147bd9b7ea79697f96930bd3f3e51fa (MD5) Previous issue date: 2016 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title APSTRAKCIJA I PRIMENA MATEMATIČKE ANALIZE U NASTAVI NA TEHNIČKIM FAKULTETIMA en_US
mf.author.birth-date 1967-07-08
mf.author.birth-place Požega en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area Mathematics en_US
mf.subject.keywords mathematical analysis, lectures, abstraction, application, Lagrange’s theorem convexity, Fourier’s series, fixed point en_US
mf.subject.subarea Analysis en_US
mf.contributor.committee Milovanović, Gradimir
mf.contributor.committee Arsenović, Miloš
mf.university.faculty Mathematical Faculty en_US
mf.document.references 139 en_US
mf.document.pages 280 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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