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High-Level Programming Tools for Interactive Mathematics. Douglas B. Meade University of South Carolina meade@math.sc.edu Phillip B. Yasskin Texas A&M University yasskin@math.tamu.edu. Communicating Mathematics in the Digital Era Aveiro, Portugal 15 – 18 August 2006. The Bottom Line.

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high level programming tools for interactive mathematics

High-Level Programming Tools for Interactive Mathematics

Douglas B. Meade

University of South Carolina

meade@math.sc.edu

Phillip B. Yasskin

Texas A&M University

yasskin@math.tamu.edu

Communicating Mathematics in the Digital Era

Aveiro, Portugal

15 – 18 August 2006

the bottom line
The Bottom Line
  • Lecturers are best suited to preparing the most appropriate materials for their students.

More specifically …

the bottom line3
The Bottom Line
  • Mathematics lecturers are best suited to preparing mathematically appropriate materials for their mathematics students.
outline
Outline
  • Disclaimers
  • Traditional Tools
  • Higher-Level Tools
  • Immediate Needs
  • Examples
  • Final Remarks
disclaimers
Disclaimers
  • We are mathematicians

who want to use digital media to communicate mathematics to the world

  • We want to communicate research results to a wider audience
  • We want to utilize the benefits of the digital era to improve my teaching
traditional tools
Traditional Tools
  • Computer Algebra (CAS)
    • Excellent tools for doing mathematics
    • Far from optimal for communicating mathematics
    • Not universally available, not intuitive, not robust
  • Examples
    • Maple ( http://www.maplesoft.com )
    • Mathematica ( http://www.wolfram.com )
traditional tools7
Traditional Tools
  • CGI scripts and forms
    • Requires extensive knowledge of CGI / HTML / …
    • Non-trivial to connect CAS to web applications
    • License and security concerns
  • Example
    • irreducibility test for lacunary polynomials[http://www.math.sc.edu/~filaseta/irreduc.html]424 lines of CGI + 327 lines of Maple + …
traditional tools8
Traditional Tools
  • Java
    • Requires programming expertise
    • Much greater control over effects and actions
    • Same concerns about CAS connectivity, license, and security
  • Example
    • Tracing the locus of the vertex of a parabola[ ParabolaVertex.html ] 225 lines of Java code
higher level tools
Higher-Level Tools
  • Maplets
    • front-end to Java
    • still problematic to program
  • Example
    • Antiderivative calculator[ Antideriv.mw ] [ Antideriv.maplet ]16 lines of Maple
higher level tools10
Higher-Level Tools
  • Embedded Components
    • more intuitive and graphical
    • weak on features
  • Example
    • Irreducibility test for lacunary polynomials(w/ Michael Filaseta, J Algorithms, 2005; support from NSA)[ http://maplenet.math.sc.edu/research/Irreduc.mw ] [ MapleNet ]0 lines of visible Maple code
higher level tools11
Higher-Level Tools
  • Geometry Expressions
    • typical dynamic geometry interface
    • with built-in symbolics
  • Example
    • Shrinking circle[ ShrinkCircle.gx ]0 commands ( <5 minutes total time )*** add symbolic formula for distance*** copy to Maple worksheet
immediate needs
Immediate Needs
  • User-Interface: Layout Design
    • Graphical
    • Intuitive
    • Flexible
    • Robust
immediate needs13
Immediate Needs
  • User-Interface: Functionality
    • Dynamic layout
    • Full use of traditional Java effects
      • Color and image effects
      • Default text as instruction
      • Popups
immediate needs14
Immediate Needs
  • Full integration with Internet via hyperlinks
    • to external webpages
    • to online documents
  • Inter-application communication
    • grading / course management software
  • Universal availability
examples
Examples
  • Maplets for Calculus[ http://www.math.sc.edu/calclab/M4C/ ] [ MapleNet ]
    • Textbook independent (both + and -)
    • Nearly complete coverage
    • No grading capability
    • 32,327 lines of Maple programming in 70 files( not counting the HTML, … )
examples16
Examples
  • WebALThttp://www.webalt.net/http://www.webalt.com/
    • Complete online courses
    • Affordable
    • Multilingual
examples17
Examples
  • Maplets for WebALT Calculus (secure)
    • Currently in pre-alpha version
    • For additional information, including access,contact WebALT or the authors
the bottom line18
The Bottom Line
  • Mathematics lecturers are best suited to preparing mathematically appropriate materials for their mathematics students.
    • Good mathematics requires good communication
    • Development tools must support mathematical communication
    • No intrusive overhead
    • Expectations increase as technology improves