1 / 18

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.

ikia
Download Presentation

High-Level Programming Tools for Interactive Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related