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- Douglas B. Meade
- University of South Carolina
- meade@math.sc.edu
- Phillip B. Yasskin
- Texas A&M University
- yasskin@math.tamu.edu
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- Lecturers are best suited to preparing the most appropriate materials
for their students.
- More specifically …
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- Mathematics lecturers are best suited to preparing mathematically
appropriate materials for their mathematics students.
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- Disclaimers
- Traditional Tools
- Higher-Level Tools
- Immediate Needs
- Examples
- Final Remarks
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- 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
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- 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 )
- …
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- 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 + …
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- 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
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- Maplets
- front-end to Java
- still problematic to program
- Example
- Antiderivative calculator
[ Antideriv.mw ] [ Antideriv.maplet ]
16 lines of Maple
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- 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
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- 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
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- User-Interface: Layout Design
- Graphical
- Intuitive
- Flexible
- Robust
- …
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- User-Interface: Functionality
- Dynamic layout
- Full use of traditional Java effects
- Color and image effects
- Default text as instruction
- Popups
- …
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- Full integration with Internet via hyperlinks
- to external webpages
- to online documents
- Inter-application communication
- grading / course management software
- Universal availability
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- 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, … )
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- WebALT
http://www.webalt.net/
http://www.webalt.com/
- Complete online courses
- Affordable
- Multilingual
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- Maplets for WebALT Calculus (secure)
- Currently in pre-alpha version
- For additional information, including access,
contact WebALT or the authors
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- 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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