## Eigenpairs - Live!

by:

You are teaching linear algebra, or perhaps a differential equations course that contains a unit on first-order linear systems. You need to get across the notion of the eigenpair of a matrix, that is, eigenvalues and eigenvectors, what they mean, how are they found, for what are they useful.

Of course, Maple's Context Menu can, with a click or two of the mouse, return both eigenvalues and eigenvectors. But that does not satisfy the needs of the student: an answer has been given but nothing has been learned. So, of what use is Maple in this pedagogical task? How can Maple enhance the lessons devoted to finding and using eigenpairs of a matrix?

In this webinar I am going to demonstrate how Maple can be used to get across the concept of the eigenpair, to show its meaning, to relate this concept to the by-hand algorithms taught in textbooks.

Ah, but it's not enough just to do the calculations - they also have to be easy to implement so that the implementation does not cloud the pedagogic goal. So, an essential element of this webinar will be its Clickable format, free of the encumbrance of commands and their related syntax. I'll use a syntax-free paradigm to keep the technology as simple as possible while achieving the didactic goal.

Notes added on July 7, 2015:

## Maplesoft’s First Live Streaming Webinar!

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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.

## Building a model of the Star Wars BB-8 Droid in...

by:

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:

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!

## April’s Featured Live Webinars

by: Maple

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.

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.

## The MapleCloud Goes Online

by:

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!

## March’s Featured Live Webinar

by: Maple 2015

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

See What’s New in Maple 2015 for Educators

Maple 2015 is a major new release of Maple, the technical computing software used for education, research, and development involving mathematics, engineering, and the sciences. With Maple 2015, Maplesoft offers important new abilities to both educators and researchers, particularly in the areas of data analysis, application development and statistics education. This webinar will provide a complete overview of these new features, including:

• A new interface to access, work with, and visualize millions of datasets in the areas of finance, economics, and demographics.
• New facilities for developing Math Apps, including a new microphone and speaker component.
• Advances in integration, differential equations, interactive maps, group theory, physics, and more.
• New Clickable Math tools, including palettes and 60 new interactive Math Apps.
• New tutors, palettes and Math Apps designed explicitly for teaching and learning statistics.
• And more!

## Maple 2015 is now available!

by: Maple 2015

Math powers the world. From tracking the spread of an epidemic to designing a new rocket engine, mathematical equations allow us to understand a challenge and formulate an approach to solving it. Everywhere around us, math is ubiquitous; an equation determines how your thermostat controls your home furnace; a mathematical algorithm is used to encode the signal from your cell phone. More than ever, we rely on mathematics to make our lives better. And continually, our mathematical techniques get more refined as we solve more and more complex problems.

## February’s Featured Live Webinars

by:

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.

Introduction to the Maple T.A. MAA Placement Test Suite – Part #2

This webinar will provide attendees with a more detailed guide to the Maple T.A. MAA Placement Test Suite. The presentation will go beyond the basics to introduce each type of placement test, including algorithmic tests, calculator-based tests, concept readiness tests, and more. A few topics will be explored in the context of each different test type. The presentation will conclude with an explanation of how to set cut-off scores for your institution, as well as how the placement tests were created and validated by the Mathematical Association of America.

Creating Questions in Maple T.A. – Part #3

This presentation is the third installment of a series that explores question authoring in Maple T.A., Maplesoft’s testing and assessment solution for courses involving mathematics. This final webinar will focus on creating advanced Maple-graded questions using intuitive algorithms.

In case you missed them, the first webinar in the series provided an overview of the question repository and how to create various types of basic questions. The second webinar in the series focused on how to create better questions using the question designer, and introduced more advanced question types such as sketch and free body diagram.

## Top 10 Webinars of 2014

Happy New Year! Now that 2014 is behind us, I thought it would be interesting to look back on the year and recap our most popular webinars. I’ve gathered together a list of the top 10 academic webinars from 2014 below. All these webinars are available on-demand, and you can watch the recording by clicking on the webinar titles below.

-----------------------------------------------

See What’s New in Maple 18 for Educators

In this webinar, an expert from Maplesoft will explore new features in Maple 18, including improved tools for developing quizzes, enhanced tools for visualizations, updated user interface, and more.

Introduction to Teaching Calculus with Maple: A Complete Kit

During this webinar you will learn how to boost student engagement with highly interactive lectures, reinforce concepts with built-in “what-if” explorations, consolidate learning with carefully-constructed homework questions, and more.

Maplesoft Solutions for Math Education

In this webinar, you will learn how Maple, The Möbius Project, and Maplesoft’s testing and assessment solutions are redefining mathematics education.

Teaching Concepts with Maple

This webinar will demonstrate the Teaching Concepts with Maple section of our website, including why it exists and how to use it to help students learn concepts more quickly and with greater insight and understanding.

Revised Calculus Study Guide - A Clickable-Calculus Manual

This webinar will provide an overview of the Revised Calculus Study Guide, the most complete guide to how Maple can be used in teaching and learning calculus without first having to learn any commands.

Clickable Engineering Math: Interactive Engineering Problem Solving

In this webinar, general engineering problem-solving methods are presented using clickable techniques in the application areas of mechanics, circuits, control, and more.

Hollywood Math 2

In this second installment of the Hollywood Math webinar series, we will present some more examples of mathematics being used in Hollywood films and popular hit TV series.

In this webinar, learn how to quickly create multi-link robots by simply defining DH parameters in MapleSim. After a model is created, learn to extract the kinematic and dynamic equations symbolically in Maple.

Introduction to Maple T.A. 10

This webinar will demonstrate the key features of Maple T.A. from both the instructor and student viewpoint, including new features in Maple T.A. 10.

The Möbius Project: Bringing STEM Courses Online

View this presentation to better understand the challenges that exist today when moving a STEM course online and to find out how the Maplesoft Teaching Solutions Group can help you realize your online course vision.

-----------------------------------------------

Are there any topics you’d like to see us present in 2015? Make sure to leave us a comment with your ideas!

Kim

## November Live Webinars

by: Maple

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.

Creating Questions in Maple T.A. – Part #1

This webinar will demonstrate how to create questions in Maple T.A., Maplesoft’s testing and assessment solution for any course involving mathematics. The presentation will begin with an overview of the basic types of questions available, and then delve into how to create various types of questions in Maple T.A. Incorporating algorithms and feedback directly into questions will also be touched on. Finally, the session will wrap up with an explanation and several examples of how to create better questions using the question designer.

This first webinar in a two part series will cover true/false, multiple choice, numeric, mathematical formula, fill in the blank, sketch, and FBD questions. A second webinar that demonstrates more advanced question types will follow.

Clickable Calculus: Linear Algebra

In this webinar, Dr. Robert Lopez will apply the techniques of “Clickable Calculus” to standard calculations in Linear Algebra.

Clickable Calculus, the idea of powerful mathematics delivered using very visual, interactive point-and-click methods, offers educators a new generation of teaching and learning techniques. Clickable Calculus introduces a better way of engaging students so that they fully understand the materials they are being taught. It responds to the most common complaint of faculty who integrate software into the classroom – time is spent teaching the tool, not the concepts.

## October Live Webinars

by: Maple

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

Maplesoft Solutions for Math Education

This webinar will demonstrate how Maplesoft’s solutions for mathematics education help teachers bring complex problems to life, allow students to focus on concepts rather than the mechanics of solutions, and offer students the necessary practice to master the concepts being taught.

Key takeaways include:

• How to quickly and painlessly place incoming students in the correct math courses

• How you can use hundreds of intuitive Clickable Math tools to demonstrate and explore up to advanced-level problems and algorithms in the classroom

• How to automate your testing and assessment needs, specifically for math courses

• How to bring your STEM courses to life in an online environment

Introduction to Maple T.A. Placement Test Suite 10

This webinar will provide an overview and demonstration of the latest release of the Maple T.A. MAA Placement Test Suite. A result of the ongoing partnership between the Mathematical Association of America (MAA) and Maplesoft, this product gives you the ability to provide the renowned MAA placement tests in an online testing environment. Learn how the Maple T.A. MAA Placement Test Suite can greatly simplify your placement process and explore the latest additions, including a streamlined interface and new tests to determine your students’ readiness for Precalculus and Algebra courses.

There is also a recording available from another live webinar we did earlier this month: Introduction to Maple T.A. 10.

## Announcing Maple T.A. 10

by:

After lots of hard work, vast amounts of testing, and enormous anticipation, Maple T.A. 10 is now available! Maple T.A. 10 is by far our biggest release to date - and we’re not just saying that. When we compare the list of new features and improvements in Maple T.A. 10 with that of previous releases, it’s clear that Maple T.A. 10 has the largest feature set and improvements to date.

## June Live Webinars

by: Maple

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

Bring Statistics Education to Life!

This exciting new webinar will demonstrate some of the ways that educators can take advantage of Maple’s symbolic and numeric approach for statistics education. Examples will include basic statistics theory including descriptive statistics such as measures of central tendency and spread, hypothesis testing, as well as discrete and continuous random variables.

Many examples presented in this webinar will be taken from the new Student Statistics package that was introduced in Maple 18. The Student Statistics was designed with classroom use in mind, and features detailed explanations and instructions, interactive demonstrations, and visualizations, all of which are great learning tools for teaching a course involving probability and statistics.

Symbolic Computing for Engineering

As engineering applications become more complex, it is becoming increasingly difficult to satisfy the often-conflicting project constraints using traditional tools. As a result, we’ve found there is a growing interest within the engineering community for tools that make engineering calculations transparent and capture not just results but also the knowledge and analysis used throughout the engineering workflow. Engineering organizations are achieving this goal by making symbolic techniques an integral part of their tool set.

In this webinar, Laurent Bernardin will demonstrate how to enhance the early-stage design phase by making mathematical computations explicit and transparent, and then integrating the results into an existing tool chain.

## Multiple Choice Questions: Not So Ordinary Anymore...

by:

I think we all know the routine. We walk to a large classroom, we sit down for a test, we receive a large stack of questions stapled together and then we fill in tiny bubbles on a separate sheet that is automatically graded by a scanning machine. We’ve all been there. I was thinking recently about how far the humble multiple choice question has come over the last few years with the advent of systems like Maple T.A., and so I did a little research.

Multiple choice questions were first widely-distributed during World War I to test the intelligence of recruits in the United States of America. The army desired a more efficient way of testing as using written and oral evaluations was very time consuming. Dr. Robert Yerkes, the psychologist who convinced the army to try a multiple choice test, wanted to convince people that psychiatry could be a scientific study and not just philosophical. A few years later, SATs began including multiple choice questions. Since then, educational institutions have adopted multiple choice questions as a permanent tool for many different types of assessments.

One of the biggest advances in the use of multiple choice questions was the birth of automatic grading through the use of machine-readable papers. These grew in popularity during the mid-70s as teachers and instructors saved time by not having to grade answer sheets manually.

Until recently, there has not been much advancement in this area.  It’s true, Maple T.A. can do so much more than just multiple choice questions, so this style of question is less important in large-scale testing than it used to be. But multiple choice questions still have their place in an automated testing system, where uses include leveraging older content, easily detecting patterns of misunderstanding, requiring students to choose from different images, and minimizing student interaction with the system. Luckily, Maple T.A. takes even the humble multiple choice questions to the next level. Now you might be thinking, how is that even possible given the basic structure of multiple choice questions? What could possibly be done to enhance them?

Well, for starters, in Maple T.A., you can permute the answers. This means you have the option to change the order of the choices for each student. This is also possible with machine-readable papers, but this does require multiple solution sets for a teacher or instructor to keep track of. With Maple T.A., everything is done for you. For example, if you have a multiple choice question in Maple T.A. with 5 answer choices, there are 120 different possible answer orders that students can be presented with. You don’t have to keep track of extra solution sets or note which test version each student is receiving. Maple T.A. takes care of it all.

Maple T.A. allows you to create Algorithmic questions - multiple choice questions in which you can vary different values in your question. And you aren’t limited to selecting values from a specific range, either. For example, you can select a random integer from a pre-defined list, a random number that satisfies a mathematical condition, such as ‘divisible by 3’ or ‘prime’, or even a random polynomial or matrix with specific characteristics. It allows an instructor to create a single question template, but have tens, hundreds, or even thousands of possible question outcomes based on the randomly selected values for the algorithmic variables. The algorithmic variables not only apply to the question being asked by a student, but also the choices they see in a multiple choice question.

You can even create a question where every student gets the same fixed list of choices, but the question varies to ensure that the correct response changes.  That’s going to confuse some students who are doing a little more “collaboration” than is appropriate!

Some of the other advantages of using Maple T.A. for multiple choice are also common to all Maple T.A. question types. For example, you can provide instant, customized feedback to your students. If a student gets a multiple choice question correct, you can provide feedback showing the solution (who is to say the student didn’t guess and get this question correct?) If a student gets a multiple choice question incorrect, you can provide targeted feedback that depends on which response they chose. This allows you to customize exactly what a student sees in regards to feedback without having to write it out by hand each time.

And of course, like in other Maple T.A. questions, multiple choice questions can include mathematical expressions, plots, images, audio clips, videos, and more – in the questions and in the responses.

Finally, let’s not forget, in an online testing environment, there is no panic when you realized you accidently skipped line 2 while filling out your card, no risk of paper cuts, and no worrying about what kind of pencil to use!

References:

http://www.edutopia.org/blog/dark-history-of-multiple-choice-ainissa-ramirez

http://xkcd.com/499/

http://io9.com/5908833/the-birth-of-scantrons-the-bane-of-standardized-testing

## Announcing Maple 18

by:

This is one of my favorite events of the year. When we launch a new release of Maple, I get to see the work of so many talented individuals at Maplesoft come together in a form that I am sure will delight, and maybe even surprise you.

We are holding true to our principles with Maple 18. Hundreds of new mathematical algorithms further strengthen a computational engine that will help you tackle your toughest challenges. The user interface experience continues to become smarter, allowing you to focus on getting results without fighting with syntax. Connectivity options are again becoming richer.

A personal favorite of mine is the newly enhanced Explore functionality, which allows you to, with a couple of clicks, go from a mathematical expression to an interactive Math App. Math Apps allow you to explore the parameter space of the expression, gain insight into its behavior and even, in conjunction with Maple T.A., produce a gradeable Möbius App that allows you to assess a student’s interaction with the app and hence their understanding of the underlying concepts. The expanded Explore functionality is just part of a collection of advancements in Maple 18 that support The Möbius Project.

Overall, the new features of Maple 18 are quite numerous and I won’t try to list them all here. However, I do want to mention a few areas that have received special attention:

• Statistics: Maple 18 includes lots of enhancements to statistics computations and visualization, such as new time series functionality that allows you to find patterns, make forecasts, and visualize time-based data. For the classroom, a new Student Statistics package, together with a range of bundled Math Apps, provide a simplified and interactive environment for instructors and students alike.

• Physics: This package for representing and computing with concepts from general relativity to quantum mechanics continues to grow by leaps and bounds, with over 500 enhancements just in this release alone. We are convinced that this is the best computational environment available for researchers in this area.

• Engineering: Key enhancements for control analysis, signal processing, and code generation to Python and Perl are just a few of the new features that engineers will note and appreciate. There’s even import/export for STL graphics files, which, amongst other things, means you can now print out your favorite Maple plots on a 3-D printer!

I think you will agree that Maple 18 exemplifies all the effort and attention that we have put into it.  And there’s more to come - this release is just the start of a stream of product announcements that you can expect from us in the coming months. Stay tuned!

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