The Bohemian Matrix Calendar 2022 is up!  You may find it at https://rcorless.github.io/ (four versions: letter/A4 paper, Sunday/Monday start to the week).

It prints quite well (with proper equipment).  I wish you all the best for 2022.

Since the start of the pandemic, I have been involved in online mathematics tutoring. I tried many different applications to best communicate with my students, and ended up sticking with Maple Learn. Here’s my setup, and why I chose Maple Learn.

My Setup

When I have an online tutoring session, I join a scheduled video call to “see” my students. I then open a blank Maple Learn document, and share my screen. I explain whatever I need to explain, while writing key information on the Maple Learn document. When I don’t want Learn to interpret what I write, I go into text mode; when I do (e.g. when I want to graph a function), I stay in math mode. When the class is over, I send the document’s sharelink to my students by email, so that they can access it. 

Here is an example of a Maple Learn document (pictured below) that I created while teaching trigonometry to a student. Keep in mind that I typed this while on call with the student, so the document is very simple - it only uses the most basic features of Maple Learn.

Why I Chose Maple Learn

My main student wants me to teach him trigonometry ahead of it being taught to him at school. For this, I need to be able to write lots of text and math easily, while on video call with him. 

Microsoft Word is not good enough for this: the equation editor is too clumsy. I also tried drawing tools where you can move your mouse to draw on the screen, but they make it too hard to write text. I even tried pointing a camera at my desk and writing the notes by hand, but my handwriting is terrible, and I could never find the right position for the camera. That’s the main reason why I chose Maple Learn: it lets me write both text and math quickly and simply, unlike many other applications.

There are some other benefits to using Maple Learn. I like that I can organize what I write in a visually appealing manner on the canvas, by moving groups around. I like that I can graph functions within Maple Learn, without having to open a graphing calculator in a separate tab. Finally, I find the sharelink feature convenient for sending the notes to my students after class.

Disclaimer: I discovered Maple Learn while working at Maplesoft during a co-op term.

Dear all,

The November issue of Maple Transactions is now up (we will be adding a few more items to that issue over the course of the month).  See https://mapletransactions.org/index.php/maple/index for the articles.

More importantly, Maple Primes seems to have a great many interesting posts, some of which could well be worked up into a paper (or a video).  Maple Transactions accepts worksheets (documents, workbooks) for publication, as well, although we want a high standard of readability for that.  I invite you to contribute.

The next issue of Maple Transactions will be the Special Issue that is the Proceedings of the Maple Conference 2021 (see my previous post :)

-r

Hi to all,

Dr. Lopez's "Advanced Engineering Mathematics with Maple" is just excellent... I strongly advise...

That book is my most favorite and Dr. Lopez is my favorite teacher :)

Dear all,

Recently I discovered the noncommuting variables in the Physics package due to Edgardo Cheb-Terrab; doubtless there are many posts here on Maple Primes describing them.  Here is one more, which shows how to use this package to prove the Schur complement formula.

https://maple.cloud/app/6080387763929088/Schur+Complement+Proof+in+Maple

I guess I have a newbie's question: how well-integrated are Maple Primes and the Maple Cloud?  Anyway that seemed the easiest way to share this.

-r

Dear all,

Recently we learned that the idea of "anti-secularity" in perturbation methods was known to Mathieu already by 1868, predating Lindstedt by several years.  The Maple worksheet linked below recapitulates Mathieu's computations:

https://github.com/rcorless/MathieuPerturbationMethod

Nic Fillion and I wrote a more general introduction to perturbation methods using Maple and you can find that paper at 

https://arxiv.org/abs/1609.01321

and the supporting Maple code in a workbook at 

https://github.com/rcorless/Perturbation-Methods-in-Maple

For instance, one of the problems solved is the lengthening pendulum and when we do so taking proper account of anti-secularity (we use renormalization for that one, I seem to remember) we get an error curve that is bounded over time.

Hope that some of you find this useful.

Hi everyone! It's been a remarkably long time since I posted on MaplePrimes -- I should probably briefly reintroduce myself to the community here. My name is Erik Postma. I manage the mathematical software group at Maplesoft: the team that writes most of the Maple-language code in the Maple product, also known as the math library. You can find a longer introduction at this link.

One of my tasks at Maplesoft is the following. When a request for tech support comes in, our tech support team can usually answer the request by themselves. But no single person can know everything, and when specialized knowledge of Maple's mathematical library is needed, they ask my team for help. I screen such requests, answer what I can by myself, and send the even more specialized requests to the experts responsible for the appropriate part of the library.

Yesterday I received a request from a user asking how to unwrap angles occurring in an expression. This is the general idea of taking the fact that , and similarly for the other trig functions; and using it to modify an expression of the form  to make it look "nicer" by adding or subtracting a multiple of  to the angle. For a constant, real value of  you would simply make the result be as close to 0 as possible; this is discussed in e.g. this MaplePrimes question, but the expressions that this user was interested in had arguments for the trig functions that involved variables, too.

In such cases, the easiest solution is usually to write a small piece of custom code that the user can use. You might think that we should just add all these bits and pieces to the Maple product, so that everyone can use them -- but there are several reasons why that's not usually a good idea:

• Such code is often too specialized for general use.
• Sometimes it is reliable enough to use if we can communicate a particular caveat to the user -- "this will not work if condition XYZ occurs" -- but if it's part of the Maple library, an unsuspecting user might try it under condition XYZ and maybe get a wrong answer.
• This type of code code generally doesn't undergo the careful interface design, the testing process, and the documentation effort that we apply to the code that we ship as part of the product; to bring it up to the standards required for shipping it as part of Maple might increase the time spent from, say, 15 minutes, to several days.

That said, I thought this case was interesting enough to post on MaplePrimes, so that the community can take a look - maybe there is something here that can help you with your own code.

So here is the concrete question from the user. They have expressions coming from an inverse Laplace transform, such as:

with(inttrans):
F := -0.3000*(-1 + exp(-s))*s/(0.0500*s^2 + 0.1*s + 125);
f := invlaplace(F, s, t)*u(t);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t-
#         49.98999900)-357.*cos(49.98999900*t-49.98999900))+.1680672269e-1*(-7.141428429*sin
#         (49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

I interpreted their request for unwrapping these angles as replacing the expressions of the form  with versions where the constant term was unwrapped. Thinking a bit about how to be safe if unexpected expressions show up, I came up with the following solution:

unwrap_trig_functions := module()
local ModuleApply := proc(expr :: algebraic, $)
  return evalindets(expr, ':-trig', process_trig);
end proc;

local process_trig := proc(expr :: trig, $)
  local terms := convert(op(expr), ':-list', ':-`+`');
  local const, nonconst;
  const, nonconst := selectremove(type, terms, ':-complexcons');
  const := add(const);
  local result := add(nonconst) + (
    if is(const = 0) then
      0;
    else
      const := evalf(const);
      if type(const, ':-float') then
        frem(const, 2.*Pi);
      else
        frem(Re(const), 2.*Pi) + I*Im(const);
      end if;
    end if);
  return op(0, expr)(result);
end proc;
end module;

# To use this, with f defined as above:
f2 := unwrap_trig_functions(f);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t+
#         .27548346)-357.*cos(49.98999900*t+.27548346))+.1680672269e-1*(-7.141428429*sin(
#         49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

Exercise for the reader, in case you expect to encounter very large constant terms: replace the calls to frem above with the code that Alec Mihailovs wrote in the question linked above!

HI Maple Primes people and other interested parties,

I was a teacher for more that ten years.  Most of my teaching was at community college level.

Although I am not a biological father, my extended family is important to me.

I graduated from university two times with special diplomas.  The next two years (99 to 01) were hectic for me.  After that I went to see about females, and now I am in the happily married club.

I'm glad I kept my Maple 13 student version software because like my father, I like to make computer code.

0_2_20_tuple_to_share.pdf

Mathematical truth will outlast the stars in the sky.  but government and good behavior will always kick the ass of any expression.

Consider this 

Regards

Matt

C_MRB is defined below. See http://mathworld.wolfram.com/MRBConstant.html.

Starting by using Maple on the Inverse Symbolic Calculator, with over 21 years of research and ideas from users like you, I developed this shortlist of formulas for the MRB constant.

• C_MRB=  

That is proven below by an internet scholar going by the moniker "Dark Malthorp:"

•  denoting the kth derivative of the Dirichlet eta function of k and 0 respectively was first discovered in 2012 by Richard Crandall of Apple Computer.

The left half is proven below by Gottfried Helms and it is proven more rigorously considering the conditionally convergent sum, below that. Then the right half is a Taylor expansion of η(s) around s = 0.

At https://math.stackexchange.com/questions/1673886/is-there-a-more-rigorous-way-to-show-these-two-sums-are-exactly-equal,

it has been noted that "even though one has cause to be a little bit wary around formal rearrangements of conditionally convergent sums (see the Riemann series theorem), it's not very difficult to validate the formal manipulation of Helms. The idea is to cordon off a big chunk of the infinite double summation (all the terms from the second column on) that we know is absolutely convergent, which we are then free to rearrange with impunity. (Most relevantly for our purposes here, see pages 80-85 of this document, culminating with the Fubini theorem which is essentially the manipulation Helms is using.)"

I am a high school Teacher in Denmark, who have been using Maple since version 12, more than 12 years ago. I suggested it for my school back then and our math faculty finally decided to purchase a school license. We are still there. We have watched Maple improve in a lot of areas (function definitions, context panels, graphically etc., etc ). Often small changes makes a big difference! We have been deligted. We we are mostly interested in improvements in GUI and lower level math, and in animations and quizzes. I have also been enrolled as a beta tester for several years yet. 

One of the areas, which is particually important is print and export to pdf, because Danish students have to turn in their papers/solutions at exams in pdf format! I guess the Scandinavian countries are ahead in this department. They may quite possible be behind in other areas however, but this is how it is. 

Now my point: Maplesoft is lacking terrible behind when regarding screen look in comparison with print/export to pdf. 

I am very frustrated, because I have been pinpointing this problem in several versions of Maple, both on Mapleprimes and in the beta groups. Some time you have corrected it, but it has always been bouncing back again and again! I have come to the opinion that you are not taking it seriously? Why?

Students may loose grades because of missing documentations (marking on graphs etc.). 

I will be reporting yet another instance of this same problem. When will it stop?

Erik

 

I make a maple worksheet for generating Pythagorean Triples Ternary Tree :

Around 10,000 records in the matrix currently !

You can set your desire size or export the Matrix as text ...

But yet ! I wish to understand from you better techniques If you have some suggestion ?

the mapleprimes Don't load my worksheet for preview so i put a screenshot !

Pythagoras_ternary.mw

Pythagoras_ternary_data.mw

Pythagoras_ternary_maple.mw

Download Godel_universe_and_Tedrads.mw

A few weeks ago a television station in Toronto asked me if I’d share some tips on how parents could help their kids stay engaged with remote learning. My initial reaction was to run for the hills – appearing on live TV is not my cup of tea. However my colleagues persuaded me to accept. You can see a clip of that segment here - I’ve included it in this post because otherwise someone on the marketing team would have ;-)

My tips are based on a wide variety of experiences. My role at Maplesoft requires me to speak with educators at all levels, and remote learning has been a hot topic of conversation lately, as you can imagine. As well, in my past life (i.e. life before kids) I was a high school math tutor, and now as a parent I’m in the thick of it helping my son navigate Kindergarten remotely.

So here are my 5 tips on how parents of elementary and high-school aged children can help their kids stay engaged with remote learning. If you have other tips, including suggestions for university students, feel free to leave them in the comments sections. And if these tips help you, please let me know. It will have made the stress of my appearance on TV worthwhile!

Tip 1: Look for the positives

These are unprecedented times for kids, parents and teachers. Over the course of the last 6-7 months, learning as we’ve grown to know it has changed radically. And while the change has been incredibility difficult for everyone, it’s helpful to look for the positives that remote learning can bring to our children:

• Remote learning can help some kids focus on their work by minimizing the social pressures or distractions they may face at school.
• Older kids are appreciating the flexibility that remote learning can offer with respect to when and how they complete their work.  
• Younger kids are loving the experience of learning in the presence of mom and dad. My 4 year old thinks it’s awesome that I now know all the lyrics to the songs that he learns in school.
• As many remote learning classrooms include students from across the school board, this can provide kids with the opportunity to connect with their peers from different socio-economic backgrounds living across the city.

Tip 2: Don’t shy away from your kid’s teacher

While some kids are thriving learning from home, we know that others are struggling.

If your high school student is struggling at school, do whatever it takes to convince them to connect with their teacher. If your child is younger, make the connection yourself.

In my role, I’ve had the opportunity to work with many teachers, and rest assured, many of them would welcome this engagement.  They want our kids to succeed, but without the face-to-face classroom interaction it’s becoming increasingly more difficult for them to rely on visual cues to see how your child is doing and if they are struggling with a concept.

So I encourage you to reach out to your kid’s teacher especially if you notice your child is having difficulty.

Tip 3: Get creative with learning

Another benefit of remote learning is that it presents us with a unique opportunity to get creative with learning.

Kids, especially those in middle school and high school, now have the time and opportunity to engage with a variety of different online learning resources. And when I say online learning resources, I mean more than just videos. Think interactive tools (such as Maple Learn), that help students visualize concepts from math and science, games that allow students to practice language skills, repositories of homework problems and practice questions that allow kids to practice concepts, the list goes on.

Best of all, many content providers and organizations, are offerings these resources and tools available for free or at a substantially reduced cost to help kids and parents during this time.

So if your child is having difficulty with a particular subject or if they are in need of a challenge, make sure to explore what is available online.

Tip 4: Embrace the tech

To be successful, remote learning requires children to learn a host of new digital skills, such as how to mute/unmute themselves, raise their hands electronically, turn on and off their webcam, toggle between applications to access class content and upload homework, keep track of their schedule via an electronic calendar, etc. This can be daunting for kids who are learning remotely for the first time.

As a parent you can help your child become more comfortable with remote learning by setting aside some time either before or after class to help them master these new tools. And since this is likely new to you, there are some great videos online that will show you how to use the system your school has mandated be it Microsoft Teams, Google Classroom or something else.  

Tip 5: It’s a skill

Remember that remote learning is a skill like any other skill, and it takes time and practice to become proficient.

So remember to be patient with yourself, your kids, and their teachers, as we embark on this new journey of learning. Everyone is trying their best and I truly believe a new rhythm will emerge as we progress through the school year.

We will find our way.

This is an animation of the spread of the COVID-19 over the U.S. in the first 150 days.  It was created in Maple 2020, making extensive use of DataFrames. 

https://www.youtube.com/watch?v=XHXeJKTeoRw

The animation of 150 Day history includes COVID-19 data published by the NY Times and geographic data assembled from other sources. Each cylinder represents a county or in two special cases New York City and Kansas City. The cross-sectional area of each cylinder is the area in square miles of the corresponding county. The height of each cylinder is on a logarithmic scale (in particular it is 100*log base 2 of the case count for the county. The argument of the logarithm function is the number of cases per county divided by the are in square miles-so an areal density.  Using a logarithmic scale facilitates showing super high density areas (e.g., NYC) along with lower density areas.  The heights are scaled by a prefactor of 100 for visualization.