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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.

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High-Level Programming Tools for Interactive Mathematics

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  1. 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

  2. The Bottom Line • Lecturers are best suited to preparing the most appropriate materials for their students. More specifically …

  3. The Bottom Line • Mathematics lecturers are best suited to preparing mathematically appropriate materials for their mathematics students.

  4. Outline • Disclaimers • Traditional Tools • Higher-Level Tools • Immediate Needs • Examples • Final Remarks

  5. 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

  6. 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 ) • …

  7. 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 + …

  8. 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

  9. Higher-Level Tools • Maplets • front-end to Java • still problematic to program • Example • Antiderivative calculator[ Antideriv.mw ] [ Antideriv.maplet ]16 lines of Maple

  10. 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

  11. 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

  12. Immediate Needs • User-Interface: Layout Design • Graphical • Intuitive • Flexible • Robust • …

  13. Immediate Needs • User-Interface: Functionality • Dynamic layout • Full use of traditional Java effects • Color and image effects • Default text as instruction • Popups • …

  14. Immediate Needs • Full integration with Internet via hyperlinks • to external webpages • to online documents • Inter-application communication • grading / course management software • Universal availability

  15. 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, … )

  16. Examples • WebALThttp://www.webalt.net/http://www.webalt.com/ • Complete online courses • Affordable • Multilingual

  17. Examples • Maplets for WebALT Calculus (secure) • Currently in pre-alpha version • For additional information, including access,contact WebALT or the authors

  18. 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

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