# Interactive Presentation of Mathematics

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Information about Interactive Presentation of Mathematics
Education

Published on September 30, 2008

Author: aSGuest313

Source: authorstream.com

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

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