uu.seUppsala University Publications

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt144",{id:"formSmash:upper:j_idt144",widgetVar:"widget_formSmash_upper_j_idt144",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt145_j_idt147",{id:"formSmash:upper:j_idt145:j_idt147",widgetVar:"widget_formSmash_upper_j_idt145_j_idt147",target:"formSmash:upper:j_idt145:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Studies in the Conceptual Development of Mathematical AnalysisPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Matematiska Institutionen , 2009. , p. 31
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 64
##### Keywords [en]

History of mathematics, conceptual development, mathematical analysis
##### National Category

Other Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-101349ISBN: 978-91-506-2080-1 (print)OAI: oai:DiVA.org:uu-101349DiVA, id: diva2:212686
##### Public defence

2009-06-05, Häggsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 10:15 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt434",{id:"formSmash:j_idt434",widgetVar:"widget_formSmash_j_idt434",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt440",{id:"formSmash:j_idt440",widgetVar:"widget_formSmash_j_idt440",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true}); Available from: 2009-05-15 Created: 2009-04-23 Last updated: 2011-11-07Bibliographically approved
##### List of papers

This dissertation deals with the development of mathematical concepts from a historical and didactical perspective. In particular, the development of concepts in mathematical analysis during the 19th century is considered. The thesis consists of a summary and three papers. In the first paper we investigate the Swedish mathematician E.G. Björling's contribution to uniform convergence in connection with Cauchy's sum theorem from 1821. In connection to Björling's convergence theory we discuss some modern interpretations of Cauchy's expression x=1/n. We also consider Björling's convergence conditions in view of Grattan-Guinness distinction between history and heritage. In the second paper we study visualizations in mathematics from historical and didactical perspectives. We consider some historical debates regarding the role of intuition and visual thinking in mathematics. We also consider the problem of what a visualization in mathematics can achieve in learning situations. In an empirical study we investigate what mathematical conclusions university students made on the basis of a visualization. In the third paper we consider Cauchy's theorem on power series expansions of complex valued functions on the basis of a paper written by E.G. Björling in 1852. We discuss Björling's, Lamarle's and Cauchy's different conditions for expanding a complex valued function in a power seris. In the third paper we also discuss the problem of the ambiguites of fundamental concpets that existed during the mid-19th century. We argue that Cauchy's and Lamarle's proofs of Cauchy's theorem on power series expansions of complex valued functions are correct on the basis of their own definitions of the fundamental concepts involved.

1. Visualizations in mathematics$(function(){PrimeFaces.cw("OverlayPanel","overlay171161",{id:"formSmash:j_idt495:0:j_idt499",widgetVar:"overlay171161",target:"formSmash:j_idt495:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. E.G. Björling's view of power series expansions of complex valued functions$(function(){PrimeFaces.cw("OverlayPanel","overlay212683",{id:"formSmash:j_idt495:1:j_idt499",widgetVar:"overlay212683",target:"formSmash:j_idt495:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. E.G Björling's version of the Cauchy sum theorem$(function(){PrimeFaces.cw("OverlayPanel","overlay51244",{id:"formSmash:j_idt495:2:j_idt499",widgetVar:"overlay51244",target:"formSmash:j_idt495:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1156",{id:"formSmash:j_idt1156",widgetVar:"widget_formSmash_j_idt1156",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1209",{id:"formSmash:lower:j_idt1209",widgetVar:"widget_formSmash_lower_j_idt1209",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1210_j_idt1212",{id:"formSmash:lower:j_idt1210:j_idt1212",widgetVar:"widget_formSmash_lower_j_idt1210_j_idt1212",target:"formSmash:lower:j_idt1210:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});