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“Project Trinity ” Mathematical Computation Environment Supports Program Proposal

“Project Trinity ” Mathematical Computation Environment Supports Program Proposal Sage-Math Development Project. 2009.10.21 Duk -Sun Kim mass@skku.edu. Background. Jan. 2008 JMMC Conference in San Diego, Sage-Math has a good presentation.

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“Project Trinity ” Mathematical Computation Environment Supports Program Proposal

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  1. “Project Trinity” Mathematical Computation Environment Supports Program Proposal Sage-Math Development Project 2009.10.21 Duk-Sun Kim mass@skku.edu

  2. Background • Jan. 2008 • JMMC Conference in San Diego, Sage-Math has a good presentation. • (Introduction for the Sage-Math and its usage) • Jun. 2008 • First Sage-Math server was prepared in the department of mathematics. • (http://math1.skku.ac.kr) under the guidance of Prof. Sang-Gu Lee • Version : 2.5 / A PC server was donated by Prof. Sang-Gu Lee • For other testing, we prepared one tentative server on the old-PC. • (http://galois10.skku.ac.kr) : Now it was not available. • Sep. 2008 • Prof. Dan Drake showed his interest on our service of Gage-Math and informed • a warning for the security • Throughout this communication, we made a connection with Prof. W. Stein • who is a leader of the development team for Sage-Math.

  3. Background • Jan. 2009 • With J.-Y. Bak, we made some outcome with our Sage-Math. • (published at the JKSME, Series E) • Apr. 2009 • Prof. Dan Drake gave an invited talk on his Sage-Math at • SungkyunkwanUniversity. • Jun. 2009 • First step for Korean version of Sage-Math was completed. • (with J.-Y. Bak, http://math1.skku.ac.kr) • In spring, we had made some outcome with our Sage-Math in our Linear Algebra • classes (with J.-Y. Bak and R.-Y. Koh) • Sep. 2009 • Prof. Dan Drake was invited to introduce Sage-Math at KSME fall conference. • We developed the Mobile Service on the Sage-Math (with J.Y. Park)

  4. Situation

  5. Math1 Re-Design

  6. Useful Functions in our classes Explanatory example: Taylor Series This is the code and a mockup animation of the interact command. It defines a slider, seen on top, that can be dragged. Once dragged, it changes the value of the variable "order" and the whole block of code gets evaluated. This principle can be seen in various examples presented on the pages above!

  7. Useful Functions in our classes: Calculus Directional Derivatives This interact displays graphically a tangent line to a function, illustrating a directional derivative (the slope of the tangent line). 3D graph with points and curves By Robert Marik This sagelet is handy when showing local, constrained and absolute maxima and minima in two variables

  8. Useful Functions in our classes: Linear Algebra Gerschgorin Circle Theorem by Marshall Hampton. This animated version requires convert (imagemagick) to be installed, but it can easily be modified to a static version. The animation illustrates the idea behind the stronger version of Gerschgorin's theorem, which says that if the disks around the eigenvalues are disjoint then there is one eigenvalue per disk. The proof is by continuity of the eigenvalues under a homotopy to a diagonal matrix.

  9. Useful Functions in our classes http://wiki.sagemath.org/interact

  10. Future Plan Make the “Trinity Structure” for the persistency Math1 Main Server Support Classes: Calculus and LA RPGS Math2 Support Main Server Lecture Dominator Load-Balancer (Distribution of all loads) (Parallel Algorithm Support) Galois09 Math3 Research Server WAP For the research

  11. Specifications All system will be constructed with PC-Server Math1 Main Server CPU: Intel E6400(Dual-Core) RAM : 2Gbyte (Already Prepared) CPU: Intel E6600(Dual-Core) RAM : 2Gbyte (Not prepared) RPGS CPU : P-IV 2.4G (Built in 1999) RAM : 512Mbyte (Already Prepared) CPU : P-IV 2.4G (Built in 1999) RAM : 512Mbyte (Not prepared) Math2 Support Main Server Lecture Dominator Load-Balancer (Distribution of all loads) (Parallel Algorithm Support) Galois09 Math3 Research Server WAP CPU: Intel E6600(Dual-Core) RAM : 2Gbyte (Already Prepared) CPU : P-IV 2.4G (Built in 1999) RAM : 512Mbyte (Already Prepared)

  12. Schedules Detail schedule with server groups RPG with Sage-Math : Oct. 2009 Mobile RPG with Sage-Math : Nov. 2009 Dynamic Multimedia Contents with RPG and Sage-Math : Dec. 2009 Math1 Main Server Already Completed RPGS Nov. 2009 : TBA Feb. 2010 : LBS will be appeared Math2 Support Main Server Lecture Dominator Load-Balancer (Distribution of all loads) (Parallel Algorithm Support) Galois09 Math3 Research Server WAP Continuous Proceeding (Support Web-Functions) Dec. 2009 : TBA

  13. Effectiveness • Cost • Sage-Math is a free software which have similar functions with the Mathematica, • MATLAB and Maple. • It will reduce our cost to buy expensive softwares for our class. • Connectivity • Sage-Math is based on our internet environment. • When researchers want to do computation in any place, we can make them to find • the result whenever they have internet connection. (We offer our publication • system in our Sage-Math server.) • Teaching • Students obtain chance to use a good mathematical software without any cost. • We can solve problems involving large size computation over simple text-book • problems and students can think of proper mathematical models in real world • problems.

  14. Thank you for your interesting in my proposal.

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