Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary

Antoni Chronowski; Zbigniew Powązka

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia (2012)

  • Volume: 4, page 31-60
  • ISSN: 2080-9751

Abstract

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In the education of mathematicians, including teachers of mathematics, the measure theory plays an important role. From the experience in and research on teaching the measure theory it follows that on of the important reasons why students encounter difficulties in the subject is their insufficient ability to apply their knowledge of other branches of mathematics, especially of the set theory and topology. In this article we propose a series of problem analyses and exercises aimed at preparing students to study the measure theory, especially to understand the proofs of theorems on properties of the measure, including the Lebesgue measure. Most of these problems and exercises are presented with solutions, outlines of solutions, hints, didactic remarks and comments. In this paper we point out, in a practical way, the significance of active reading of mathematical texts and skilful use of mathematical literature. This article is dedicated to both students of mathematics and their academic teachers.

How to cite

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Antoni Chronowski, and Zbigniew Powązka. "Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary." Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia 4 (2012): 31-60. <http://eudml.org/doc/296274>.

@article{AntoniChronowski2012,
abstract = {In the education of mathematicians, including teachers of mathematics, the measure theory plays an important role. From the experience in and research on teaching the measure theory it follows that on of the important reasons why students encounter difficulties in the subject is their insufficient ability to apply their knowledge of other branches of mathematics, especially of the set theory and topology. In this article we propose a series of problem analyses and exercises aimed at preparing students to study the measure theory, especially to understand the proofs of theorems on properties of the measure, including the Lebesgue measure. Most of these problems and exercises are presented with solutions, outlines of solutions, hints, didactic remarks and comments. In this paper we point out, in a practical way, the significance of active reading of mathematical texts and skilful use of mathematical literature. This article is dedicated to both students of mathematics and their academic teachers.},
author = {Antoni Chronowski, Zbigniew Powązka},
journal = {Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia},
keywords = {measure; problems; exercises},
language = {pol},
pages = {31-60},
title = {Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary},
url = {http://eudml.org/doc/296274},
volume = {4},
year = {2012},
}

TY - JOUR
AU - Antoni Chronowski
AU - Zbigniew Powązka
TI - Przykłady zagadnień z różnych działów matematyki niezbędnych do studiowania teorii miary
JO - Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
PY - 2012
VL - 4
SP - 31
EP - 60
AB - In the education of mathematicians, including teachers of mathematics, the measure theory plays an important role. From the experience in and research on teaching the measure theory it follows that on of the important reasons why students encounter difficulties in the subject is their insufficient ability to apply their knowledge of other branches of mathematics, especially of the set theory and topology. In this article we propose a series of problem analyses and exercises aimed at preparing students to study the measure theory, especially to understand the proofs of theorems on properties of the measure, including the Lebesgue measure. Most of these problems and exercises are presented with solutions, outlines of solutions, hints, didactic remarks and comments. In this paper we point out, in a practical way, the significance of active reading of mathematical texts and skilful use of mathematical literature. This article is dedicated to both students of mathematics and their academic teachers.
LA - pol
KW - measure; problems; exercises
UR - http://eudml.org/doc/296274
ER -

References

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  15. Pardała, A.: 2012, Współczesne problemy i praktyka kształcenia matematycznego studentów, Annales Academiae Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia IV, 113-137. 
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  17. Powązka, Z.: 2009, Uwagi o kształtowaniu rozumienia pojęcia miary na różnych poziomach edukacji, Prace monograficzne z dydaktyki matematyki, Współczesne problemy nauczania matematyki 2, 141-149. 
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  19. Powązka, Z.: 2012, Z badań nad trudnościami studentów w rozumieniu pojęcia miary i całki, Annales Academiae Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia IV, 139-154. 
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  21. Sikorski, R.: 1969, Rachunek różniczkowy i całkowy. Funkcje wielu zmiennych, PWN, Warszawa. 

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