We’re trying out something new with our webinars and are hosting our first ever live streaming webinar. Broadcast in real time, and featuring Jonny Zivku, our Maple T.A. Product Manager, this will be your chance to see the face behind the voice, as well as learn more about how academic institutions around the world are using Maple T.A. We hope you can join us.

Here are the full details:

Transforming Testing and Assessment with Maple T.A.

In this webinar, you will learn how Maplesoft's testing and assessment system, Maple T.A., is being used to improve learning, save money, reduce drop-out rates, and increase student satisfaction at academic institutions around the world.

The following Maple T.A. case studies will be presented:

• The University of Waterloo saved $100,000/year on their grading budget
• At the Amsterdam University of Applied Science, student pass rates went up approximately 20% within one year
• The University of Canterbury continued to offer their full academic program after an earthquake damaged classrooms
• At the University of Guelph, drop-out rates were reduced by more than 10%
• ...And more!

All attendees of this webinar will be sent a complimentary copy of the Maplesoft magazine Transforming Testing and Assessment.

To join us for the live streaming webinar, please click here to register.

In case anyone is interested, we recently posted a new application on the Application Center,

Time Series Analysis: Forecasting Average Global Temperatures

While interesting in itself (well, I think so, anyway), this application also provides tips and techniques for analyzing time series data in Maple, and shows how to access online data sets through the new data sets functionality in Maple 2015.

eithne

The trailers for the new Star Wars movie (Star Wars: The Force Awakens) introduced a new Droid called BB-8. This curious little guy features a spherical body and a controlled instrumented head. More recently, the BB-8 droid was showcased in a Star Wars celebration event and to many peoples' surprise it is real and not a CGI effect!

We have a Sphero robot from Orbotix here at the office, and there was an immediate connection between BB-8 and the Sphero. All that remains is to add the head!

Many have already put together their version of the BB-8, but I wanted to have a physical model that I can play with in a virtual environment and explore some design options.

Preparation:

To build a model of BB-8 like robotic system in MapleSim (Maplesoft's physical modeling software environment), I first needed a couple things in place before going forward:

1. A few simple CAD shapes (half-sphere, wheels)
   
   
2. A component to represent the contact between two spheres (both outside contact and inside contact)

I used Maple’s plottools package to build the CAD files I needed. First a half-spherical shape:

Then a wheel:

The next step was to create the contact component in MapleSim. I used a Modelica custom component to bring together vector calculations of normal and tangential forces with a variety of options for convenience into one component:

Build the model:

We start with a spherical shape contacting the ground:

Then we add two wheels inside it, and a hanging mass to keep the reference axis vertical when the wheels turn:

Learning from published diagrams showing the internal mechanism of a Sphero, another set of free wheels improves the overall stability when motion commands are given to the two active wheels:

Now this model can be used to move around the surface by giving speed commands to the individual motors that drive to the two bottom wheels. What is needed next is the head and the mechanism to move it around.

Since the head can move almost freely, independent of body rotation, it has to be controlled via magnetic contacts and a controlled arm.

First, we add the control arm:

Now we need to build the head.

The head has an identical triangle to the one at the end of the control arm. At each vertex there is a ball bearing that would slide on the surface of the main spherical body without friction. The magnetic force between the corresponding vertices of the two triangles is modeled via the available point-to-point force element in MapleSim.

Once assembled, the MapleSim model diagram looks like this:

...and our BB-8 droid looks like this:

Seeing the BB-8 in action:

Now that we have constructed our droid in MapleSim, we can animate and see it in action!

With this application we can meet safety characteristics of a relationship and simple or compound functions. Made with maple 2015.

Relaciones_y_Funciones.mw

(in spanish)

L.AraujoC.

PLATFORM_2.mw

Two platforms (tripod) and abstract mechanism.

https://vk.com/doc242471809_379935473
https://vk.com/doc242471809_380837279
https://vk.com/doc242471809_378352452
https://vk.com/doc242471809_380217387

And six degrees of freedom of a rigid body



https://vk.com/doc242471809_383336706

Download Discovery_with_Maple.mw

I'd like to pay attention to an application "Interaural Time Delay" by Samir Khan. His applications are interesting, based on  real data, and  mathematically accurate. Here is its introduction:

"Humans locate the origin of a sound with several cues. One technique employs the small difference in the time taken for the sound to reach either ear; this is known as the interaural time delay (ITD). This application modifies a single-channel audio file so that the sound appears to originate at an angle from the observer. It does this by introducing an extra channel of sound. Despite both channels having the same amplitude, the sound appears to come from an angle simply by delaying one channel".

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Case Study: Transforming a University's Placement Testing Process

This webinar will feature the story of how the University of the Virgin Islands moved their placing testing process from paper and pen to using the Mathematical Association of America’s (MAA) placement tests offered through the Maple T.A. testing environment. Instructors at the university now handpick questions to create their own placement tests that best fit the course they are teaching. From there, they are able to analyze the data and craft lessons based on student performance. The end result is that students are more satisfied with the education they are receiving and instructors have made enormous gains with regards to efficiency and flexibility.

To join us for the live presentation with Dr. Celil Ekici from the University of the Virgin Islands, please click here to register.

Getting Started with Maple

This webinar is designed for the user who comes to Maple for the first time. It will demonstrate “how to get started” by clarifying the user interface and the ways math can be entered into Maple, and then “processed.” Coverage includes

• Entering mathematical expressions and interacting with them in a syntax-free way.
• The difference between input in mathematical notation and “linear” or text form.
• The role of the Context Sensitive Menu system for interacting with mathematical objects.
• Graphing and interacting with various types of graphs, including animations, surfaces, and implicit plots.
• Use of built-in tools such as Assistants, Tutors, and Task Templates.
• The Maple help system and the Maple Portal.
• Introduction to differential equations and matrix manipulations.

To join us for the live presentation, please click here to register.

The new Import and Export commands introduced in Maple 2015 provide a unified approach to all data import and export activities, replacing the need to use different commands in different situations. They can be used with many of the wide variety of file types supported by Maple, including 3-D graphics data, numeric and tabular data, images, audio files, special-purpose formats for mathematical objects such as graphs, and much more.

In the following example, you can see how to use these commands in order to bring 3-D models from the popular website Thingiverse and to export 3-D plots to a format suitable for 3-D printing.

Tips and Techniques: 3-D Model Import/Export and Printing

Another application for the study of rational numbers in operations, generating fraction, etc.

Numeros_Racionales.mw

(in spanish)

Atte.

L.AraujoC.

As you saw in the Maple 2015 What’s New, the MapleCloud is now online at maplecloud.maplesoft.com.  In addition to accessing MapleCloud content from within Maple, you can now use a web browser to view and interact with MapleCloud documents. The new online MapleCloud is based on HTML5 and works across a broad range of browsers. No plugins. No Java.

The MapleCloud was first introduced about five years ago, in Maple 14, and has allowed Maple users around the globe to share worksheets and Math Apps with fellow users. The Maple Cloud allows you to create groups in order to share content with specific people, as well as sharing them publicly.  Today we count over 1400 such groups that have been created for a class, a project or a workgroup, hosting tens of thousands of Maple worksheets, with thousands of worksheets being up- and down-loaded every month. Feedback has been tremendous, and clearly, this feature has hit a nerve with our user community and has attracted a strong following.

A common use case is to set up a MapleCloud group for a class in order to exchange Maple material among students and instructors. Some teachers are using this as the primary mechanism for submitting and marking assignments. Just as common is to use the MapleCloud as a convenient way to exchange and review documents while working on a joint project. Many users also use the Cloud to store their own documents in a private online space so that they can access them from multiple computers and locations. Wherever they have access to Maple, they also have access to all their Maple documents.

Then, there are the public groups in the MapleCloud, where users around the world freely share applications and examples; it’s a treasure trove of material covering all sorts of topics from calculus to fractals.

Now online, the MapleCloud continues to be a great repository for Maple content, but in addition, there are also some new aspects. For starters, it is really easy to share a Maple worksheet or Math App with someone else by simply giving them a URL. Click on it and the Maple worksheet opens in your web browser and all interactive components and plots are live - you can change parameters, calculate new results and update plots. For example, you can try out a Password Security tool or explore the Vertex of a Parabola. Maple is not required for consuming content in this way. But if you do have Maple, another click downloads the document to your local copy of Maple, where you can modify and extend it.

The online MapleCloud is a great way to manage your documents and share Maple content with students and colleagues.  This, of course, is only one more step towards making all of our technology available online and you will see more unfold over the course of this year!

The work contains two procedures called  SetPartition  and  NumbPart .

The first procedure  SetPartition  generates all the partitions of a set  S  into disjoint subsets of specific sizes defined by a list  Q. The third optional parameter is the symbol  `ordered`  or  `nonordered`  (by default) . It determines whether the order of subsets in a partition is significant.

The second procedure  NumbPart  returns the number of all partitions of the sizes indicated by  Q .

Codes of these procedures:

SetPartition:=proc(S::set, Q::list(posint), K::symbol:=nonordered)  # Procedure finds all partitions of the set  S  into subsets of the specific size given Q.

local L, P, T, S1, S2, n, i, j, m, k, M;

uses ListTools,combinat;

if `+`(op(Q))<>nops(S) then error "Should be `+`(op(Q))=nops(S)" fi;

L:=convert(Q,set);

T:=[seq([L[i],Occurrences(L[i],Q)], i=1..nops(L))];

P:=`if`(K=ordered,convert(T,list),convert(T,set));

S1:=S;  S2:={`if`(K=ordered,[],{})}; n:=nops(P);

for i to n do

m:=P[i,1]; k:=P[i,2];

for j to k do

S2:={seq(seq(`if`(K=ordered,[op(s),t],{op(s),t}), t=choose(S1 minus `union`(op(s)),m)), s=S2)};

od; od;

if K=ordered then {map(op@permute,S2)[]} else S2 fi;

end proc:

NumbPart:=proc(Q::list(posint), K::symbol:=nonordered)  # Procedure finds the number of all partitions of a set into subsets of the specific size given  Q

local L, T, P, n, S, N;

uses ListTools;

L:=convert(Q,set);

T:=[seq([L[i],Occurrences(L[i],Q)], i=1..nops(L))];

P:=`if`(K=ordered,convert(T,list),convert(T,set));

n:=nops(P);  N:=add(P[i,2], i=1..n);

S:=add(P[i,1]*P[i,2],i=1..n)!/mul(P[i,1]!^P[i,2],i=1..n)/mul(P[i,2]!,i=1..n);

if K=nonordered then return S else  S*N! fi;

end proc:

Examples of use:

SetPartition({a,b,c,d,e}, [1,1,3]);  nops(%);  # Nonordered partitions and their number

SetPartition({a,b,c,d,e}, [1,1,3], ordered);  nops(%);  # Ordered partitions and their number

Here's a more interesting example. 5 fruits  {apple, pear, orange, mango, peach}  must be put on three plates so that  on each of two plates there are 2  fruits, and there is one fruit  on one plate. Two variants to solve: 1) plates are indistinguishable and 2) different plates. In how many ways can this be done?

SetPartition({apple,pear,orange,mango,peach}, [1,2,2]);  nops(%);  # plates are indistinguishable

NumbPart([1,2,2], ordered);  # Number of ways for  different plates

                                                              90

Another example - how many ways can be divided  100 objects into 10 equal parts?

NumbPart([10$10]);

    64954656894649578274066349293466217242333450230560675312538868633528911487364888307200

 SetPartition.mws

Application of the properties of real numbers such as divisible factors, quantity and sum of prime divisors, DCM and MCM among others. All the technology embedded components of Maple.

Propiedad_de_los_Numeros.mw

Atte.

L.AraujoC.

I would like to pay attention to an article by David Austin "The Stable Marriage Problem and School Choice"

Here is its inroduction:

" Every year, 75,000 New York City eighth graders apply for admission to one of the city's 426 public high schools. Until recently, this process asked students to list five schools in order of preference. These lists were sent to the schools, who decided which applicants to accept, wait-list, or reject. The students were then notified of their status and allowed to accept only one offer and one position on a waiting list. After the students had responded to any offers received, schools with unfilled positions made a second round of offers, and this process continued through a concluding third round.

This process had several serious problems. At the end of the third round of offers, nearly half of the students, usually lower-performing students from poor families, had not been accepted into a school. Many of these students waited through the summer only to learn they had been matched with a school that was not on their list of five schools.

This process also encouraged students and their parents to think strategically about the list of schools they submitted. Students that were rejected by the school at the top of their list might find that their second-choice school had no vacancies in the second round of offers. This made it risky for many students to faithfully state their true preferences, a view encouraged by the Education Department's advice that students "determine what your competition is" before creating their lists of preferred schools.

Lastly, schools would often underrepresent their capacity hoping to save positions for students who were unhappy with their initial offerings.

In the end, the process couldn't place many students while it encouraged all parties, both students and schools, to strategically misrepresent themselves in an effort to obtain more desirable outcomes not possible otherwise. Widespread mistrust in the placement process was a natural consequence.

Using ideas described in this column, economists Atila Abdulkadiroglu, Parag Pathak, and Alvin Roth designed a clearinghouse for matching students with high schools, which was first implemented in 2004. This new computerized algorithm places all but about 3000 students each year and results in more students receiving offers from their first-choice schools. As a result, students now submit lists that reflect their true preferences, which provides school officials with public input into the determination of which schools to close or reform. For their part, schools have found that there is no longer an advantage to underrepresenting their capacity.

The key to this new algorithm is the notion of stability, first introduced in a 1962 paper by Gale and Shapley. We say that a matching of students to schools is stable if there is not a student and a school who would prefer to be matched with each other more than their current matches. Gale and Shapley introduced an algorithm, sometimes called deferred acceptance, which is guaranteed to produced a stable matching. Later, Roth showed that when the deferred acceptance algorithm is applied, a student can not gain admittance into a more preferred school by strategically misrepresenting his or her preferences.

This column will present the game-theoretic results contained in the original Gale-Shapley paper along with Roth's subsequent analysis. Pathak calls the deferred acceptance algorithm "one of the great ideas in economics," and Roth and Shapley were awarded the 2012 Nobel Prize in economics for this work"

It would be nice to realize that in Maple.

Maple T.A. 10 introduced two new question types: Sketch and Free Body Diagram. To assist users in learning the new question types, Maplesoft has created a few hundred samples to look at. These sample questions are already featured on the Maple T.A. Cloud, but you can also download the course modules below. 

Sketching Questions - This course module contains 309 sketch questions. Areas covered include: functions, exponential functions, inequalities, linear equations, logarithmic functions, piecewise functions, quadratic equations, systems of equations and transformations of functions.

Free Body Diagram Questions - This course module contains 118 free body diagram questions. Areas covered include: Electricity, Magnetism and Mechanics.

Jonny Zivku
Maplesoft Product Manager, Maple T.A.