From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6910 Path: news.gmane.org!not-for-mail From: Martin Escardo Newsgroups: gmane.science.mathematics.categories Subject: Re: Finding the inverse of a function. Date: Wed, 21 Sep 2011 14:02:42 +0100 Message-ID: References: Reply-To: Martin Escardo NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1316716292 15245 80.91.229.12 (22 Sep 2011 18:31:32 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 22 Sep 2011 18:31:32 +0000 (UTC) Cc: peasthope@shaw.ca, categories@mta.ca To: Dusko Pavlovic Original-X-From: majordomo@mlist.mta.ca Thu Sep 22 20:31:25 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1R6o3Q-0007WP-LD for gsmc-categories@m.gmane.org; Thu, 22 Sep 2011 20:31:24 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:38637) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1R6o1S-0006y3-Cj; Thu, 22 Sep 2011 15:29:22 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1R6o1Q-0006Qx-L2 for categories-list@mlist.mta.ca; Thu, 22 Sep 2011 15:29:20 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6910 Archived-At: This has been further developed in several papers by Rutten and other people. (This is entertaining but is not categorical: http://www.cs.dartmouth.edu/~doug/music.ps.gz) Martin On 20/09/11 18:55, Dusko Pavlovic wrote: > infinite series and analytic functions can be simply and conveniently manipulated in categories of coalgebras. their taylor and laplace transforms turn up as coalgebra isomorphims. the basics of this approach are in my LICS 98 paper with martin escardo, > http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5684# > or > http://www.isg.rhul.ac.uk/dusko/coalgebra.html > neither martin nor i really pursued this path, which is perhaps a mistake, since it seems that a powerful categorical tool lies there. > > 2c, > -- dusko > > On Sep 16, 2011, at 5:42 PM, peasthope@shaw.ca wrote: > >> Is CT any help in getting an overview of infinite series? >> >> I'm curious to find an inverse of f(\theta) = \theta \sin \theta >> and wonder whether there is an approach more insightful than >> the traditional course in applied analysis. >> >> Thanks, ... Peter E. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]