On Dynamically Presenting a Topology Course

Authors of traditional mathematical texts often have difficulty balancing the amount of contextual information and proof detail. We propose a simple hypermedia framework that can assist in the organisation and presentation of mathematical theorems and definitions. We describe the application of the framework to convert an existing course in general topology to a web-based set of materials. Two user evaluations of the materials indicated both successful and unsuccessful aspects of the framework. We discuss further lines of investigation, in particular, the presentation of larger bodies of work.

[1]  P. Ramsden Learning to Teach in Higher Education , 1991 .

[2]  J. B. Brooke,et al.  SUS: A 'Quick and Dirty' Usability Scale , 1996 .

[3]  D. Bligh Learning to teach in higher education , 1993 .

[4]  Philip E. B. Jourdain The Study of Mathematics , 1908 .

[5]  Leslie Lamport,et al.  How to Write a Proof , 1995 .

[6]  Jakob Nielsen,et al.  Usability engineering , 1997, The Computer Science and Engineering Handbook.

[7]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[8]  Harold W. Thimbleby,et al.  Addressing Design and Usability Issues in Hypertext and on the World Wide Web by Re-Examining the "Lost in Hyperspace" Problem , 1998, J. Univers. Comput. Sci..

[9]  G. Pólya Mathematics and Plausible Reasoning , 1958 .

[10]  I. Lakatos PROOFS AND REFUTATIONS (I)*† , 1963, The British Journal for the Philosophy of Science.

[11]  Jim Grundy,et al.  A Browsable Format for Proof Presentation , 1996 .

[12]  池内 健二,et al.  Document preparation system , 2006 .

[13]  Michael Kohlhase,et al.  OMDoc - An Open Markup Format for Mathematical Documents [version 1.2] , 2006, Lecture Notes in Computer Science.

[14]  M. Rudin Nikiel's conjecture , 2001 .

[15]  G. Pólya,et al.  Mathematics and Plausible Reasoning , 1956 .

[16]  Jean-Pierre Serre,et al.  Fermat ’ s Last Theorem , 2017 .

[17]  Lawrence C. Paulson,et al.  Mechanizing set theory , 1996, Journal of Automated Reasoning.

[18]  Imre Lakatos,et al.  On the Uses of Rigorous Proof. (Book Reviews: Proofs and Refutations. The Logic of Mathematical Discovery) , 1977 .

[19]  David Flanagan,et al.  JavaScript: The Definitive Guide , 1996 .

[20]  Luca Padovani,et al.  Mathematical Knowledge Management in HELM , 2003, Annals of Mathematics and Artificial Intelligence.

[21]  Wilson A. Sutherland,et al.  Introduction to Metric and Topological Spaces , 1975 .