logging in or signing up Interactive Presentation of Mathematics aSGuest313 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 1131 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: September 30, 2008 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Interactive Presentations of Mathematics : Interactive Presentations of Mathematics Jeremy Gow & Paul Cairns Computer Science Middlesex University, London Overview : Overview Why interactive proofs? Polya-Lamport framework The IMP system Interactive topology course Theory presentation Future plans Mathematical Proof : Mathematical Proof Central to mathematics Mixture of prose and notation Deductive presentation Detail - incomplete, but convincing Context - extra-logical content Problems with Proof : Problems with Proof How much detail? Convincing Unintelligible and boring How much context? Helpful Justification Unnecessary and distracting You can’t please everyone Using Hypermedia : Using Hypermedia HTML, Java, XML, ... Reader controls proof presentation Aims Dynamic presentation of detail/context Easy to read/navigate Easy to write Polya’s Four Stages : Polya’s Four Stages Understand - terms, unknowns, diagrams Plan - abstract solution Execute - detailed solution Reflect - uses, alternatives, related theory Proof presentation format Argument vs. pre/post context Lamport’s Structured Proof : Lamport’s Structured Proof How To Write A Proof Labeled hierarchy Explicit argument structure Reader chooses own depth Manages complex detail Exposes errors Ideal for hypertext Polya-Lamport Framework : Polya-Lamport Framework Interactive proof format (with hyperlinks) Statement of theorem Understand - unknowns, terms, diagrams Plan/Execute - structured proof Reflect - uses, alternatives, related theory Demo The IMP System : The IMP System Authoring toolkit XML proof grammar In: Text proof file Explicit structure (XML) Maths notation (Latex) Out: Expandable proof (Java applet) Need unified tool Interactive Topology Course : Interactive Topology Course Elements of Euclidean & Metric Topology - Peter Collins Polya-Lamport framework Chapters, definitions, theorems Hand-coded HTML + IMP applet Demo (www.cs.mdx.ac.uk/imp/topology) User Evaluation : User Evaluation Seven topology students Tasks with course notes Questionnaires: background, SUS Interview Results SUS average 78%, range 63-88% Design feedback Theory Presentation : Theory Presentation Chapters/definitions/theorems frames Shallow structure Is there a deep structure? Dialectic maths - Lakatos Hard to write/present Is it worth it? Future Plans : Future Plans Evaluation feedback GUI for XML proofs Summarise sub-proofs Develop theory presentation Large evaluation Automate sub-proof expansion? Summary : Summary Dynamic proof detail/context Polya-Lamport framework IMP: XML to expandable proof Evaluated interactive course notes How to present theories? www.cs.mdx.ac.uk/imp You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Interactive Presentation of Mathematics aSGuest313 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 1131 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: September 30, 2008 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Interactive Presentations of Mathematics : Interactive Presentations of Mathematics Jeremy Gow & Paul Cairns Computer Science Middlesex University, London Overview : Overview Why interactive proofs? Polya-Lamport framework The IMP system Interactive topology course Theory presentation Future plans Mathematical Proof : Mathematical Proof Central to mathematics Mixture of prose and notation Deductive presentation Detail - incomplete, but convincing Context - extra-logical content Problems with Proof : Problems with Proof How much detail? Convincing Unintelligible and boring How much context? Helpful Justification Unnecessary and distracting You can’t please everyone Using Hypermedia : Using Hypermedia HTML, Java, XML, ... Reader controls proof presentation Aims Dynamic presentation of detail/context Easy to read/navigate Easy to write Polya’s Four Stages : Polya’s Four Stages Understand - terms, unknowns, diagrams Plan - abstract solution Execute - detailed solution Reflect - uses, alternatives, related theory Proof presentation format Argument vs. pre/post context Lamport’s Structured Proof : Lamport’s Structured Proof How To Write A Proof Labeled hierarchy Explicit argument structure Reader chooses own depth Manages complex detail Exposes errors Ideal for hypertext Polya-Lamport Framework : Polya-Lamport Framework Interactive proof format (with hyperlinks) Statement of theorem Understand - unknowns, terms, diagrams Plan/Execute - structured proof Reflect - uses, alternatives, related theory Demo The IMP System : The IMP System Authoring toolkit XML proof grammar In: Text proof file Explicit structure (XML) Maths notation (Latex) Out: Expandable proof (Java applet) Need unified tool Interactive Topology Course : Interactive Topology Course Elements of Euclidean & Metric Topology - Peter Collins Polya-Lamport framework Chapters, definitions, theorems Hand-coded HTML + IMP applet Demo (www.cs.mdx.ac.uk/imp/topology) User Evaluation : User Evaluation Seven topology students Tasks with course notes Questionnaires: background, SUS Interview Results SUS average 78%, range 63-88% Design feedback Theory Presentation : Theory Presentation Chapters/definitions/theorems frames Shallow structure Is there a deep structure? Dialectic maths - Lakatos Hard to write/present Is it worth it? Future Plans : Future Plans Evaluation feedback GUI for XML proofs Summarise sub-proofs Develop theory presentation Large evaluation Automate sub-proof expansion? Summary : Summary Dynamic proof detail/context Polya-Lamport framework IMP: XML to expandable proof Evaluated interactive course notes How to present theories? www.cs.mdx.ac.uk/imp