Education

Teaching and learning about math, Maple and MapleSim

Greetings to all.

I have been using the numtheory package for quite some time now and it has helped me advance on a number of problems. Recently an issue came to my attention that I have known about for a long time but somehow never realized that it can be fixed. This is the fact that the numtheory package does not know about Dirichlet series, finite and infinite. Here are two links:

Fourteen Clickable Calculus examples have been added to the Teaching Concepts with Maple area of the Maplesoft web site. Four are sequence and series explorations taken from algebra/precalculus, four are applications of differentiation, four are applications of integration, and two are problems from the lines-and-planes section of multivariate calculus. By my count, this means some 111 Clickable Calculus examples have now been posted to the section.

A kryptarithm - this is an example of arithmetic, in which all or some of the digits are replaced by letters. The rule must be satisfied: the different letters represent different digits, the identical letters represent the identical digits. See the link  http://en.wikipedia.org/wiki/Verbal_arithmetic.

The following procedure, called  Ksolve , solves kryptarithms in which are used four operations ...

I just wanted to remind everyone that this quarter's Möbius App Challenge closes Sept. 30.  This quarter's prize is an iPad Prize Pack, which looks very cool but sadly, I'm not allowed to enter.

To enter the contest, all you need to do is:

1) Create an interactive App in Maple

2) While in Maple, log-in to the MapleCloud through the MapleCloud palette.

3) Click on the Send Document to the Cloud button

I think Maple is missing some lines and significant points. Here I leave another contribution to the possible implementation of a new algorithm to draw the circle of Taylor.

Circle_of_Taylor.mw

Atte.

L. Araujo C.

Other work done to demonstrate that using the correct syntax leads to corroborate all the principles and theorems found in the area of geometry. The Gergonne Point is another achievement developed by Maple procedure through GergonnePoint command and use. I hope your hand corrections if any.

Point_of_Gergonne.mw

Atte

Lenin

I would like to pay attention to the article "Words and More Words" by Joseph Malkevitch. Here are a few  intriguing references:

M. Morse, A solution of the problem of infinite play in chess, Bull. Am. Math. Soc., 44 (1938) 632.

M. Morse and G. Hedlund, Symbolic dynamics, Am. J. Math. 60, (1938) 815–866.

Lothaire, M. Applied Combinatorics on Words, Cambridge U. Press, New York, 2005.

https://www.facebook.com/pages/Matemática-Computacional-Trujillo/145132492343285

A user community of Maple I leave one of my contributions to the advancement of science. Here you see the true use of Mathematics in its real dimension Geometric. Just need to improve it with Components someone can help?.The_Point_of_Nage.mw

Aquí le dejo otro de mis trabajos hechos con puro matemáticas, creo que me parecio por demás plotear las alturas y medianas ya que eso se realizo en la recta de Euler.

Nueve_puntos_de_Feue.mw

Aqui les dejo La ecuación de la Recta de Euler, calculado desde su inicio hasta la comprobación con el comando EulerLine.

Recta_de_Euler.mw

Congratulations to Christian Bär, a professor at the University of Potsdam, for winning the first individual prize of The Möbius App Challenge! Christian will be receiving a MacBook Air for his app The Cosmic Travel Planner.

Maplesoft launched the Möbius App Challenge earlier this year to give Maplesoft community members the opportunity to get involved in the creation of Möbius Apps. This contest seeks to challenge users to create Math Apps using Maple, submit them to The Möbius Project website, then award the most useful, creative, and effective submissions. Finalists from the individual level challenge are chosen four times a year, so make sure to enter the next round of the challenge for your chance at a Maplesoft prize pack!

For full contest details and to enter, please visit: http://www.maplesoft.com/lp/mobius/index.aspx.

(Presentation in Spain a month ago focusing on educational and research use)

ODEs and PDEs

 

"Computer algebra systems have evolved into powerful environments for studying and solving differential equations."

 

Some polemical questions:

 

Can a Computer Algebra system compute numerical ODE solutions as fast as for instance C or FORTRAN code ?

   

Can a computer really be more useful than a good book for finding exact ODE and PDE solutions ?

   

Aren't these computer algebra environments more like a black-box approach to the problem ?

   

Can we really study  the "differential equations" behind a problem using Computer Algebra as we would do by hand?

   

Is there something fundamentally relevant regarding ODEs and PDEs that we can only do with a computer?

   

___________________________________________________________________________

 

Special Functions

 

"Special functions, their inter-relation and representations become alive within a computer"

Conversions between mathematical functions

   

The FunctionAdvisor project

   

Differential Polynomial Form for non-polynomial expressions

   

___________________________________________________________________________

Conclusion

 

"Research and education are two things highly inter-related"

 

  

-  Constructive learning processes are mostly based on the building of logic structures by testing conjectures and analyzing the results. The proportion between success (the conjecture solves the problem) and frustration plays an important role as an emotional (+/-) accelerating factor for the whole "learning & discovery" process.

-  The simultaneous analysis of a greater number of results turns apparent the underlying logic structures more rapidly, and can strengthen the intuition unexpectedly.

  

- Genuine learning processes only happen when the individual who is learning participates actively.

  

- Inspiration is a function of intuition, excitement and fun, transformed into results through heavy exploration.

Symbolic computation can be used with these purposes, perhaps as the most important educational and research tool available at present.

___________________________________________________________________________

 

 

Santander_talk.pdf   Download Santander_talk.mw

 

Edgardo S. Cheb-Terrab
Physics, Maplesoft

I am happy to formally announce Maple T.A. 9.5! An expansion on Maple T.A. 9, this release is packed full of innovative features and new tools to assist academic institutions with a variety of different teaching and assessment tasks.

Ever have an issue on your campus where students are required to learn a new piece of technology, but you don’t know how to get them prepared for it? With Maple T.A. 9.5, we have included pre-built content to assist students in learning how to use the Maple T.A. environment, and students can take the new Readiness Test to educate themselves on how to use the system. Tasks such as enabling Java, navigating assignments, grading tests, searching for help, and much more are taught in an interactive setting, and give students the right information they need to become comfortable with Maple T.A.

We haven’t forgotten about instructors and teachers either. We have completely revamped our Instructor Examples to provide educators with a sample question of every single question type in Maple T.A. – that’s over 25 different examples! Instructors are given descriptions, feature lists, and examples for each question type. Additionally, we also created a new Sample Assignment that shows instructors what a typical assignment looks like. They can explore this assignment from both instructor and student viewpoints to test out different options and see what the experience will be like.

Essay questions have been foundational in Maple T.A. for several years now, and Maple T.A. 9.5.makes it even easier to provide feedback for students submitting essays. With the Essay Annotation feature, instructors have the ability to mark-up an essay with comments using a simple drag and drop tool. Using this new tool, your students will be able to see your comments and take note of any issues they had in their writing.

Power outages, automatic updates, computer crashes... we’ve all experienced these unpredictable events, and they can be catastrophic for students trying to meet due dates or if assignments are timed. To help with this Maple T.A. has expanded its Proctor Tools feature.  Instructors can now grant individual students with additional time or date extensions if there are ever any issues.

We’re also giving you a sneak peak at some up-and-coming technology: Gradeable Math Apps. As part of The Möbius Project, you can now embed an interactive Maple worksheet in a Maple T.A. question. Students can move sliders, push buttons, click on plot windows and much more directly inside of a Maple T.A. question. Students are then automatically graded on their interaction with the Math App – just like other question types in Maple T.A.

All these features are all for Maplesoft-hosted and self-hosted users, which also includes all the great stuff from Maple T.A. 9:

  • Adaptive Testing
  • New Question Repository
  • Maple T.A. Cloud
  • Hint Deductions
  • Reworking Assignments
  • MathJax Support
  • Distributed Load Balancing
  • Permanent User Deletion
  • Customizable User Interface
  • Multiple Instructors for a Class
  • And much more!

At Maplesoft, we are extremely excited about Maple T.A. 9.5, and can’t wait for schools all over the world to begin using it!  And as always, we are very interested in hearing from you about your experiences with Maple T.A., as well as any suggestions you have for future releases.

Thirteen Clickable Calculus examples have been added to the Teaching Concepts with Maple section of the Maplesoft web site. The additions include examples in algebra, differential and integral calculus, lines-and-planes in multivariate calculus, and linear algebra. By my count, this means some 97 Clickable Calculus examples are now available.

In the Algebra/Precalculus section, examples of an

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