The Maple Conference starts tomorrow Oct. 26 at 9am EDT! It's not too late to register: https://www.maplesoft.com/mapleconference/2023/. Even if you can't attend all the presentations, registration will allow you to view the recorded videos after the conference. 

Check out the detailed conference program here: https://www.maplesoft.com/mapleconference/2023/full-program.aspx

With Halloween right around the corner, we at Maplesoft wanted to celebrate the occasion with an activity where you can carve your own pumpkin… using math! 

Halloween is said to have originated a few hundred years back in ancient Celtic festivals, specifically one called Samhain. This was celebrated from October 31st to November 1st to mark the end of harvesting season and the beginning of winter, or the "darker quarter" of the year. Since then, Halloween has evolved into a fun celebration of candy and costumes in many countries!

With that said, here’s my take on the pumpkin carving activity: 

The great thing is, if you mess up, you can always go back; unlike carving pumpkins in real life. My design is pretty simple (although cute), so let’s see what you all can impress us with!

You can also make your own original art and publish it to your channel so that anyone can see your own artistic creations. You can also attend the Maple Conference next week on October 26 and 27, an event filled with two days of presentations from members of the Maplesoft Community. Participants will also be able to see all the artwork submitted for the Art Gallery and Creative Showcase, where you can draw inspiration for your own submissions to next year’s showcase! The conference is virtual and free of charge, and you can register here.

Looking forward to seeing you there!

The Maple Conference will be starting in two weeks! The detailed agenda, which includes abstracts of invited and contributed talks, is available here: https://www.maplesoft.com/mapleconference/2023/full-program.aspx.

Please join us on October 26 and 27 for two days of presentations from our staff members and the larger Maple community, a look at our Art Gallery and Creative Showcase, opportunities for networking with other Maple enthusiasts, and more! The conference is virtual and free of charge, and you can register at https://www.maplesoft.com/mapleconference/2023/.

We look forward to seeing you at the conference!

Almost 300 years ago, a single letter exchanged between two brilliant minds gave rise to one of the most enduring mysteries in the world of number theory. 

In 1742, Christian Goldbach penned a letter to fellow mathematician Leonhard Euler proposing that every even integer greater than 2 can be written as a sum of two prime numbers. This statement is now known as Goldbach’s Conjecture (it is considered a conjecture, and not a theorem because it is unproven). While neither of these esteemed mathematicians could furnish a formal proof, they shared a conviction that this conjecture held the promise of being a "completely certain theorem." The following image demonstrates how prime numbers add to all even numbers up to 50:

From its inception, Goldbach's Conjecture has enticed generations of mathematicians to seek evidence of its legitimacy. Though weaker versions of the conjecture have been proved, the definitive proof of the original conjecture has remained elusive. There was even once a one-million dollar cash prize set to be awarded to anyone who could provide a valid proof, though the offer has now elapsed. While a heuristic argument, which relies on the probability distribution of prime numbers, offers insight into the conjecture's likelihood of validity, it falls short of providing an ironclad guarantee of its truth.

The advent of modern computing has emerged as a beacon of progress. With vast computational power at their disposal, contemporary mathematicians like Dr. Tomàs Oliveira e Silva have achieved a remarkable feat—verification of the conjecture for every even number up to an astonishing 4 quintillion, a number with 18 zeroes.

Lazar Paroski’s Goldbach Conjecture Document on Maple Learn offers an avenue for users of all skill levels to delve into one of the oldest open problems in the world of math. By simply opening this document and inputting an even number, a Maple algorithm will swiftly reveal Goldbach’s partition (the pair of primes that add to your number), or if you’re lucky it could reveal that you have found a number that disproves the conjecture once and for all.

A salesperson wishes to visit every city on a map and return to a starting point. They want to find a route that will let them do this with the shortest travel distance possible. How can they efficiently find such a route given any random map?

Well, if you can answer this, the Clay Mathematics Institute will give you a million dollars. It’s not as easy of a task as it sounds.

The problem summarized above is called the Traveling Salesman Problem, one of a category of mathematical problems called NP-complete. No known efficient algorithm to solve NP-complete problems exists. Finding a polynomial-time algorithm, or proving that one could not possibly exist, is a famous unsolved mathematical problem.

Over years of research, many advances have been made in algorithms that can solve the problem, not in perfectly-efficiently time, but quickly enough for many smaller examples that you can hardly notice. One of the most significant Traveling Salesman Problem solutions is the Concorde TSP Solver. This program can find optimal routes for maps with thousands of cities.

Traveling Salesman Problems can also be used outside of the context of visiting cities on a map. They have been used to generate gene mappings, microchip layouts, and more.

The power of the legendary Concorde TSP Solver is available in Maple. The TravelingSalesman command in the GraphTheory package can find the optimal solution for a given graph. The procedure offers a choice of the recently added Concorde solver or the original pure-Maple solver.

To provide a full introduction to the Traveling Salesman Problem, we have created an exploratory document in Maple Learn! Try your hand at solving small Traveling Salesman examples and comparing different paths. Can you solve the problems as well as the algorithm can?

The Proceedings of the Maple Conference 2022 are up at mapletransactions.org and I hope that you will find the articles interesting.  There is a brief memorial to Eugenio Roanes-Lozano, whom some of you will remember from past meetings. 

The cover image was the "People's Choice" from the Art Gallery, by Paul DeMarco.

This provides a nice excuse to remind you to register at the conference page for the Maple Conference 2023 and in particular to remind you to submit your entries for the Art Gallery.  See you there!  The conference will take place October 26 and 27, and features plenary talks by our own Laurent Bernardin and by Tom Crawford (Oxford, but more widely known as "The Naked Mathematician" for his incredibly popular YouTube videos on mathematical topics). See Tom Rocks Maths for more (or less :)

The deadline for submission to the Proceedings (which will again be published in Maple Transactions) will be Nov 27, one month after the conference ends.  We have put new processes in place to ensure a more timely publication schedule, and we anticipate that the Proceedings will be published in early Spring 2024.

What are planes? Are they aircraft that soar through the sky, or flat surfaces you'd come across in your geometry textbook? By definition yes, but they can be so much more. In the world of math, observing a system of equations with three variables allows us to plot them as planes in ℝ³. As we plot planes, these geometric entities can start intersecting, creating captivating visualizations. However, the intersection of planes is not just an abstract mathematical concept present only in the classroom. Throughout our daily lives, we come into contact with intersecting planes everywhere. Have you ever noticed the point where two walls and the floor in your room converge? That’s an intersection in its simplest form! And the line where the pages of a book are bound together? Another everyday intersection!
 

Room image: https://unsplash.com/photos/0H-aJ06IZw4, Book image: https://unsplash.com/photos/6H9H-tYPUQQ 

However, just seeing plane intersections is but a tiny piece of the puzzle. After all, how can we delve into the intriguing properties of these intersections without quantifying them? Enter the focus of Maple Learn's newest collection: Intersection of Planes. Not sure about how you can identify the different scenarios that three planes can form in ℝ³? Check out the eight documents that provide complete walk-throughs for solving each individual case that three planes can form! With cases ranging from three parallel and distinct planes to three planes forming a triangular prism to three planes intersecting in a line, you’ll gain a mastery of understanding the intersection of planes by the time you’re finished with the examples.

Once you’ve gained an understanding of how to identify and solve the cases that three planes can form, it’s time to test your knowledge! This quiz-like document takes you through the steps of solving for the intersection of three planes with guiding questions and comprehensive feedback. Once you successfully find the intersection or identify the case, you’ll be provided with an interactive 3D plot that allows you to see what the math you’ve been doing looks like. This opportunity to solve any of the 16 different possible systems of equations allows you to prove that you’re on another level!

With your newfound mastery of solving systems of equations, check out similar documents in the recently added linear algebra collection! Try calculating the volume of a parallelepiped or deriving the formula for the distance between a point and a plane. 

What are you waiting for? Gear up and join us on Maple Learn today! Whether you're diving deep into the world of linear algebra or merely dabbling, there’s a world of discovery waiting for you.

Jill is walking on some trails after a long and stressful day at work. Suddenly, her stress seems to be lifted off her shoulders as her attention gets drawn to nature's abundant beauty. From the way the flowers blossom to the way the leaves grow on their stems, it is stunning.

When many think of mathematics, what comes to mind is often numbers, equations, and calculations. While these aspects are essential to math, they only scratch the surface of a profoundly creative discipline. Mathematics is much more than mere numerical manipulation. It is a rich and intricate realm that influences everything from art and science to philosophy and technology.

Just as Jill was stunned by the beauty of nature, you too can be amazed by the beauty of math! The golden ratio is one math concept that garners a reputation for being particularly beautiful, perhaps due to its presence in different parts of nature. You can explore it through some Maple Learn documents.

Check out the Fibonacci sequence and golden ratio document to better understand the golden ratio and its relationships. Perhaps, once you have a good grasp on the basics, you would like to check out the golden spiral document. Notice how the spiral that results resembles the outline of a nautilus shell and the arms of a spiral galaxy!

Nautilus shell image: https://en.wikipedia.org/wiki/File:NautilusCutawayLogarithmicSpiral.jpg -- Spiral galaxy image: https://www.cnet.com/pictures/natures-patterns-golden-spirals-and-branching-fractals/

Next, you may want to understand why the golden ratio is considered the most irrational number. You can do that by checking out the most irrational number document. Or you could explore this golden angle document to see how the irrationality of the number can be used to reproduce structures found in nature, such as the arrangement of seeds in a sunflower's centre!

Sunflower image: https://commons.wikimedia.org/wiki/File:Helianthus_whorl.jpg
 

That's all for this post! No worries, though. Maple Learn has hundreds of documents that can aid you in exploring the abundant beauty of math. Enjoy!

Advanced Engineering Mathematics with Maple (AEM) by Dr. Lopez is such an art.

Mathematics and Control Theory talks easily in Maple...

Thanks Prof. Lopez. You are the MAN !!

Dr. Ali GÜZEL

Registration for Maple Conference 2023 is now open! This year’s conference will again be a free virtual event. Please visit our site to see more information about the event and to register.

Our call for presentations has now concluded, but it is not too late to submit to our Maple Conference Art Gallery and Creative Works Showcase.

The Agenda section, where you’ll find information about the conference format and an overview schedule, has been added. This will be updated as the details are finalized.  

The pendulum and the cantilever share simple-looking ordinary differential equations (ODEs), but they are challenging to solve:

This post derives solutions from Lawden and Bisshopp by Maple commands, which (to the best of my knowledge) have not been published providing not only results but also the accompanying computer algebra techniques. A tabulated format has been chosen to better highlight similarities and differences.

Both solutions have in common that in a first step, the unknown function is integrated and then in a second step the inverse of the unknown function (i.e., the independent variable) is integrated. Only in combination with a well-chosen set of initial/boundary conditions solutions are possible. This makes these two cases difficult to handle by generic integration methods.

Originally, I was not looking for this insight. I was more interested in an exact solution for nonlinear deformations to benchmark numerical simulation results.  Relatively quickly, I was able to achieve this with the help of this forum, but after that I was left with some nagging questions:

Why does Maple not provide a solution for the pendulum although one exists?

Why isn’t there an explicit solution for the cantilever when there is one for the pendulum?

Why is it so difficult to proof that elliptic expressions are equal?

Repeatedly, whenever there was time, I came back to these questions and got more and more a better understanding of the two problems and the overall context. It also required me to learn more of Maple, and I had to revisit fundamentals of functions, differential equations, and integration, which was entirely possible within Maples help system. Today, I am satisfied to the point that I think it is too much to expect Maple to provide a high-level general integration method for such problems.

I am also satisfied that I was able to combine all my findings scattered across many documents and Mapleprime questions into a single executable textbook-style document with hidden Maple code that:

Exclusively uses and manipulates equation expressions (no assignment operators := were required),

Avoids differentials that are often used in textbooks but (for good reasons) are not supported by Maple,

Exclusively applies high-level commands (i.e. no extraction of subexpression, manipulation
           and subsequent re-assembly of expressions was needed).

The solutions for the pendulum and the cantilever are substantially different although the ODEs and essential derivation steps are similar. I think that an explicit solution for the cantilever, as it exists for the pendulum, is impossible (using elliptic integrals and functions). I leave it open to comments: whether this is correct and whether it is attributable to the set of initial and boundary conditions, the different symmetry of the sine and cosine functions in the ODEs, or both. I hope that the tabular presentation will provide an easy overview, allowing to form an own opinion.

If you are patient enough to work through the table, you will find a link between the cantilever and the pendulum that you are probably not expecting. 

Finally, I have to give credit to Bisshopp, who was probably the first to provide a solution for the cantilever. The clarity and compactness on only 3 pages and the way how the inverse of functions was determined before the age of computers makes this paper worth studying. Also, Lawden has to be mentioned, who did the same on 3 pages for the pendulum in a marvelous book on elliptic functions and applications. It happens that he is overlooked in more recent publications and it’s unclear to me if he was the first who published an explicit solution. His book might be one of the last of its kind in this age of computers, and for that reason alone, it is worth enjoying as he enjoyed writing it.

Download Cantilever_and_pendulum_side_by_side_-_input_hidden.mw

Disability Pride Month happens every July to celebrate people with disabilities, combat the stigma surrounding disability, and to fight to create a world that is accessible to everyone. Celebrating disability pride isn’t necessarily about being happy about the additional difficulties caused by being disabled in an ableist society: as disabled blogger Ardra Shephard puts it, “Being proud to be disabled isn’t about liking my disability… [It] is a rejection of the notion that I should feel ashamed of my body or my disability. It’s a rejection of the idea that I am less able to contribute and participate in the world, that I take more than I give, that I have less inherent value and potential than the able-bodied Becky next to me.” The celebration started in the US to commemorate the passing of the Americans with Disabilities Act, which prohibits discrimination based on disability, and since then it has spread around the world.

So what does any of this have to do with us here in the math community? Well, while it’s easy to think of mathematics as an objective field of study that contains no barriers, the institutions and tools used to teach math are not always so friendly. For an obvious example, if there's a few steps leading up to your math classroom and you use a wheelchair, that's going to be a challenge. And that's just scratching the surface—there are countless ways to be disabled, many of which are invisible, and many of which make a typical classroom environment very challenging to learn in for a variety of different reasons. As well, it can be difficult for prospective mathematicians to ask for accommodations, because of both the stigma against disability and the systemic barriers to receiving the proper accommodations. Just ask Daniel Reinholz, a disabled math professor at San Diego State University, whose health forced them to drop out of several engineering courses during their undergraduate degree: “Throughout it all, I never had a notion that I could receive accommodation or support, or that I deserved it. (Even though I’ve never really fit into the “right” category of disabled to be accommodated, so who knows what difference it really would have made.)” While Daniel was lucky enough to find a path to mathematics that worked for them, not all disabled people currently have that path available to them. As math professor Allison Miller puts it in her AMS blog post about disability in math, “Success in mathematics should not depend on whether someone’s needs happen to mesh sufficiently well with institutional structures and spaces that have been designed to serve only certain kinds of minds and bodies.”

While we can’t make systemic changes on our own, we here at Maplesoft can still do our part to make tools for math that are something everyone can use and enjoy. As such, we’re excited to share that Maple Learn is now compatible with the screen reader NVDA. By using this screen reader, and with our extensive keyboard shortcuts that negate the need for a mouse, individuals with low or no vision can now use Maple Learn to help them explore mathematics. All you need to do is select “Enable Accessibility” from the hamburger menu, and you’ll be ready to go! Maple Learn also includes the colour palette CVD, which is designed to be accessible to colourblind users. To learn how to access the colour palettes, check out this How-To document.

There is still more work for us to be done to ensure that we’re doing our part to make math accessible to everyone. Not only are there still ways in which we’re working to improve the accessibility of our products, but we all as a math community need to strive towards recognizing the barriers we may have previously overlooked and finding ways to provide accommodation for all mathematicians. One organization, called Sines of Disability, is already working towards that very goal. They are a community of disabled mathematicians dedicated to dismantling the systemic ableism present in mathematics. For this Disability Pride Month, consider taking the time to check out these resources and learn more about this issue.

Can’t seem to find the mistake in your math? Instead of painfully combing through each line, let the new “Check my work” operation in Maple Learn help! Now in Maple Learn, you can type out a solution to a variety of math problems, and let Maple Learn check your work! Additionally, by signing on to Maple Learn and the Maple Calculator app, you can take a photo of your handwritten math, import it into Maple Learn, and check your work with the click of a button.

Whether you’re solving a system of linear equations or an algebra problem, computing an integral or a partial derivative, “Check my work” can help. Maple Learn will tell you which steps are “Ok” and which steps to double-check. If you get a step wrong, Maple Learn will point out which line has an error, then proceed to check whether the rest of your work followed the right procedure.

Here’s an example of a solution to a system of linear equations written out by hand. All I had to do was snap a picture in the Maple Calculator app, and Maple Learn instantly had my equation set ready to go in the Cloud Expressions menu. Then, I just clicked “Check my work” in the Context Panel.

Maple Learn identified that I was trying to solve a system with 3 equations, checked my steps, and concluded my solution set was correct.

What happens if you make a mistake? Here’s an example of evaluating an improper integral with a u-substitution that involves a limit. This time, I directly typed my steps into Maple Learn and pressed “Check my work” in the Context Panel. Check my work recognized the substitution step and noted what step was incorrect; can’t forget to change the limits of integration! After pointing out where my mistake was, Maple Learn continued to evaluate the rest of my steps while taking my error into account. It confirmed that the rest of the process was correct, even though the answer wasn’t.

After making my change in Maple Learn and checking again, I’ve found the correct value.

Checking your work has never been easier with Maple Learn. Whether you want to type your solution directly in Maple Learn or import math with Maple Calculator, the new “Check my work” feature has you covered. Visit the how-to document for more examples using this new feature and let us know what you think!

What was established in 1788 in Prussia, is derived from the Latin word for “someone who is going to leave”, and can be prepared for using the many capabilities of Maple Learn? Why, it’s the Abitur exam! The Abitur is a qualification obtained by German high school students that serves as both a graduation certificate and a college entrance exam. The exam covers a variety of topics, including, of course, mathematics.

So how can students prepare for this exam? Well, like any exam, writing a previous year’s exam is always helpful. That’s exactly what Tom Rocks Math does in his latest video—although, with him being a math professor at Oxford University, I’d wager a guess that he’s not doing it as practice for taking the exam! Instead, with his video, you can follow along with how he tackles the problems, and see how the content of this particular exam differs from what is taught in other countries around the world.

Oh, but what’s this? On question 1 of the geometry section, Tom comes across a problem that leaves him stumped. It happens to the best of us, even university professors writing high school level exams. So what’s the next step?  Well, you could use the strategy Tom uses, which is to turn to Maple Learn. With this Maple Learn document, you can see how Maple Learn allows you to easily add a visualization of the problem right next to your work, making the problem much easier to wrap your head around. What’s more, you don’t have to worry about any arithmetic errors throwing your whole solution off—Maple Learn can take care of that part for you, so you can focus on understanding the solution! And that’s just what Tom does. In his video, after he leaves his attempt at the problem behind, he turns to this document to go over the full solution, making it easy for the viewer (and any potential test-takers!) to understand where he went wrong and how to better approach problems like that in the future.

So to all you Abitur takers out there—that’s just one problem that can be transformed with the power of Maple Learn. The next time you find yourself getting stuck on a practice problem, why not try your hand at using Maple Learn to solve it? After that, you’ll be able to fly through your next practice exam—and that’ll put you one step ahead of an Oxford math professor, so it’s a win all around!

This is a reminder that we are seeking presentation proposals for the Maple Conference.

Details on how to submit your proposal can be found on the Call for Participation page. Applications are due July 11, 2023.

We would love to hear about your work and experiences with Maple! Presentations about your work with Maple Learn are also welcome.