PUMA publications for /user/jaeschke/mathhttps://puma.uni-kassel.de/user/jaeschke/mathPUMA RSS feed for /user/jaeschke/math2024-03-29T00:25:43+01:00Mathematics of Web science: structure, dynamics and incentiveshttps://puma.uni-kassel.de/bibtex/23f77f26601231ba891aa65a702b8c867/jaeschkejaeschke2013-02-19T09:41:42+01:00dynamics incentive math structure webscience <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Jennifer Chayes" itemprop="url" href="/author/Jennifer%20Chayes"><span itemprop="name">J. Chayes</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences</em></span></span> </span>(<em><span>2013<meta content="2013" itemprop="datePublished"/></span></em>)Tue Feb 19 09:41:42 CET 2013Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences1987Mathematics of Web science: structure, dynamics and incentives3712013dynamics incentive math structure webscience Dr Chayes’ talk described how, to a discrete mathematician, ‘all the world’s a graph, and all the people and domains merely vertices’. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online world) in the following way: first, we can model online networks as large finite graphs; second, we can sample pieces of these graphs; third, we can understand and then control processes on these graphs; and fourth, we can develop algorithms for these graphs and apply them to improve the online experience.What To Do When The Trisector Comeshttps://puma.uni-kassel.de/bibtex/21f7857c3d17534019af8dcbb6494fe6e/jaeschkejaeschke2012-11-02T11:09:56+01:00crank fun geometry math trisector <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Underwood Dudley" itemprop="url" href="/author/Underwood%20Dudley"><span itemprop="name">U. Dudley</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>The Mathematical Intelligencer</em></span></span> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">5 </span></span>(<span itemprop="issueNumber">1</span>):
<span itemprop="pagination">20--25</span></em> </span>(<em><span>1983<meta content="1983" itemprop="datePublished"/></span></em>)Fri Nov 02 11:09:56 CET 2012New YorkThe Mathematical Intelligencer120--25What To Do When The Trisector Comes51983crank fun geometry math trisector The man who loves only numbershttps://puma.uni-kassel.de/bibtex/2947cc4cf4cbfdd3df48916237c7cd694/jaeschkejaeschke2012-05-15T17:46:56+02:00erdös history math number <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="P. Hoffman" itemprop="url" href="/author/P.%20Hoffman"><span itemprop="name">P. Hoffman</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>The Atlantic Monthly</em></span></span> </span>(<em><span>November 1987<meta content="November 1987" itemprop="datePublished"/></span></em>)Tue May 15 17:46:56 CEST 2012The Atlantic Monthlynov60--74The man who loves only numbers1987erdös history math number Paul Erdös is certainly the most prolific - and probably the most eccentric - mathematician in the world.An introduction to probability theory and its applicationshttps://puma.uni-kassel.de/bibtex/2cf464e5e44fbad2b68e11a80cbded06e/jaeschkejaeschke2012-05-15T12:15:02+02:00math probability theory toread <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="William Feller" itemprop="url" href="/author/William%20Feller"><span itemprop="name">W. Feller</span></a></span>. </span><em><span itemprop="publisher">Wiley</span>, </em><em>New York, </em>(<em><span>1968<meta content="1968" itemprop="datePublished"/></span></em>)Tue May 15 12:15:02 CEST 2012New YorkAn introduction to probability theory and its applications1968math probability theory toread Stepwise construction of the Dedekind-MacNeille completionhttps://puma.uni-kassel.de/bibtex/20c986e520647b86c202633cc6945d524/jaeschkejaeschke2011-12-01T13:54:50+01:00algebra completion lattice math <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Bernhard Ganter" itemprop="url" href="/author/Bernhard%20Ganter"><span itemprop="name">B. Ganter</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Sergei Kuznetsov" itemprop="url" href="/author/Sergei%20Kuznetsov"><span itemprop="name">S. Kuznetsov</span></a></span>. </span><span itemtype="http://schema.org/Book" itemscope="itemscope" itemprop="isPartOf"><em><span itemprop="name">Conceptual Structures: Theory, Tools and Applications</span>, </em><em>Volume 1453 von Lecture Notes in Computer Science, </em><em><span itemprop="publisher">Springer</span>, </em><em>Berlin/Heidelberg, </em></span>(<em><span>1998<meta content="1998" itemprop="datePublished"/></span></em>)Thu Dec 01 13:54:50 CET 2011Berlin/HeidelbergConceptual Structures: Theory, Tools and Applications295--302Lecture Notes in Computer ScienceStepwise construction of the Dedekind-MacNeille completion14531998algebra completion lattice math Lattices are mathematical structures which are frequently used for the representation of data. Several authors have considered the problem of incremental construction of lattices. We show that with a rather general approach, this problem becomes well-structured. We give simple algorithms with satisfactory complexity bounds.Formal Concept Analysis: Mathematical Foundationshttps://puma.uni-kassel.de/bibtex/2ae14b00b5489de8da6e4578ac3062bfc/jaeschkejaeschke2011-01-27T13:46:01+01:00analysis concept fca formal math <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Bernhard Ganter" itemprop="url" href="/author/Bernhard%20Ganter"><span itemprop="name">B. Ganter</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Rudolf Wille" itemprop="url" href="/author/Rudolf%20Wille"><span itemprop="name">R. Wille</span></a></span>. </span><em><span itemprop="publisher">Springer</span>, </em><em>Berlin/Heidelberg, </em>(<em><span>1999<meta content="1999" itemprop="datePublished"/></span></em>)Thu Jan 27 13:46:01 CET 2011Berlin/HeidelbergFormal Concept Analysis: Mathematical Foundations1999analysis concept fca formal math This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thoroughly and illuminated by means of numerous examples.Concrete Mathematics: A Foundation for Computer Sciencehttps://puma.uni-kassel.de/bibtex/2ccef670ef39186763ecd379d2cca1e0a/jaeschkejaeschke2008-04-23T10:18:06+02:00computer knuth latex math science <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Ronald L. Graham" itemprop="url" href="/author/Ronald%20L.%20Graham"><span itemprop="name">R. Graham</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Donald E. Knuth" itemprop="url" href="/author/Donald%20E.%20Knuth"><span itemprop="name">D. Knuth</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Oren Patashnik" itemprop="url" href="/author/Oren%20Patashnik"><span itemprop="name">O. Patashnik</span></a></span>. </span><em><span itemprop="publisher">Addison-Wesley</span>, </em><em>Reading, </em>(<em><span>1989<meta content="1989" itemprop="datePublished"/></span></em>)Wed Apr 23 10:18:06 CEST 2008ReadingConcrete Mathematics: A Foundation for Computer Science1989computer knuth latex math science Mechanizing Proof:
Computing, Risk, and Trusthttps://puma.uni-kassel.de/bibtex/23ea6b663f1ba9a440b352c887e1173cf/jaeschkejaeschke2007-07-20T11:25:34+02:00computer computing history math proof risk toread trust <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Donald MacKenzie" itemprop="url" href="/author/Donald%20MacKenzie"><span itemprop="name">D. MacKenzie</span></a></span>. </span><em><span itemprop="publisher">The MIT Press</span>, </em>(<em><span>Oktober 2001<meta content="Oktober 2001" itemprop="datePublished"/></span></em>)Fri Jul 20 11:25:34 CEST 2007OctoberMechanizing Proof:
Computing, Risk, and Trust2001computer computing history math proof risk toread trust Most aspects of our private and social lives -- our safety, the integrity of the financial system, the functioning of utilities and other services, and national security -- now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants.
MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof -- the need to predict the behavior of the computer systems upon which human life and security depend -- and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.social history of computer based proof