Maplesoft Blog

The Maplesoft blog contains posts coming from the heart of Maplesoft. Find out what is coming next in the world of Maple, and get the best tips and tricks from the Maple experts.

I am very pleased to announce a new user community centered around Maplesoft's online testing and assessment and courseware products. The new site is specifically for instructors and administrators currently using Maple T.A. or Möbius. This community of users are a small, specialised group who we want to bring together so they can share ideas and best practices. To find the community, go to either mapletacommunity.com or mobiuscommunity.com.

"The Maple T.A. Community has grown organically to support new developers as they pool their knowledge and queries. This has resulted in a fluid searchable structure, with answers available for all levels of question - from beginner to pushing the frontiers of what Maple T.A. has been designed to do. Our summer student interns rely on the Community as they become proficient in their question writing skills - and many have become contributors as they realise that they are in a position to teach others. Opening it out more broadly will be great in sharing good practice on a 'need to know now' basis.”

----Professor Nicola Wilkin, University of Birmingham

 

What content is in the community?

The community has many posts from active Maple T.A. and Möbius users from beginners to advanced users. The site is broken down into categories like 'Best Practices' - longer form posts that cover a broader concept in more detail and 'Quick Code snippets' that are small piece of code that you can drop straight into your question algorithms.

Much of the content is openly available and can be found by google, however there is additional content that can only be accessed by members of the community, such as the Maple T.A. school material which teaches you how to author content in Maple T.A. and Möbius.

 

Who runs the community

The community is jointly run by users based at the Univeristy of Birmingham, TU Wien, The University of Turin and TU Delft.

 

How does this fit into Mapleprimes?

It began as an offshoot of a private, internal customer forum. As this community grows, the ultimate goal is to eventually roll it into MaplePrimes proper. But this alternative site gave us the quickest way to get up and running. Maple T.A. and Möbius questions and posts are still welcome on MaplePrimes, and will continue to be monitored by Maplesoft.

 

How do I access the community?

You can find the community by going to either mapletacommunity.com or mobiuscommunity.com.

 

Where else can I get support for Maple T.A. and Mobiüs?

Official support for Maple T.A. and Möbius is provided by the wonderful Customer Success Team at Maplesoft. You can contact them at help@maplesoft.com. For other contact methods see www.maplesoft.com/support/.

 

 

I am pleased to announce the public release of Möbius, the online courseware environment that focuses on science, technology, engineering, and mathematics education. After months of extensive pilot testing at select leading academic institutions around the world, Möbius is now available to everyone for your online learning needs.

We are very excited about Möbius. As you can imagine, many of us here at Maplesoft have backgrounds in STEM fields, and we are truly excited to be working on a project that gives students a hands-on approach to learning math-based content.  You can’t learn math (or science, or engineering, or …) just by reading about it or listening to someone talk about it. You have to do it, and that’s what Möbius lets students do, online, with instant feedback.  Not only can students explore concepts interactively, but they can find out immediately what they’ve understood and what they haven’t - not a few hours after the lecture as they are reviewing their notes, not two weeks later when they get their assignments back, but while they are in the middle of learning the lesson.

During its pilot phase, Möbius was used by multiple institutions around the world for a variety of projects, such as preparing students in advance for their first year math and engineering courses, and for complete online courses.  Over one hundred thousand students have already used Möbius, and the experiences of these students and their instructors has fed back into the development process, resulting in this public release.  You can read about the experiences of the University of Waterloo, the University of Birmingham, and the Perimeter Institute for Theoretical Physics on our web site.

We are also happy to announce that Maplesoft has partnered with the University of Waterloo, one of the largest institutions in the world for STEM education, to provide institutions and professors with rich online courses and materials that enable students to learn by doing.  These Möbius courses are created by experts at the University of Waterloo for use by their own students and for their outreach programs, and will be made available to other Möbius users.  Course materials range from late high school to the graduate level, with initial offerings available soon and many more to follow.

Visit the Möbius section of our web site for lots more information, including videos, whitepapers, case studies, and upcoming user summits.

Ilias Kotsireas is a Professor and Director of the CARGO lab at Wilfrid Laurier University, in Waterloo Ontario.

Throughout my career as a teacher, I’ve had the opportunity to work with students from around the globe. I’ve been able to work with students in other countries, immersing myself in their culture and learning environment. This has allowed me to experience the differences in educational delivery first hand, and to assess how education is viewed in other parts of the world.

On more than one occasion, I’ve visited the city of Guangzhou, China, to teach summer and winter school courses, beginning in 2007 and most recently in 2015 and 2016. During this time, I have witnessed tremendous growth in the development of Chinese Universities, as well as Chinese culture as a whole.  For example, the two largest supercomputers in the world - according to the website www.top500.org  - are located in China.  Another indication of the scale of this extraordinary growth is the fact that China currently has more than 2,000 universities, government research facilities and laboratories.  Furthermore, China Central Television (CCTV) programs report that China is planning the creation of an additional 10 mega-cities, each comparable in size to Shanghai.

Ilias Kotserias stands with students and fellow professors at South China Normal University (SCNU) in Guangzhou, China.

 

Summer and winter school courses in China are incredibly intensive. Such courses can run for one or two weeks and include two lectures per day, one on the morning and one in the afternoon. A tremendous amount of material must be covered in a short amount of time to accommodate the entire course.

Overall, my experiences have shown that students in China are very enthusiastic about education. They are heavily engaged with the learning materials and often spend time with professors at the conclusion of a lecture to converse and ask questions about what they have just learned. Class sizes are significantly smaller and there is a lot of one-on-one time with students. Students in China take their studies very seriously; they are very focused and motivated to do well in their studies, and they bring a great deal of knowledge and curiosity to the classroom.  Professors cannot gloss over material or deliver a scripted lecture. Students hold professors accountable, and expect them to be knowledgeable and have a strong understanding of the material. They have a strong desire to learn and gain experiences and relevant skills that they can carry forward with them in their educational and professional careers.

Maplesoft graciously offered short term licenses to my students in China, so they could use Maple in the mathematics courses I was teaching. Using Maple allowed me to continue using an experimental approach to teaching that I use for my students back home in Canada.  This approach encourages students to start with simple experimentation that may also contain visual components, develop a plausible conjecture and subsequently attempt to solve it step by step.  This promotes a “learn by doing” paradigm that promotes active learning and helps students better understand key mathematical concepts. In a delightful episode, one Chinese student told me “I don’t understand your English accent,” but in teaching with Maple there are no accents I need to worry about!  Chinese students are inquisitive, respectful and conscientious; it is an absolutely gratifying experience working with them. 

I was first introduced to Maple when I was completing my Masters and Ph.D in France in the late 1990s. When I began teaching in 2001, I introduced Maple into my classrooms to improve my students’ ability to learn the materials, understand difficult concepts, and to create more sustainable engagement with them. Initially, it took some work to convince them to use Maple, as it was not among the conventional learning methods they were used to. Eventually students came to embrace Maple as a learning tool and I was able to use visual and interactive examples to engage them. With Maple, experimentation is at your fingertips and it allows me to incorporate an example-driven learning experience for my students.

It was a valuable experience to work with students from another culture and be able to engage them using the same method I use to engage my students back home. Maple is not only a powerful and convenient teaching tool, but it can also assist in bridging cultural gaps and creating a learning experience that is uniform across the globe.

   Maplesoft aims to promote innovation in science, technology, engineering and math (STEM) in high school students by partnering with various organizations, and sponsoring initiatives in education, research and innovation. Every year, Maplesoft commits time, funds and people to enhance the quality of math-based learning and discovery and to encourage high school students to strengthen their math skills.

   One such organization we partner with is The Perimeter Institute, a leading centre for scientific research, training and educational outreach in foundational theoretical physics.  Maplesoft currently serves as its Educational Outreach Champion, supporting various initiatives that promote math learning and exploration. Perhaps the most popular of its student outreach program is the annual International Summer School for Young Physicists (ISSYP), a two-week camp that brings together 40 exceptional students from high schools across the globe.  Each year students receive a complimentary copy of Maple, and use the product to practice and strengthen their math skills.  The ISSYP program also uses Möbius, the comprehensive online STEM courseware platform from Maplesoft, to offer preparatory course materials to students.  Completing lessons in Möbius aid in making the summer program a more productive and dynamic experience for the students.

  

International Summer School for Young Scientists at Perimeter Institute

 

   Who Wants to Be a Mathematician is a competition organized by the American Mathematical Society (AMS) for high school students in North America. Maplesoft has been a sponsor of the contest for many years.  Maple T.A., the testing and assessment tool by Maplesoft, is used to administer the tests online, saving significant time and money for the organizers. When Maplesoft first introduced Maple T.A. to the contest, taking the competition from pen-and-paper tests to online tests, the number of contestants doubled, with about 2000 students participating in the contest. Maplesoft also donates prizes to the games in order to promote the use and love of math by high school students.  This year will be first time the competition moves international. Six students in the UK took the Round 2 qualifying test, with the use of Maple T.A., and qualified for the live, on-stage finals of the UK edition of the competition that took place at the 2017 Maths Fest in London. Maplesoft is also supporting the spread of the WWTBAM contest to Canada in 2017.


Who Wants to be a Mathematician finals

Maplesoft also sponsors two outreach initiatives in Texas A&M University.  The Summer Educational Enrichment (SEE) Math Program is a summer workshop attended by gifted middle school students. Students spend two weeks exploring ideas such as algebra, geometry, graph theory, and topology.  The University also conducts the Integral Bee every year, a math based contest for high school students.

In addition to the above key projects, throughout the year Maplesoft also sponsors and is associated with a number of other competitions, conferences, and educational initiatives. A few of these are listed below.

  • The Connecticut Science & Engineering Fair is a yearly, statewide science and engineering fair open to all 7th through 12th grade students.  An important objective of their program is to attract young people to careers in science and engineering while developing skills essential to critical thinking.
  • FIRST Robotics Competition is a high school robotics competition. Each year, teams of high school students and mentors work during a six-week period to build game-playing robots that weigh up to 120 pounds.

 

FIRSTRobotics Competition

  • ScienceExpo Conference is a student-run event that engages students with STEM-related opportunities and workshops
  • SWATposium is an annual robotics conference that brings together nearly 40 First Robotic Competition teams from both Canada and the United States for a day of guest speakers, workshops and social activities.

        

SWATposium

  • FIRST LEGO League gives elementary and middle school students and their adult coaches the opportunity to work and create together to solve a common problem.

      

FIRST LEGO League at St. Luke's School in Waterloo

   Maplesoft’s objective of these sponsorships is to support those who inspire and channel young minds to be STEM focussed. By engaging them in exciting contests and programs the hope is that they build science, engineering, and technology skills at a young age and grow to be innovators and technology leaders of tomorrow.

Recently, I came across an addendum to a problem that appears in many calculus texts, an addendum I had never explored. It intrigued me, and I hope it will capture your attention too.

The problem is that of girding the equator of the earth with a belt, then extending by one unit (here, taken as the foot) the radius of the circle so formed. The question is by how much does the circumference of the belt increase. This problem usually appears in the section of the calculus text dealing with linear approximations by the differential. It turns out that the circumference of the enlarged band is 2*Pi ft greater than the original band.

(An alternate version of this has the circumference of the band increased by one foot, with the radius then being increased by 0.16 ft.)

The addendum to the problem then asked how high would the enlarged band be over the surface of the earth if it were lifted at one point and drawn as tight as possible around the equator. At first, I didn't know what to think. Would the height be some surprisingly large number? And how would one go about calculating this height.

It turns out that the enlarged and lifted band would be some 616.67 feet above the surface of the earth! This is significantly larger than the increase in the diameter of the original band. So, the result is a surprise, at least to me.

This is the kind of amusement that retirement affords. I heartily recommend both the amusement and the retirement. The supporting calculations can be found in the attached worksheet: Girding.mw

I am pleased to announce that we have just released a significant update to Maple T.A. 2016, our online assessment system.

Maple T.A. 2016.1 includes a wide range of features and improvements that have been requested by customers, including new options for questions and assignments, improved content management, and enhanced integration with course management systems. It also includes a substantial number of small enhancements and corrections across all areas of the product, providing improved responsiveness, more efficient load handling, and smoother workflow for instructors and students.

For more information, visit What’s New in Maple T.A.

Jonny Zivku
Product Manager, Online Education Products

Everything is simple, until you go underwater – This is what the University of Waterloo Submarine Racing team, or in short ‘WatSub’ coined as their motto. Never mind learning to scuba dive, and dealing with such things as rust, this newly formed team would have to compete against university teams with a decade or more of experience.

But that did not deter the team, and they started work on Ontario’s first submarine racing project. The team approached Maplesoft to be a sponsor and we are proud to have supported this ingenious venture. The team has used Maplesoft technology in the design and testing of the submarine.

“Maple has been our go-to calculations and analysis tool throughout the development of Amy (2015-2016 season), and we will continue using it throughout the development of Bolt (2016-2017 season),” said Gonzalo Espinoza Graham, President of the WatSub Team. “Its familiar interface and computing environment allowed us to set design benchmark targets from early on the design process and follow through with them on the later stage.”

What started as an engineering project in December 2014, becoming officially the first submarine racing team in Ontario. The team soon grew to over 130 general members and a tight core-team, who were eager to tackle new challenges.  The team resides inside the Sedra Student Design Centre, University of Waterloo’s state of the art facility that houses over 25 student teams, the largest of its kind in North America.  

WatSub made its first appearance on the European International Submarine Races (eISR) back in July 2016, with its 1st submarine ‘Amy’, where a single scuba diver piloted the submarine and propelled it through an unforgiving winding course marked by obstacles and turns 10 meters underwater. The team has since then participated in other competitions and is constantly improving the design and performance of the submarine, learning from each competition they participate in.  Next year Amy will participate in the 14th edition of the eISR international competition. “I think the greatest thing we learned is never to give up,” said Ana Krstanovic, a third-year political science student who manages communications for the team. “We’re more motivated now than ever.”

 

Ojaswi Tagore, Gonzalo Espinoza Graham, and Janna Henzl represented WatSub at the European International Submarine Race in Gosport, UK.

 

Another example of an innovative project that Maplesoft supported in 2016 is Waterloop: The Canadian SpaceX Hyperloop Competition Team, Canada's only SpaceX Hyperloop Pod Competition team. This project, which could change the way we travel in the future, is driven by a group of dedicated University of Waterloo students who have taken on the challenge to design and build a functional prototype Hyperloop pod. They will test it on a one-mile test track in Hawthorne, California in January 2017, pitting it against 22 of the 1200+ teams who originally entered the competition.

The Hyperloop is a conceptual next generation high-speed transit system that will take commuters between cities at speeds over 1,000 km/h. The technology will differ from previous rail transit by having pods ride on a cushion of air in a reduced pressure tube in order to reach greater speeds with a smoother ride, and is powered entirely by renewable energy.

 The Hyperloop Pod Competition was launched by Elon Musk, the billionaire engineer and founder of SpaceX and Tesla Motors.  The competition is separated into 3 rounds. The first one was held in late December, where selected teams sent in their initial designs to be reviewed. From there, 180 teams were chosen to compete at Texas A&M University. Each team set up a booth and a panel of judges critiqued them and chose 31 teams to move onto the final, build and test stage.

Waterloop Goose I

Waterloop Goose X

The GOOSE I is Waterloop’s half-scale, functional prototype vehicle pod, which will be the one in the competition.  The GOOSE X pod is a conceptual full size Hyperloop vehicle inspired by the prototype they are building. The full size pod will have a capacity of 26 passengers per pod.

"Our prototype has been designed to be as simple and economical as possible, while still performing all necessary functions for the full size Hyperloop. If it is successful, it has the potential to revolutionize the transit industry in the same manner the train and airplane has before it," said Montgomery de Luna, architectural design lead for Waterloop. “We would like to thank Maplesoft for their generous support.  Without sponsors like Maplesoft supporting our vision and encouraging innovative student projects, we wouldn’t be able to achieve our goal.”

Revolutionizing the transportation industry isn’t easy and is at times frustrating and time consuming for these teams, but having the best tools and resources will ensure that the teams have a good chance at excelling in competitions and creating innovative models that could change our future.

The Joint Mathematics Meetings are taking place this week (January 4 – 7) in Atlanta, Georgia, U.S.A. This will be the 100th annual winter meeting of the Mathematical Association of America (MAA) and the 123nd annual meeting of the American Mathematical Society (AMS).

Maplesoft will be exhibiting at booth #118 as well as in the networking area. Please stop by our booth or the networking area to chat with me and other members of the Maplesoft team, as well as to pick up some free Maplesoft swag or win some prizes.

There are also several interesting Maple-related talks and events happening this week:

 

Teaching Cryptology to Increase Interest in Mathematics for Students Majoring in Non-Technical Disciplines and High School Students

Wednesday, January 4, 0820, L401 & L402, Lobby Level, Marriott Marquis

Neil Sigmon, Radford University

 

Enigma: A Combinatorial Analysis and Maple Simulator

Wednesday, January 4, 0900, L401 & L402, Lobby Level, Marriott Marquis

Rick Klima, Appalachian State University

 

MYMathApps Calculus - Building on Maplets for Calculus

Thursday, January 5, 0800, Courtland, Conference Level, Hyatt Regency

Philip B. Yasskin, Texas A&M University 
Douglas B. Meade, University of South Carolina 
Andrew Crenwelge, Texas A&M University

 

Maple Software Technology as a Stimulant Tool for Dynamic Interactive Calculus Teaching and Learning

Thursday, January 5, 1000, Courtland, Conference Level, Hyatt Regency

Lina Wu, Borough of Manhattan Community College-The City University of New York 

 

Collaborative Research: Maplets for Calculus

Thursday, January 5, 1400, Marquis Ballroom, Marquis Level, Marriott Marquis

Philip Yasskin, Texas A&M University 
Douglas Meade, U of South Carolina

 

Digital Graphic Calculus Art Design in Maple Software

Thursday, January 5, 1420, International 7, International Level, Marriott Marquis

Lina Wu, Borough of Manhattan Community College-The City University of New York 

 

Maplesoft will also be hosting a catered reception and brief presentation on Teaching STEM Online: Challenges and Solutions, Thursday January 5th, from 6:00pm – 7:30pm, at the Hyatt Regency, Hanover AB, on the exhibitor level. Please RSVP at www.maplesoft.com/jmm or at Maplesoft booth #118.

 

If you are attending the Joint Math meetings this week and plan on presenting anything on Maple, please feel free to let me know and I'll update this list accordingly.


See you in Atlanta!

Daniel

Maple Product Manager

At 3:00 PM EST on Thursday, December 15, Maplesoft hosted a momentous hour in my life, my "retirement party" ending my career at Maplesoft. It was a day I had planned some four years ago when I dropped to a lighter schedule, and a day my wife has been awaiting for six years.

Jim Cooper, CEO at Maplesoft, presented a very brief sketch of some milestones in my life, including my high school graduation in 1958, BA in 1963, MS in 1966, PhD in 1970, jobs at the University of Nebraska-Lincoln, Memorial University of Newfoundland, and the Rose-Hulman Institute of Technology. There was a picture of me taken from my high school graduation yearbook. There was a cake. There were kind words about my contributions to Maple, including "Clickable Calculus," the term and its meaning.

I was handed the microphone - I knew what I wanted to say. My wife was present in the gathering. I pointed to her and said that all the congratulations should go to her who had waited so patiently for my retirement for six years. I thanked Maplesoft and all its employees for nearly 14 of the best years of my life, for I have thoroughly enjoyed my return to Canada and my work (more like play) at Maplesoft. 

It's been a great opportunity to be part of the Maple experience, and now it's time for new ones. There'll be more woodworking in my basement woodshop where I make mostly noise and sawdust, some extra travel, more exercise and fresh air, long-delayed household projects, and whatever else my mate of 49 years asks.

But the best part of all is that I'll still have a connection to Maplesoft - I'll continue doing two webinars a month, will maintain and update much of the content I've created for Maple while at Maplesoft, and contribute additional content of relevance to the Maple community. 

A population p(t) governed by the logistic equation with a constant rate of harvesting satisfies the initial value problem diff(p(t), t) = (2/5)*p(t)*(1-(1/100)*p(t))-h, p(0) = a. This model is typically analyzed by setting the derivative equal to zero and finding the two equilibrium solutions p = 50+`&+-`(5*sqrt(100-10*h)). A sketch of solutions p(t) for different values of a suggests that the larger equilibrium is stable; the smaller, unstable.

 

When a is less that the unstable equilibrium, p(t) becomes zero at a time t[e], and the population becomes extinct. If p(t) is not interpreted as pertaining to a population, its graph exists beyond t[e], and actually has a vertical asymptote between the two branches of its graph.

 

In the worksheet "Logistic Model with Harvesting", two questions are investigated, namely,

 

  1. How does the location of this vertical asymptote depend on on a and h?
  2. How does the extinction time t[e], the time at which p(t) = 0, depend on a and h?

To answer the second question, an explicit solution p = p(a, h, t), readily provided by Maple, is set equal to zero and solved for t[e] = t[e](a, h). It turns out to be difficult both to graph the surface t[e](a, h) and to obtain a contour map of the level sets of this function. Instead, we solve for a = a(t[e], h) and obtain a graph of a(h) with t[e] as a slider-controlled parameter.

 

To answer the first question, the explicit solution, which has the form alpha*tan(phi(a, h, t))*beta(h)+50, exhibits its vertical asymptote when phi(a, h, t) = -(1/2)*Pi. Solving this equation for t[a] = t[a](a, h) gives the time at which the vertical asymptote is located, a function that is as difficult to graph as t[e]. Again the remedy is to solve for, and graph, a = a(h), with t[a] as a slider-controlled parameter.

 

Download the worksheet: Logistic_with_Harvesting.mw

Last week Michael Pisapia, Maplesoft European VP, attended the opening reception of Mathematics: The Winton Gallery at the Science Museum in London. Ahead of being open to the public on 8th December, contributors and donors were invited to take a look behind the scenes of the new gallery, which explores how mathematicians, their tools and ideas have helped to shape the modern world over the last four hundred years.

The gallery is a spectacular space, designed by the world-renowned Zaha Hadid Architects, housing over a hundred artefacts of mathematical origin or significance. It is divided up into disciplines ranging from navigation to risk assessment, and gambling to architecture. Inspired by the Handley Page aircraft, the largest object on display, and suspended as the centrepiece, the gallery is laid out using principles of mathematics and physics. It follows the lines of airflow around it in a stunning display of imagined aerodynamics, brought to life using light and sculpture. You can learn more about its design in this video.

Guests at the reception enjoyed a specially commissioned piece of music from the Royal College of Music titled ‘Gugnunc’, named after the aircraft and inspired by the rhythms of Morse code and mathematical and mechanical processes, and performed at the centre of the gallery.

Of course any exhibit celebrating all things maths is of great interest to us here at Maplesoft, but this one especially so, since Mathematics: The Winton Gallery showcases the earliest available version of Maple.

A copy of Maple V, from 1997, sits in ‘The Power of Computers’ section of the Winton Gallery, in an exhibit which tells the story of the significant role played by mathematical software in improving the quality of mathematics education and research. Other objects in the section include a Calculating Machine from the Scientific Service circa 1939, a PDP-8 minicomputer from the 1960s, and part of Charles Babbage’s mid-19th century analytical engine, intended as a high-powered mathematical calculator.

As many of you will remember, Maple V was a major milestone in the history of Maple, providing unparalleled interactivity, powerful symbolics and creative visualization in mathematical computation and modeling. For a walk down memory lane, check out Maple V: The Future of Mathematics (ca. 1994) on YouTube.

Seeing this copy of Maple finally in place in the exhibit marks the end of a long journey – and not just in the miles it travelled to arrive at the museum from its home in Canada. When we were first approached by the Science Museum for a donation of Maple, we launched a hunt to find not just the right copy of Maple with its box and manuals, but also artefacts that showcased the origin and history of Maple. It was a journey down memory lane for the inventors of Maple as well as the first few employees as they dug out old correspondences, photos, posters and other memorabilia that could be showcased. Today they can be proud of their contribution to this display at the Science Museum. 

Although the case of historic software packages is visually less impressive than many of the other items in the gallery, it certainly attracted plenty of attention as guests made their way in for the first time. 

For fans of Maple V - and there are many - it’s reassuring that the Science Museum are now entrusted with preserving not only the iconic packaging, but with telling the story of Maple’s history and marking its place in the evolution of mathematics and technology.

To learn more about Mathematics: The Winton Gallery, its highlights and architecture, visit http://www.sciencemuseum.org.uk/mathematics

To see the timeline of Maple’s evolution over the years, visit:  http://www.maplesoft.com/25anniversary/

This MaplePrimes guest blog post is from Dr. James Smith, an Assistant Lecturer in the Electrical Engineering and Computer Science Department of York University’s Lassonde School of Engineering. His team has been working with Maplesim to improve the design of assistive devices.

As we go through our everyday lives, we rarely give much thought to the complex motions and movements our bodies go through on a regular basis. Motions and movements that seem so simple on the surface require more strength and coordination to execute than we realize. And these are made far more difficult as we age or when our health is in decline. So what can be done to assist us with these functions?

In recent years, my research team and I have been working on developing more practical and streamlined devices to assist humans with everyday movements, such as standing and sitting. Our objective was to determine if energy could be regenerated in prosthetic devices during these movements, similar to the way in which hybrid electric vehicles recover waste heat from braking and convert it into useable energy.

People use – and potentially generate – more energy than they realize in carrying out common, everyday movements. Our research for this project focused on the leg joints, and investigated which of the three joints (ankle, knee or hip) was able to regenerate the most energy throughout a sitting or standing motion. We were confident that determining this would lead to the development of more efficient locomotive devices for people suffering from diseases or disabilities affecting the muscles around these joints.

In order to identify the point at which regenerative power is at its peak, we determined that MapleSim was the best tool to help us gather the desired data. We took biomechanical data from actual human trials and applied them to a robotic model that mimics human movements when transitioning between sitting and standing positions. We created models to measure unique movements and energy consumption at each joint throughout the identified movements to determine where the greatest regeneration occurred.

To successfully carry out our research, it was essential that we were able to model the complex chemical reactions that occur within the battery needed to power the assistive device. It is a challenge finding this feature in many engineering software programs and MapleSim’s battery modeling library saved our team a great deal of time and effort during the process, as we were able to use an existing MapleSim model and simply make adjustments to fit our project.

Using MapleSim, we developed a simplified model of the human leg with a foot firmly planted on the ground, followed by a more complex model with a realistic human foot that could be raised off the ground. The first model was used to create a simplified model-based motion controller that was then applied to the second model. The human trials we conducted produced the necessary data for input into a multi-domain MapleSim model that was used to accurately simulate the necessary motions to properly analyze battery autonomy.

The findings that resulted from our research have useful and substantial applications for prostheses and orthoses designs. If one is able to determine the most efficient battery autonomy, operation of these assistive devices can be prolonged, and smaller, lighter batteries can be used to power them. Ultimately, our simulations and the resulting data create the possibility of more efficient devices that can reduce joint loads during standing to sitting processes, and vice versa.

From October 19-21, the third installment of the Maple T.A. and Möbius User Summit took place. Making the move back to Europe this year, the three-day conference was held at the beautiful Vienna University of Technology in the heart of Vienna, Austria. The scope of this year’s event expanded to include Maplesoft’s newest product, Möbius, an online courseware environment, which is designed to help academic institutions move their STEM courses online.

This year’s Summit brought together participants from 20 countries, including Australia, the Czech Republic, Poland, China, Norway, India, Egypt, Japan, the Netherlands, and many others. Needless to say, there is great interest in learning more about how Maple T.A. and Möbius can play a role in shaping the educational landscape.

Video recordings of each presentation will be made public soon, so keep an eye out for them!

Conference attendees take in the sights on the veranda at TU Wien

Getting Down to Business

Presentations were divided into 5 overarching themes as they relate to Maple T.A. and Möbius: Shaping Curriculum; Content Creation; Experiences Using Möbius; Integrating with your Technology; and The Future of Online Education. Presentations were given by representatives from schools across Europe, including DTU (Denmark), TH Köln (Germany), Imperial College of London and University of Birmingham (UK), Vienna UT (Austria), KTH Royal Institute of Technology (Sweden), Université de Lausanne (Switzerland), and others.

Many talks showcased the impressive versatility of Maple T.A. as a online assessment system, and Möbius to have practical applications in all STEM subjects, from Nuclear Engineering to Operations Management and many subjects in between.

Perhaps the discussion that gave Maplesoft the most feedback was led by Steve Furino from the University of Waterloo, who divided attendees up into groups to formulate a wish list of what they’d like to see in a courseware authoring environment. The list had over 40 items.


Linda Simonsen, Country Manager in the Nordic, records a group’s wish list

Notable Quotables

Many thought-provoking statements and questions were posed, but the following few stood out above the rest:

  • “Wouldn’t it be wonderful if you could take the best course from the best instructor anywhere in the world?”
  • “With Maple T.A., we can divert resources away from grading and over to tutoring.”
  • “Möbius rescued us!”

Get the party started!

While each day was full of invigorating conference discussions, evenings provided ample opportunity to ditch the suit jacket and tie, and enjoy the lively Austrian atmosphere. The first evening at the Zwölf Apostelkeller was the perfect venue to break the ice while satisfying those taste buds longing for some traditional Viennese cuisine. Once Schnitzel, Käsespätzle (a delicious German version of Mac and Cheese), Strudel, Kaiserschmarren (shredded pancake), and a glass or two of wine hit the table, people soon forgot about the pouring rain outside.

The evening reception took place 3-4 levels under ground

Michael Pisapia, VP of Europe, serves digestifs to guests

It would have been hard to top the social in the Apostelkeller, but the next evening sure tried.

Day 2 finished with an impressive formal dining experience at the historic Gerstner Beletage in the Palace Todesco, built in 1864 and situated directly across from the Vienna State Opera House. The 500-room palace was home to Eduard Freiherr von Todesco, a well-known Viennese banker.

View from the palace of the Vienna State Opera House

Jonny Zivku, Maple T.A. Product Manager, gives opening remarks at the Gerstner Beletage im Palais Todesco

Jonathan Watkins from the University of Birmingham and Michael Pisapia - both dressed to impress

The skies finally cleared enough to take some photos, but only after most people had gone home. Thankfully Aron Pasieka, Möbius Project Manager, was still around to get some great shots of the city. Enjoy!


Before the skies cleared vs. after the skies cleared

From beginning to end, the entire Summit was very well received by everyone who attended.

We would be remiss if we did not thank our incredible hosts at the Vienna University of Technology. Stefanie Winkler, Professor Andreas Körner, and Professor Felix Breitenecker were beyond helpful in bringing many of the finer details together, as well as helping many people overcome the language barrier.

We can’t wait to do it all again in London, England in 2017, and hope to see just as many new faces as familiar ones.

 

Photo credits: A. Pasieka, A. French, H. Zunic, J. Cooper

 

Update: The conference presentation recordings are now available here on our website.

This MaplePrimes guest blog post is from Ian VanderBurgh, the Director of the Center for Education in Mathematics and Computing (CEMC) and a Lecturer in the Faculty of Mathematics at the University of Waterloo. He has been overseeing a project to develop online, interactive mathematics curriculum for high school students, and has been integral in the development of Möbius, Maplesoft's online courseware environment.

Start with one part interest in online education, add one part increased functionality for developing online content, and mix with one part increased focus in the media and elsewhere on mathematics education.  What does this produce?  The perfect time to create high-quality online resources to support learning and teaching in mathematics.

The Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo aims to increase interest, enjoyment, confidence, and ability in mathematics and computer science among learners and educators in Canada and internationally.  For more than fifty years, we have been working with teachers to support the important work that they do in the classroom.  When online courses rose to prominence several years ago, we felt that this gave us the perfect opportunity to create materials to better support the curriculum being taught across Canada and around the world.

The content for what we now call “Phase One” was planned: Advanced Functions (Pre-Calculus) as well as Calculus & Vectors.  These materials would support the education of students in their final year of secondary school, and also provide materials to reinforce concepts for students in STEM programs at the post-secondary level.

After deciding on the content, we needed a platform.  We knew that we needed one with exceptional mathematical capabilities.  Thus, we have been working hand-in-hand with Maplesoft ever since.

With content and platform established, the style began to take shape.  It is based around what one of my colleagues calls “the five Es”: Exposition (onscreen text with synchronized audio), Experimentation (worksheets where users can manipulate mathematical objects), Evaluation (re-generating quiz questions), Exercises (with answers and solutions), and Enrichment (application and extension problems and solutions).  Have a look at the materials and watch a video about the courseware.  After less than two years of “public life”, Phase One has received more than 2 million page views and usage is accelerating.

But why stop there?  Through the development of Phase One, all of the stakeholders realized that, while what we created was great, we needed better and more efficient development tools.  Thus, Möbius was born.  (In the meantime, the CEMC separately launched Phase Two of this ambitious initiative: resources in computer science to support the teaching and learning of programming concepts.)

Now, using the full capabilities of Möbius, we are developing Phase Three, a parallel set of resources to Phase One that will support mathematics at the Grade 7/8 level.  Why Grade 7/8?  We believe that these are very important years in education, that it is vital to future success in STEM disciplines that students flourish in these years, and that we should do whatever we can to support this.

What comes next?  Time will tell.  But, the CEMC will be there supporting mathematics and STEM education.  STEM disciplines will drive almost everything in the twenty-first century, and we have an obligation to do whatever we can to give young people every possible chance for success.

As mentioned a few weeks back, we have been working on an update to MaplePrimes designed to dramatically curtail the amount of spam we have been receiving. I'm happy to say that we implemented these features earlier today, and in the hour or so since publication, they have already helped prevent multiple messages from being posted.

Using content posted to MaplePrimes over the past few months as a baseline, this new feature is successfully able to detect 90% of spam, while maintaining a false positive (i.e., incorrectly identifying a legitimate question or post) rate of 1%.

If a message is detected as spam, it is immediately quarantined and not publicly posted. Importantly, any user who posts a message seen as spam is immediately informed, and is provided with a simple mechanism to let us know so that their post can be reinstated (if it is in fact legimate.)

We will be closely monitoring these services to ensure that they are working as intended. In the meantime, I am very hopeful that they help improve the experience for our members, and require much less effort from our dedicated group of spam fighters.

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