## Announcing Maple 2019

by: Maple 2019

Last year, I read a fascinating paper that presented evidence of an exoplanet, inferred through the “wobble” (or radial velocity) of the star it orbits, HD 3651. A periodogram of the radial velocity revealed the orbital period of the exoplanet – about 62.2 days.

I found the experimental data and attempted to reproduce the periodogram. However, the data was irregularly sampled, as is most astronomical data. This meant I couldn’t use the standard Fourier-based tools from the signal processing package.

I started hunting for the techniques used in the spectral analysis of irregularly sampled data, and found that the Lomb Scargle approach was often used for astronomical data. I threw together some simple prototype code and successfully reproduced the periodogram in the paper.

After some (not so) gentle prodding, Erik Postma’s team wrote their own, far faster and far more robust, implementation.

This new functionality makes its debut in Maple 2019 (and the final worksheet is here.)

From a simple germ of an idea, to a finished, robust, fully documented product that we can put in front of our users – that, for me, is incredibly satisfying.

That’s a minor story about a niche I’m interested in, but these stories are repeated time and time again.  Ideas spring from users and from those that work at Maplesoft. They’re filtered to a manageable set that we can work on. Some projects reach completion in under a year, while other, more ambitious, projects take longer.

The result is software developed by passionate people invested in their work, and used by passionate people in universities, industry and at home.

We always pack a lot into each release. Maple 2019 contains improvements for the most commonly used Maple functions that nearly everyone uses – such as solve, simplify and int – as well features that target specific groups (such as those that share my interest in signal processing!)

I’d like to to highlight a few new of the new features that I find particularly impressive, or have just caught my eye because they’re cool.

Of course, this is only a small selection of the shiny new stuff – everything is described in detail on the Maplesoft website.

Edgardo, research fellow at Maplesoft, recently sent me a recent independent comparison of Maple’s PDE solver versus those in Mathematica (in case you’re not aware, he’s the senior developer for that function). He was excited – this test suite demonstrated that Maple was far ahead of its closest competitor, both in the number of PDEs solved, and the time taken to return those solutions.

He’s spent another release cycle working on pdsolve – it’s now more powerful than before. Here’s a PDE that Maple now successfully solves.

Maplesoft tracks visits to our online help pages - simplify is well-inside the top-ten most visited pages. It’s one of those core functions that nearly everyone uses.

For this release, R&D has made many improvements to simplify. For example, Maple 2019 better simplifies expressions that contain powers, exponentials and trig functions.

Everyone who touches Maple uses the same programming language. You could be an engineer that’s batch processing some data, or a mathematical researcher prototyping a new algorithm – everyone codes in the same language.

Maple now supports C-style increment, decrement, and assignment operators, giving you more concise code.

We’ve made a number of improvements to the interface, including a redesigned start page. My favorite is the display of large data structures (or rtables).

You now see the header (that is, the top-left) of the data structure.

For an audio file, you see useful information about its contents.

I enjoy creating new and different types of visualizations using Maple's sandbox of flexible plots and plotting primitives.

Here’s a new feature that I’ll use regularly: given a name (and optionally a modifier), polygonbyname draws a variety of shapes.

In other breaking news, I now know what a Reuleaux hexagon looks like.

Since I can’t resist talking about another signal processing feature, FindPeakPoints locates the local peaks or valleys of a 1D data set. Several options let you filter out spurious peaks or valleys

I’ve used this new function to find the fundamental frequencies and harmonics of a violin note from its periodogram.

Speaking of passionate developers who are devoted to their work, Edgardo has written a new e-book that teaches you how to use tensor computations using Physics. You get this e-book when you install Maple 2019.

The new LeastTrimmedSquares command fits data to an equation while not being signficantly influenced by outliers.

In this example, we:

• Artifically generate a noisy data set with a few outliers, but with the underlying trend Y =5 X + 50
• Fit straight lines using CurveFitting:-LeastSquares and Statistics:-LeastTrimmedSquares

LeastTrimmedSquares function correctly predicts the underlying trend.

We try to make every release faster and more efficient. We sometimes target key changes in the core infrastructure that benefit all users (such as the parallel garbage collector in Maple 17). Other times, we focus on specific functions.

For this release, I’m particularly impressed by this improved benchmark for factor, in which we’re factoring a sparse multivariate polynomial.

On my laptop, Maple 2018 takes 4.2 seconds to compute and consumes 0.92 GiB of memory.

Maple 2019 takes a mere 0.27 seconds, and only needs 45 MiB of memory!

I’m a visualization nut, and I always get a vicarious thrill when I see a shiny new plot, or a well-presented application.

I was immediately drawn to this new Maple 2019 app – it illustrates the transition between day and night on a world map. You can even change the projection used to generate the map. Shiny!

So that’s my pick of the top new features in Maple 2019. Everyone here at Maplesoft would love to hear your comments!

Recently, my research team at the University of Waterloo was approached by Mark Ideson, the skip for the Canadian Paralympic men’s curling team, about developing a curling end-effector, a device to give wheelchair curlers greater control over their shots. A gold medalist and multi-medal winner at the Paralympics, Mark has a passion to see wheelchair curling performance improve and entrusted us to assist him in this objective. We previously worked with Mark and his team on a research project to model the wheelchair curling shot and help optimize their performance on the ice. The end-effector project was the next step in our partnership.

The use of technology in the sports world is increasing rapidly, allowing us to better understand athletic performance. We are able to gather new types of data that, when coupled with advanced engineering tools, allow us to perform more in-depth analysis of the human body as it pertains to specific movements and tasks. As a result, we can refine motions and improve equipment to help athletes maximize their abilities and performance. As a professor of Systems Design Engineering at the University of Waterloo, I have overseen several studies on the motor function of Paralympic athletes. My team focuses on modelling the interactions between athletes and their equipment to maximize athletic performance, and we rely heavily on Maple and MapleSim in our research and project development.

The end-effector project was led by my UW students Borna Ghannadi and Conor Jansen. The objective was to design a device that attaches to the end of the curler’s stick and provides greater command over the stone by pulling it back prior to release.  Our team modeled the end effector in Maple and built an initial prototype, which has undergone several trials and adjustments since then. The device is now on its 7th iteration, which we felt appropriate to name the Mark 7, in recognition of Mark’s inspiration for the project. The device has been a challenge, but we have steadily made improvements with Mark’s input and it is close to being a finished product.

Currently, wheelchair curlers use a device that keeps the stone static before it’s thrown. Having the ability to pull back on the stone and break the friction prior to release will provide great benefit to the curlers. As a curler, if you can only push forward and the ice conditions aren’t perfect, you’re throwing at a different speed every time. If you can pull the stone back and then go forward, you’ve broken that friction and your shot is far more repeatable. This should make the game much more interesting.

For our team, the objective was to design a mechanism that not only allowed curlers to pull back on the stone, but also had a release option with no triggers on the curler’s hand. The device we developed screws on to the end of the curler’s stick, and is designed to rest firmly on the curling handle. Once the curler selects their shot, they can position the stone accordingly, slide the stone backward and then forward, and watch the device gently separate from the stone.

For our research, the increased speed and accuracy of MapleSim’s multibody dynamic simulations, made possible by the underlying symbolic modelling engine, Maple, allowed us to spend more time on system design and optimization. MapleSim combines principles of mechanics with linear graph theory to produce unified representations of the system topology and modelling coordinates. The system equations are automatically generated symbolically, which enables us to view and share the equations prior to a numerical solution of the highly-optimized simulation code.

The Mark 7 is an invention that could have significant ramifications in the curling world. Shooting accuracy across wheelchair curling is currently around 60-62%, and if new technology like the Mark 7 is adopted, that number could grow to 70 or 75%. Improved accuracy will make the game more enjoyable and competitive. Having the ability to pull back on the stone prior to release will eliminate some instability for the curlers, which can help level the playing field for everyone involved. Given the work we have been doing with Mark’s team on performance improvements, it was extremely satisfying for us to see them win the bronze medal in South Korea. We hope that our research and partnership with the team can produce gold medals in the years to come.

## Improve Your Chess Rating with Math

by:

Over the holidays I reconnected with an old friend and occasional
chess partner who, upon hearing I was getting soundly thrashed by run
of the mill engines, recommended checking out the ChessTempo site.  It
has online tools for training your chess tactics.  As you attempt to
solve chess problems your rating is computed depending on how well you
do.  The chess problems, too, are rated and adjusted as visitors
attempt them.  This should be familar to any chess or table-tennis
player.  Rather than the Elo rating system, the Glicko rating system is
used.

You have a choice of the relative difficulty of the problems.
After attempting a number of easy puzzles and seeing my rating slowly
climb, I wondered what was the most effective technique to raise my
rating (the classical blunder).  Attempting higher rated problems would lower my
solving rate, but this would be compensated by a smaller loss and
larger gain.  Assuming my actual playing strength is greater than my
current rating (a misconception common to us patzers), there should be a
rating that maximizes the rating gain per problem.

The following Maple module computes the expected rating change
using the Glicko system.

Glicko := module()

export DeltaRating
,  ExpectedDelta
,  Pwin
;

# Return the change in rating for a loss and a win
# for player 1 against player2
DeltaRating := proc(r1,rd1,r2,rd2)
local E, K, g, g2, idd, q;

q := ln(10)/400;
g := rd -> 1/sqrt(1 + 3*q^2*rd^2/Pi^2);
g2 := g(rd2);
E := 1/(1+10^(-g2*(r1-r2)/400));
idd := q^2*(g2^2*E*(1-E));

K := q/(1/rd1^2+idd)*g2;

(K*(0-E), K*(1-E));

end proc:

# Compute the probability of a win
# for a player with strength s1
# vs a player with strength s2.

Pwin := proc(s1, s2)
local p;
p := 10^((s1-s2)/400);
p/(1+p);
end proc:

# Compute the expected rating change for
# player with strength s1, rating r1 vs a player with true rating r2.
# The optional rating deviations are rd1 and rd2.

ExpectedDelta := proc(s1,r1,r2,rd1 := 35, rd2 := 35)
local P, l, w;
P := Pwin(s1,r2);
(l,w) := DeltaRating(r1,rd1,r2,rd2);
P*w + (1-P)*l;
end proc:

end module:


Assume a player has a rating of 1500 but an actual playing strength of 1700.  Compute the expected rating change for a given puzzle rating, then plot it.  As expected the graph has a peak.

Ept := Glicko:-ExpectedDelta(1700,1500,r2):
plot(Ept,r2 = 1000...2000);


Compute the optimum problem rating

fsolve(diff(Ept,r2));

{r2 = 1599.350691}


As your rating improves, you'll want to adjust the rating of the problems (the site doesn't allow that fine tuning). Here we plot the optimum puzzle rating (r2) for a given player rating (r1), assuming the player's strength remains at 1700.

Ept := Glicko:-ExpectedDelta(1700, r1, r2):
dEpt := diff(Ept,r2):
r2vsr1 := r -> fsolve(eval(dEpt,r1=r)):
plot(r2vsr1, 1000..1680);


Here is a Maple worksheet with the code and computations.

Glicko.mw

Later

After pondering this, I realized there is a more useful way to present the results. The shape of the optimal curve is independent of the user's actual strength. Showing that is trivial, just substitute a symbolic value for the player's strength, offset the ratings from it, and verify that the result does not depend on the strength.

Ept := Glicko:-ExpectedDelta(S, S+r1, S+r2):
has(Ept, S);
false


Here's the general curve, shifted so the player's strength is 0, r1 and r2 are relative to that.

r2_r1 := r -> rhs(Optimization:-Maximize(eval(Ept,r1=r), r2=-500..0)[2][]):
p1 := plot(r2_r1, -500..0, 'numpoints'=30);


Compute and plot the expected points gained when playing the optimal partner and your rating is r-points higher than your strength.

EptMax := r -> eval(Ept, [r1=r, r2=r2_r1(r)]):
plot(EptMax, -200..200, 'numpoints'=30, 'labels' = ["r","Ept"]);


When your playing strength matches your rating, the optimal opponent has a relative rating of

r2_r1(0);
-269.86


The expected points you win is

evalf(EptMax(0));
0.00956


## Making Math Fun – the Teenage Way!

by: Maple

Fourteen year old Lazar Paroski is an exceptional student. Not only is he an overachiever academically, but he has a passion to help struggling students, and to think of innovative ways to help them learn. Lazar is particularly fond of Math, and in his interactions with other students, he noticed how students have a hard time with Math.

Putting on his creative cap, Lazar came up with the idea of an easily accessible “Math Wall” that explains simple math concepts for students in a very visual way.

“The Music Wall on Pinterest was my inspiration,” says Lazar. “I thought I can use the same idea for Math, and why not a Math Wall”?

"The math wall is basically all the tools you'll have on the wall in your classroom outside," said Lazar. Making the Math Wall and getting it set up, took time and effort. But he had help along the way, which, fueled by his passion and enthusiasm, helped turn his creative dream into reality. Lazar received a grant of $6000 from the local government to implement the project; his teachers, principal and family helped promote it; and the community of parents provided encouragement. The Math Wall covers fundamental math concepts learnt in grades 1 to 6. Lazar engaged with over 450 students in the community to understand what would really be helpful for students to see in this Math Wall, and then he carefully picked the top themes he wanted to focus on. The three meter Math Wall is located in the Morrison community park, and was officially inaugurated by the Mayor of Kitchener in July 2018. Many students have already found it to be useful and educative. Parents who bring their children to the park stop by to give their kids a quick math lesson. At Maplesoft, we love a math story like this! And that too in our backyard! We wanted to appreciate and encourage Lazar and his efforts in making math fun and easy and accessible to students. So we invited Lazar to our offices, gifted him a copy of Maple, and heard more about his passion and future plans. “In many ways, Lazar embodies the same qualities that Maplesoft stands for – making it easy for students to understand and grasp complex STEM concepts,” said Laurent Bernardin, Maplesoft’s Chief Operating Officer. “We try to impress upon students that math matters, even in everyday life, and they can now use advanced, sophisticated technology tools to make math learning fun and efficient.” We wish Lazar all the very best as he thinks up new and innovative ways to spread his love for math to other kids. Well done, Lazar! ## Great Hall Floor and Maple by: Maple I have recently visited the Queen's House at Greenwich (see wiki), an important building in British architectural history (17th century). I was impressed by the Great Hall Floor, whose central geometric decoration seems to be generated by a Maple program :-) Here is my code for this. I hope you will like it. restart; with(plots): with(plottools): n:=32: m:=3:# n:=64: m:=7: a[0], b[0] := exp(-Pi*I/n), exp(Pi*I/n): c[0]:=b[0]+(a[0]-b[0])/sqrt(2)*exp(I*Pi/4): for k to m+1 do c[k]:=a[k-1]+b[k-1]-c[k-1]; b[k]:=c[k]*(1+exp(2*Pi*I/n))-b[k-1]; a[k]:=conjugate(b[k]) od: b[-1]:=c[0]*(1+exp(2*Pi*I/n))-b[0]: a[-1]:=conjugate(b[-1]): c[-1]:=a[-1]+b[-1]-c[0]: seq( map[inplace](evalf@[Re,Im], w), w=[a,b,c] ): Q:=polygonplot([seq([a[k],c[k],b[k],c[k+1]],k=0..m-1), [c[m],a[m],b[m]], [a[-1],b[-1],c[0]]]): display(seq(rotate(Q, 2*k*Pi/n, [0,0]),k=0..n-1), disk([0,0],c[m][1]/3), axes=none, size=[800,800], color=black);  ## Meet Your Developers - Margaret Hinchcliffe We’re excited to bring you another Meet Your Developers post. This one comes from Senior Developer, Margaret Hinchcliffe. Enjoy! 1. What do you do at Maplesoft? I work on the software team that develops the user interface for Maplesoft products. In my time at Maple, I’ve worked on Maple, MapleSim, and MapleNet. 1. What did you study in school? I studied Computer Science at the University of Waterloo, in the Co-op program. 1. What area(s) of Maple or MapleSim are you currently focusing on in your development? I’m currently working on MapleNet and on ways to bring Maple functionality to the web. 1. What’s the coolest feature of Maple or MapleSim that you’ve had a hand in developing? I helped develop the feature that lets you embed videos in a Maple worksheet. I thought that was pretty cool. 1. What do you like most about working at Maplesoft? How long have you worked here? I celebrated my twentieth anniversary at Maplesoft this spring. Obviously, I like working here. What I like most is the opportunity to learn new skills in a supportive environment. Our company gym is pretty awesome, too. 1. Favourite hobby? I took up boxing a couple of years ago and I really enjoy it. It’s a great workout and there’s always something new to learn. 1. What do you like on your pizza? Pepperoni, mushrooms, and fresh basil. 1. What’s your favourite movie? The Wizard of Oz. When people say “The book is always better”, I point to this movie as a counterexample. 1. What skill would you love to learn? Why? I’d like to try archery. If nothing else, it would come in handy in a zombie apocalypse. 1. Who’s your favourite mathematician? Alan Turing. He made important contributions to computer science and he helped fight the Nazis. Thanks Margaret! ## What makes an expert? by: Maple Who should be considered an 'expert'? How does one achieve expert status? In this guest MaplePrimes blog post, 'Understanding Maple' author Ian Thompson discusses his view of what makes an expert, his journey of becoming an expert in Maple, and the process of putting together and perfecting this resource for Maple users. In days of 8-bit computers, one would sometimes encounter individuals who knew everything about a particular device or piece of software. Single programmers wrote entire applications or games, and some could debug their work by looking directly at a core dump (a printout of the numbers stored in the computer’s memory). Some even managed to take computers beyond their specifications by exploiting design loopholes that the manufacturers hadn’t foreseen or intended. It would be fair to classify such individuals as ‘experts’. Fast forward twenty five years, and the picture is far less clear. The complexity of computers and software has grown to such an extent that even relatively small smartphone applications are created by teams of developers, and nobody understands every aspect of a CPU chip, much less an entire PC or tablet. Who now should be classified as an expert? One possibility is that an expert is a person who may sometimes need to look up the details of a rarely used command or feature, but who is never confused or frustrated by the behavior of the system or software in question (except where there is a bug), and never needs help from anyone, except perhaps on rare occasions from its creators. This rather stringent definition makes me an expert in only two areas of computing: the Fortran programming language, and the mathematical computation system Maple. An argument could be made for the typesetting system LATEX, but whilst this has a large number of expert users, there is also a much smaller group of more exalted experts, who maintain the system and develop new packages and extensions. It would be fair to say that I fall into the first category, but not the second.* How does one achieve expert status? Some software actively prevents this, by hiding its workings to such an extent that fully understanding its behavior is impossible. Where it is possible to gain expert status, I have experienced two very different routes, both starting during my time as a research student, when it became clear that Fortran and Maple would be useful in my work. There were several parallels. I knew a little about both, having used them for basic tasks as an undergraduate. However, working out why things went wrong and how to fix them was time-consuming and unrewarding, since it often relied on magic recipes obtained from unreliable sources, and in many cases I didn’t really understand why these worked, any more than I understood why my own attempts had not. I realized then that knowing a little was at the root of these problems. Partial knowledge, supplemented by contradictory, outdated and even downright bad advice from websites and well-meaning individuals (some of whom invariably labor under false pretences of their own expert status) is not an efficient way to approach scientific computing. In fact it’s just a recipe for frustration. In the case of Fortran, fixing this turned out to be easy, because there are lots of good books on the subject. Reading one of these eliminated all of my problems with the language at a stroke. I can’t claim that I remembered every command and its syntax, nor do I know them all now. This is hardly surprising — the Fortran Language Standard (a very terse document that sets out everything the language provides) now extends to more than 600 pages. Instead, the book provided a general picture of how things work in Fortran, and showed the right way to go about tackling a problem. This investment in time has since paid itself back hundreds of times over. The route to expert status in Maple was far more challenging. Its own help pages give a very comprehensive description of individual commands, but they are intended as a reference guide, and if it’s possible to become an expert using these alone, then I never discovered the correct order in which to read them. I found a number of books on Maple in the university library, but most were too basic to be useful, and others focused on particular applications. None seemed likely to give me the general picture — the feel for how things work — that would make Maple into the time-saving resource it was intended to be. The picture became clearer after I taught Maple to students in three different courses. Nothing encourages learning better than the necessity to teach someone else! Investigating the problems that students experienced gave me new opportunities to properly understand Maple, and eventually the few remaining gaps were filled in by the Programming Guide. This is a complex document, similar in length to the Fortran Language Standard, but with more examples. Personally I would only recommend it to readers with experience of programming language specifications. Students now started to ask how I came to know so much about Maple, and whether there was a book that would teach them the same. Since no such book existed, I decided to write one myself. As the old adage goes, if you want something doing properly, do it yourself. The project soon began to evolve as I tried to set down everything that the majority of Maple users need to know. I’ve always hated books that skirt around important but difficult topics, so where before I might have used a dirty trick to circumnavigate a problem, now I felt compelled to research exactly what was going on, and to try to explain it in a simple, concise way. When the first draft was complete, I approached Cambridge University Press (CUP). The editor arranged for reviews by four anonymous referees**, and by Maplesoft’s own programming team. This led to several major improvements. My colleague, Dr Martyn Hughes, also deserves a mention for his efforts in reading and commenting on four different drafts. Meanwhile, Maplesoft continued to release new editions of their software, and the drafts had to be revised to keep up with these. The cover was created by one of CUP’s designers, with instructions that it should not look too ‘treeish’ — one might be surprised by the number of books that have been written about Maple syrup, and it would be a shame for Understanding Maple to be mixed up with these by potential readers browsing the internet. Then there were the minor details: how wide should the pages be? What font should be used? Should disk be spelled with a ‘c’ or a ‘k’? Could quotes from other sources be used without the threat of legal action over copyright infringement? One rights holder laughably tried to charge$200 for a fragment of text from one of their books. Needless to say, no greenbacks were forthcoming.

The resulting book is concise, with all the key concepts needed to gain an understanding of Maple, alongside numerous examples, packed into a mere 228 pages. It gives new users a solid introduction, and doesn’t avoid difficult topics. It isn’t perfect (in fact I have already started to list revisions that will be made if a second edition is published in the future) but I’ve seen very few problems that can’t be solved with the material it contains. Only time will tell if Understanding Maple will it create new experts. At the very least, I would certainly like to think it will make Maple far easier to grasp, and help new users to avoid some of the traps that caught me out many years ago.

## Induction is just a solid gamble

by: Maple

I just feel that if at least one person less experienced than me reads this it will be a worth while post, because it will help them avoid things that eluded me when I was younger.

The omitted function definitions are not relevant to the reason for which I decided to post about this. I would like the maple user to simply observe how many variables are involved in the relation's (R) three equalities in the consideration of the output.

The reason I believe this is important, is that it is sometimes very easy to believe induction is sufficient proof of the truth value of a relation over the superset of a subset that has been enumerated, much like the example of the coefficients of the

 >
 (1)

## Meet Your Product Manager – Samir Khan

Typically, we publish a “Meet Your Developers” profile, where you can get an inside look at the lives of our developers. Today, we’re excited to bring you something a little different, a glimpse into the life of Maple Product Manager, Samir Khan.

Let's get right to it.

1. What do you do at Maplesoft?

I’m 50% of the product management team for Maple. I act as an interface between our developers, mathematicians, marketing, sales, and users.

I spend a lot of time speaking to current and potential customers – this is the most important part of my job.

At the beginning of each development cycle, I work with the developers to put together a list of proposed features. Then, during the year, I try to keep development on track to meet the proposed goals and provide continual feedback.

I also develop applications that demonstrate Maple’s functionality in new and different ways (most are on the Application Center).

2. What did you study in school?

I studied Chemical Engineering.

3. What area(s) of Maple are you currently focusing on in your development?

While I don’t do any direct development of Maple features, I sometimes prototype code as a proof of concept. The developers then look at me with a sense of disdain, tear my prototype apart, and rewrite my code from the ground up.

4. What’s the coolest feature of Maple that you’ve had a hand in developing?

While I generally don’t develop any production code, I’ve been responsible for driving the ThermophysicalData package forward

5. What do you like most about working at Maplesoft? How long have you worked here?

I’ve worked at Maplesoft since 2008. It’s a cliché, but I like the people first and foremost.

I also like the flexibility of my role. Within reason, I can devote part of my time doing things that I think will benefit the company. For example, I get to write lots of applications about subjects that interest me (usually thermodynamics or chemistry).

6. Favourite hobby?

I gave up all my hobbies when kids appeared on the scene. Before that, I wrote spreadsheets for financial modeling

Now, I like to do home science experiments with my son. Yesterday, I mixed yeast with hydrogen peroxide to demonstrate an exothermic reaction.

7. What do you like on your pizza?

Pineapple and mushrooms.

I don’t really have a single favourite movie, but these movies that have the greatest impact on me over the last few years

• Interstellar
• Annihilation
• Dunkirk
• The Witch
• Frozen (yes, really)

9. What skill would you love to learn? (That you haven’t already) Why?

I want to learn how to juggle to amuse my kids. However, I don’t have the hand-eye coordination to be any good

That’s a really dreary question.

• My favorite kids TV show is Ben and Holly’s Little Kingdom
• I usually listen to Slayer on the drive into work

Thanks Samir!

## High School Students Tackle Real-World Mathematical...

by: Maple

Last week, my colleague Erik Postma and I had the pleasure of spending a few hours with a group of bright and motivated high school students at the Math for Real: High School Math Solves Real Problems workshop held at the Fields Institute for Research in Mathematical Sciences in Toronto, and sponsored by the Fields Institute and NSERC PromoScience. The purpose of this three-day workshop was to train students for the International Mathematical Modeling Challenge, also known as IM2C.

The IM2C is hosted by York University and run by the IM2C-Canada committee, consisting of parents and high school teachers, as well as faculty and students in York’s Department of Mathematics and Statistics. In this competition, students working in small teams have five days to solve a mathematical modelling problem in diverse application areas. To support the “Real World” aspect of the contest, students are expected not just to showcase their mathematical creativity and problem-solving skills, but they are also asked to clearly communicate their analyses and conclusions through a written report and visualizations.

The contest allows students to use appropriate software tools to help them with their tasks. Of course I am biased but I can’t help thinking that Maple is the perfect tool for students wanting to do a combination of prototyping, modelling, visualization and document-preparation. The IM2C organizers also thought that the students could benefit from our software, so Erik gave an hour-long introduction to Maple. I was impressed by the students’ enthusiastic remarks and sometimes challenging questions, though admittedly they were partly motivated by the chance to receive as prizes our highly coveted limited-quantity “Math Matters” t-shirts.

The workshop also introduced the students to other software products, taught modelling and writing skills, and had them work on fun practice problems. Over the lunch break, I was struck by the sense of camaraderie at this event, which probably should not have surprised me, as unlike many other competitions involving mathematics, this one is a true team-based activity. Both Erik and I are eager to see what the students will be doing with Maple. Responding to the students’ enthusiasm and interest, Maplesoft has agreed to offer complimentary Maple licenses to all students participating in IM2C.

As a Corporate Affiliate of the Fields Institute, Maplesoft is pleased to provide training and support to students and researchers that come to Fields for its many events. Developers like myself are encouraged to participate in the institute’s events when possible, and I’ve had the opportunity to attend a number of workshops in the past few years. I encourage you to look at their wide range of activities and to consider visiting the culturally diverse city of Toronto!

## Tribute to Alan Baker

by: Maple

Hello,

It has come to my attention that Alan Baker has recently passed away, and not being of an institutional affliation it was some what late in me finding out.

But his work was of huge inspiration to me, so I felt as if it should be noted how brilliant this man was, and how much he ought to be missed be the mathematical community at large.

https://en.wikipedia.org/wiki/Alan_Baker_(mathematician)

## Maple 2017 Training Session

by: Maple

--- Prolog.ue ---

The best things in life come free of charge.

Happiness, love, and wisdom of expertise are first few that hit my mind.

As a business economist, I keep my eyes keenly open to opportunities for growth; such as Maple 2017 training session.

It was a Saturday afternoon in Waterloo, ON, this chilly Feburary which was blessed by snowstorm warning.

--- Encountering with Maple ---

I was aware of Maple for many years back when my academic career began.

In fact, Maple was available in the lab computers at university.

But I did not know what to do with it.

Nor did I use any mathematics softwares until recently, but I had this thought : one day I could learn.

The motivation for this learn how to use it' did not occur to me for a long time (14 years!!).

Things changed this year when I enrolled to an Electrical Engineering program at Lassonde.

Mind you, I have already been using various types of languages and tools such as: Python, C, Java, OpenOfficeSuites, Stata, SAS, Latex just to mention a few.

These stuffs also run on multiple platforms which I am sure you have heard of if you're reading this post; Windows, OSX and Linux. And Maple supports all these major operating systems.

--- Why do I like Maple ---

During the first week of school, Dr. Smith would ask us to purchase and practice using MATLAB because it had a relatively easy learning curve for beginners like python and we were going to use it for labs.

Furthermore, students get a huge discount (i.e. $1500 to$50) for these softwares.

Then, the professor also added; "Maple is also a great tool to use, but we won't use it for this class".

ME: ' Why not ? '

The curiosity inside me gave in and I decided to try both!

After all, my laziness in taking derivatives by hand or the possibility of making mistake would disappear if I can verify results using software.

That's it...!

Being able to check correct answer was already worth more than $50. I can not emphasize this point enough; For people in the industry being paid for their time, or students like me who got a busy schedule can not afford to waste any time. (i.e. need to minimize homework effort & frustration, while maximizing the educational attainment & final grades) Right? Time is money. Don't we all just want more spare time for things we care? Googling through many ambiguous Yahoo Answers or online forums like Stackoverflow replies are often misleading and time consuming. I have spent years (estimated 3000+ hours) going through those wildly inaccurate webpages hoping for some clearly written information with sub-optimal outcome. Diverting many hours of study time is not something a first year S.T.E.M. students can afford. --- Maple Training --- Now you know about my relationships with Maple; Let me describe how the training session went. I will begin with the sad news first, =( First of all, there was no coffee available when I arrived. It arrived only after lunch. Although it was a free event aside other best things in life, this was only a material factor I didn't enjoy at the site. Still a large portion of Canadians start their work with a zolt of caffeine in my defence. Secondly, there was a kind of assumption which expected attendee were familiar with software behavior. A handful of people were having trouble opening example file, perhaps because of their browser setting or link to preferred software by OS. Not being able to follow the tutorials as the presenter demonstrated various facets of software substantially diminished the efficacy of training session for those who could not be on the same page. These minor annoyances were the only drawbacks I experinced from the event. Here comes the happy side, =) 1. The staffs were considerate enough to provide vegetarion options for inclusive lunch as well as answering all my curious, at times orthogonal questions regarding Maplesoft company. 2. Highly respectable professionals were presenting themselves; That is, Prof. Illias Kotsireas, Dr. Erik Postma and Dr. Jürgen Gerhard. I can not appreciate enough of their contribution for the training in an eloquent and humble manners. To put it other way, leading of the presentation was well structured and planned out. In the beginning, Prof. Kotsireas presented Introduction to Maple' which included terminology and basic behaviors of Maple (i.e. commands and features) with simple examples you can quickly digest. Furthermore, Maple has internal function to interface with Latex! No more typing hours of$\$s and many frac{}{}, \delta_{} to publish. In order for me to study all this would have been two-weeks kind of commitment in which he summarized in a couple of hours time. Short-cut keys that are often used by his project was pretty interesting, which will improve work efficiency.

After a brief lunch, which was supplied more than enough for all, Dr. Erik Postma delivered a critical component of simluation. That is, Random Number Generation'. Again, he showed us some software-related tricks such as Text mode' vs. Math mode'.  The default RNG embedded in the software allows reproducible results unless we set seed and randomize further. Main part of the presentation was regarding Optimization of solution through simulation'. He iteratively improved efficiency of test model, which I will not go in depth here. However, visually and quantitatively showing the output was engaging the attendees and Maple has modularized this process (method available for all the users!!).

Finally, we got some coffee break that allowed to me to push through all the way to the end. I believe if we had some coffee earlier less attendees would have left.

The last part of the training was presented by Dr. Jürgen Gerhard. In this part, we were using various applications of Maple in solving different types of problems. We tackled combinatorics of Fibonacci sequence by formula manipulation. In this particular example he showed us how to optimize logic of a function that made a huge impact in processing time and memory usage. Followed by graph theory example, damped harmonic oscillator, 2 DOF chaotic system, optimization and lastly proof of orthocentre by coding. I will save the examples for you to enjoy in future sessions.

The way they went through examples were super easy to follow. This can only be done with profound understanding of the subject and a lot of prior effort in preparing the presentation.

I appreciate much efforts put together by whom organized this event, allocating their own precious weekend time and allowing many to gain opportunity to learn directly from the person in the house.

--- Epilogue ---

My hope for Maple usage lies in enhancing education outcome for first year students, especially in the field of Science and Economics. This is a free opportunity for economic empowerment which is uncaptured.

Engineering students are already pretty good at problem solving, and will figure things out as I witnessed my colleagues have.

However, students of natural sciences and B.A. programs tend to skimp on utilizing tools due to lack of exposure.

Furthermore, I am supporting their development of SaaS, software as service, which delivers modules like gRPC does.

Also, I hope the optimization package from prior version written by Dr. Postma will become available to public sometime.

Here's a BIG thank you to staffs once again, and forgive me for any grammatical errors from rushed writing. I tried to incorporate as much observation as possible gathered from the event.

To contact me, my email is hyonwoo.kee (at) gmail.com;

## An example of the kinds of worksheets that i make...

by: Maple

Hello,

I study mainly subjects that fall under umbrella of number theory, but i have specified a little further in the worksheet. This is really a request for assistance, because in as much as i have met so many brilliant people online via social media etc,  I would always love to meet more, and especially ones who are more experienced in this field.

Basically i am too cheap and old to think about going to a good university, so I am trying to get free advice from the people who have probably completed doctorates in the relevant field. Got to be honest I say.

Anyway my contact email is at the top of the attached worksheet.

First thing that stood out to me about the distributions produced in this worksheet is how sparse the number of points is for N=17 relative to all the other values of N.

EXAMPLE_FOR_MAPLE3.mw

MAPLE_EXAMPLE_13.mw

## Meet Your Developers - Erik Postma

Maple

We’re kicking off 2018 right, with another Meet Your Developers interview! This edition comes from Erik Postma, Manager of the Mathematical Software Group.

To catch up on previous interviews, search the “meet-your-developers” tag.

1. What do you do at Maplesoft?
I’m the manager of the mathematical software group, a team of 7 mathematicians and computer scientists working on the mathematical algorithms in Maple (including myself). So my work comes in two flavours: I do the typical managerial things, involving meetings to plan new features and solve my team’s day to day problems, and in the remaining time I do my own development work.

2. What did you study in school?
I studied at Eindhoven University of Technology in the Netherlands. The first year, I took a combined program of mathematics and computer science; then for the rest of my undergrad, I studied mathematics. The program was called Applied Mathematics, but with the specialization I took it really wasn’t all that applied at all. Afterwards I continued in the PhD program at the same university, where my thesis was on a subject in abstract algebra (Lie algebras over finite fields).

3. What area(s) of Maple are you currently focusing on in your development?
I’ve spent quite a bit of time over the past two years making the facilities for working with units of measurement in Maple easier to use. There is a very powerful package for doing this that has been part of Maple for many years, but we keep hearing from our users it’s difficult to use. So I’ve worked on keeping the power of the package but making it easier to use.

4. What’s the coolest feature of Maple that you’ve had a hand in developing?
This was actually working on a problem in a part of the code that existed long before I started with Maplesoft. We have a very clever algorithm for drawing random numbers according to a custom, user-specified probability distribution. I wrote about it on MaplePrimes in a series of four blog posts, here. I’ve talked at various workshops and the like about this algorithm and how it is implemented in Maple.

5. What do you like most about working at Maplesoft? How long have you worked here?
I love working at the crossroads of mathematics and computer science; there aren’t many places in the world where you can do that as much as at Maplesoft. But the best thing is the people I work with: us mathematicians are all crazy in slightly different ways, and that makes for a very interesting working environment.

6. Favourite hobby?
Ultimate frisbee. I captain a mixed (i.e., coed) team called The Clockwork. (We play in orange jerseys – it references the book/movie A Clockwork Orange.) We play in a couple of local leagues, and some of the other members also work here. We don’t win much – but we work hard and have fun!

7. What do you like on your pizza?
Mushrooms. Mushrooms on everything!

Probably Black Book, a dark movie about the Dutch resistance in the second world war from 2006, directed by Paul Verhoeven. I think what I like best about it is that it highlights the moral shades of grey in even so morally elevated a group as the resistance.

9. What skill would you love to learn? Why?
I’d love to learn to speak Russian! I’m trying, but I have a very hard time with it. It would allow me to communicate with my in-laws more easily; they speak Russian.

Oh, so many to choose from! I’m torn between:
• Ada Lovelace (1815-1852), known as the first programmer.
• Felix Klein (1849-1925), driving force behind a lot of research into geometries and their underlying symmetry groups.
• Wilhelm Killing (1847-1923), a secondary school teacher who made big contributions to the theory of Lie algebras.

Or wait, can I choose my wife?

## Meet Your Developers - John May

Maple

Many of you enjoyed our profile on one of our developers, Paulina Chin, so we’re happy to bring you another one!

Today, we’ll be talking with John May, Senior Developer of Maple. Let’s get started.

1. What do you do at Maplesoft?
Until recently I was consulting on-site at the NASA Jet Propulsion Laboratory helping people there more effectively solve their engineering problems using Maplesoft products.  But my main job that I am back to full time now is the development and maintenance of various parts of the Maple library.

2. What did you study in school?
I studied both Pure and Applied Mathematics at the University of Oregon,  focusing a lot on Abstract Algebra.  In graduate school, I specialized more in computation mathematics like computer algebra and numerical analysis.  My Ph.D. work focused on effective numerical algorithms for problems in polynomial algebra – with implementations in Maple!

3. What area(s) of Maple are you currently focusing on in your development?
Right now I am focused on addressing complaints I’ve gotten from engineers about the usability of units with other parts of the math library.

4. What’s the coolest feature of Maple that you’ve had a hand in developing?
A lot of the cool things I’ve built live pretty deep in the internals of Maple.  I’ve done a lot of meta-heuristic tuning to seamlessly integrate high-performance libraries into top-level Maple commands.

I had a lot of fun developing a lot of the stuff for manipulation and visualization of colors in the ColorTools package.

5. What do you like most about working at Maplesoft? How long have you worked here?
I started working at Maple in 2007, but I’ve been a Maple user since 1997.  I love being part of the magic that brings powerful algorithmic mathematics to everyone.  The R&D team is also full of eccentric nerds who are great fun to work with.

6. Favourite hobby?
It varies by the season, but right now it is prime for mountain biking in southern California.  I ride my local trails a couple times a week, and when I get I chance, I love to get away on epic bikepacking adventures (like this one: https://www.bikemag.com/features/two-wheeled-escape-one-hour-from-l-a/  this is me: https://cdn.bikemag.com/uploads/2016/05/16File.jpg ).

7. What do you like on your pizza?
Anything and everything. Something different every time. My all-time favorite pie my from grad school days is the “Rio Rancho” from the dearly departed That’s Amore Pizza (which was next to the comic book store and across the street from North Carolina State University).  It was an olive oil and mozzarella pizza with chopped bacon that was covered in sliced fresh roma tomatoes and drizzled with ranch dressing when it came out of the oven.

It’s really hard to pick just one.  So, I’ll go with the safe answer and say the greatest movie of all time, and “Weird Al” Yankovic’s only foray into movies, UHF, is my favorite.
http://www.imdb.com/title/tt0098546/

9. What skill would you love to learn? (That you haven’t already) Why?
Another hard one.  I feel like I’ve dabbled in lots of things that I would like to get better at.  At the top of the list is probably unicycling.  I’d love to get good enough to play Unicyle Football or do Muni (mountain unicyling).
https://en.wikipedia.org/wiki/Mountain_unicycling
http://www.unicyclefootball.com/