I could use some advice on recommended ways to write functions. The function I am trying to write factors numbers. I am specifically targeting large numbers that have two prime factors. I want to eliminate all of the obvious factors (e.g. 2, 3, 5 etc.) So I started to write the following function, where c is the number being factored. I imagine there are several ways to factor a number by inspection, so far my function only has two tests, but could have more. Should I use Catch[] and Throw[] or Return[] or something different?

factorByInspection[c_]:= (
Catch[
If[EvenQ[c], Throw[{2, c/2}] ]
If[divFiveQ[c],Throw[ {5, c/5}]]
])

Arben, in the Elementary Introduction book interactive course chapter 11, there was an exercise about finding how many words in a list-o-words start with [some particular letter]. I answered:

StringContainsQ[StringTake[WordList[],1],"q"] // Counts // Lookup[True]

I thought that was a clever method, but the engine grades my response with a "Try Again". Is there something lacking in my response? Where does one go to report glitches in the exercise-engine for this course?

As an aside, I really like the numerous exercises in that course. It has more of a "practice the scales" component than study group tests. Nothing is as good as your live courses, but this interactive course is pretty darn neat.

I downloaded my own copy of the quiz, and I left the original in my collection of web artifacts. I filled in the answers and got an automatic grade for the test. I saved the test back to the collection of web artifacts, but when I open it, it's blank. Did the quiz results make it to you, and where can I find my filled in copy of the quiz?

Hi, Robert. After observing the quiz behaviors over several study groups, I've concluded that the cloud quiz engine is a "live wire" -- it is running asynchronous code back to the mother ship. I once left a filled-out-but-unsubmitted cloud-quiz sitting around for a day. My answers got cleared before submitting; that was definitely a Teachable Moment. It seems up to each student to identify the quirky behaviors of cloud-based Wolfram-U Notebooks and figure out how to work with them.

The quizzes have a button to download the quiz-notebook; I have gotten in the habit of downloading the notebook, working through the questions in that quiz notebook in my own version of Wolfram Desktop, and answering the questions there. That locally-running version of the quiz isn't a "live wire"; it doesn't ever self-clear or have any unexpected behaviors. When I'm ready to submit my quiz, I manually transfer my answers to the cloud-version of the quiz.

If you don't have access to a local version of Wolfram Desktop/Mathematica, you could grab images of the quiz questions and put them in a new cloud notebook. That would give you the quiz without getting the quirky behaviors of their quiz-engine.

Quizzes are hard to create and hard to administer -- and sometimes hard to take. With ChatGPT and other LLMs, quiz mechanics may become even more difficult. Or maybe the AIs will rapidly become skilled at teaching us with automatically-generated Wolfram-Lessons. Interesting times for sure!

Hi, Arben! I very much appreciate the work that you and your Wolfram colleagues put into this class --and all the other classes I've taken. You make it fun to work on and learn even the most complex topics.

I have some questions about the admin of the final quiz. I downloaded my own copy of the quiz, and I left the original in my collection of web artifacts. I filled in the answers and got an automatic grade for the test. I saved the test back to the collection of web artifacts, but when I open it, it's blank. Did the quiz results make it to you, and where can I find my filled in copy of the quiz? Thanks for a great course! Bob

This has been a great course with lots of inspirational gold nuggets. I can only dream of what a mind blowing experience going to college these days could be like with a tool like this at my finger tips.

Quick question: I got tired of the beeps warning me that the class notes were created in a newer version of Mathematica so I downloaded and installed is labeled as the latest version 13.2.1.0 on my current service plan, and I am still getting the beeps that tell me the notebooks I am opening were created on a newer version.

Does anybody know why? Are you working in a newer, perhaps unreleased version?

Hi everybody—the completed Differential Geometry notebook (with my and John's parts in addition to some of the extra references John made live) is now available in the materials folder.

Good luck on the quiz!

EDIT: I should also note that the review, including the "mini-lecture" on the intersection of linear and differential operators, Hamiltonian mechanics, differential eigensystems, and so on has also been uploaded in full.

Great point, John—we'll be doing this going forward. (We have that in our MOOC quizzes but hadn't implemented it yet in our standalone ones.)

Yes. Good course. @Wolfram U: You don't have to be a math or physics major to appreciate and learn from this course. You can quote me on that. :)

Good quiz, too. If a W SG quiz is well-written, you'll learn at least a thing or two while taking the quiz.

One resource that @Arben didn't mention WRT differential geometry (and many other things) was the Wolfram Mathworld online reference. I had found Viviani's Curve in an unlikely place (an exercise instruction video); that article helped me understand and explain that oscillating motion. While Mathworld entries are similar to Wikipedia articles, I find the quality and writing of Mathworld articles are consistently high and superior to the Wikipedia. Mathworld articles originate as Wolfram Notebooks; all are available for download. Once you're conversant in the Wolfram Language, you can directly use/modify the code implementing those graphical science articles.

Thank you Arben. Great study of simple physics. I could not do it, but know I know how.

Really enjoyed the study group. Re-learned a lot I had forgotten and many new capabilities I never knew before. The quiz is fun too. Looking forward to a next time.

Larry

FWIW, I have gone through several study groups with Version 12.2 (on MacOS). It's not optimal to do this, but I've had no major problems. For many reasons, I plan to upgrade soon. I'm certain that Wolfram U staff posts with the most recent version (which can always be found here). Current version is 13.2.1.

There's always a cost to not being current. There was a question on this quiz that I wanted to make sure my answer was correct against the current version. To do this, I opened a notebook on cloud.wolfram.com and evaluated the expressions there. In any case, it's worth being familiar with accessing WL Notebooks through the cloud.

I downloaded the notebooks for the study group today, and I found that I receive an error message on opening some of the lesson books. So, for example, I can open and read the notebook file "Linear Algebra and Graphs" but the file "WGS40-Asymptotics" does not open. I receive a Mathematica-generated error dialog box "Why the Beep" that tells me "This notebook was created in a more recent version of the Wolfram System ..." I am running version 13.2.1.0. I hope that you can help me fix the issue.

When I open the "Linear Algebra ..." notebook (and others that generate the same error message), the only page that appears in the notebook is the title page. There is no other content in the notebook (well, at least that I can see). BTW .... What version was used to create the "Linear Algebra ..." notebook?

I have a (mathematically) simple homework question today, but one that I think is a good exercise for people to try out—especially if they're newer to Wolfram Language.

1. The function tanViz from today's lecture currently only accepts a function and has predefined ranges for its two parameters. Modify tanViz so that it accepts ranges (as lists) for the two parameters u and v as inputs. That is, an input should look like: tanViz[surface,{ui,uf},{vi,vf}]. The resultant Manipulate object will then have sliders that range over the values that you specify.

2. Modify the Manipulate object such that it has a Slider2D input for the two parameters, as you saw in the Hamiltonian example from Tuesday. This will let you change u and v simultaneously.

It was in two-dimensional phase space, right? Or perhaps you mean that the phase space path was a plane curve with only one parameter? You can use ParametricPlot3D to plot space curves (for, say, a one-parameter three-dimensional phase space, like observing how position, momentum, and energy change as a function of time) or surfaces (for a two-parameter three-dimensional space).

If you mean the equation-solving itself, then you simply add more equations and variables to the (N)DSolve, though that can quickly increase the solution difficulty of course.

Thank you for your help. A Hamiltonian for a particle moving in a plane experiencing a magnetic field orthogonal to the planes is: H[q1,q2,p1,p2]= 1/2m (p1-Bq2)^2 +p2^2.

Seek solution to Hamilton's equations and the general solutions for the trajectory of the particle.

I am trying to describe the dynamics of a particle confined to the plane. There is no q1 dependence. The trajectories should be circles in the plane with the Larmour frequency. Hope I am making sense. Thanks again.

Dear Allison, it seems t has ans assigned value/expression in this case a list. Try clearing the variable, write and evaluate:

Clear[t]

above the differential equation.

Dave, the behavior I have observed repeatedly is that community.wolfram.com loses the cookie that identifies my Wolfram-ID. When I click on the reply window, I am immediately (and un-magically) forwarded to another window to log in. I click the back button in the browser; the problem persists. The fix I have found is to do a Reload of the web page, and the Wolfram BBS then knows who I am. This was horribly confusing the first 7-8 times it happened; it's now in my muscle memory to do the Reload. I pity the newbies who hit this glitch for themselves and hope they rapidly get it in their muscle memory. For background information, I"m using Safari 16.5 in MacOS 12.6.6. I reported this about 3 months ago; I haven't heard from anyone.

I truly appreciate how much Wolfram Research dogfoods their own software. The WL is used for essentially everything customer-focused in the company. OTOH, I don't believe that the community.wolfram.com bboards are the right place to use a WL-based solution. There are some superb bboard systems out there: Discourse, Discord, etc. These solutions are used by millions of people daily, have standalone clients on a bunch of computer and portable platforms, etc. Most important, the primary purpose of those companies is to provide agile world-class community-discussion systems.

BBoard functionality is not a priority for WR; it's probably not in the top 50 list (or top 100) of priorities for the company. It shouldn't be. All that WR needs is their BBS to have the proper HTML wrapping to interpret/relay the WL cloud expressions in messages. Wolfram shouldn't make a web browser or a streaming service. IMHO, they should not use a WL implementation of a bboard, either.

@Arben Kalziqi , are there any compelling technical reasons to have a WL-based bboard implementation? Is there some functionality the management thinks can't be done in Discourse/Discord/etc.? I've made repeated public comments similar to this one, but haven't received any responses. What gives?

Hi Phil,

Thank you for your feedback. We have sent you a message on your email address.

Hi, this is an admin Q.: Thanks for the great series! I have not been receiving any of the links to the session recordings (or even email reminders). Who should I contact to correct this? Thanks!

Phil is right! We did have an issue with another user's email address on BigMarker's end for some reason, so maybe the same thing is happening to you. We're looking into it!

EDIT: Actually, this was fxed during the minute I typed this post. You should be good to go now.

Hi Claude, I have reached out to our event platform and you should now receive the notification emails. It seems you had unsubscribed from the BigMarker emails at some point.

Please let me know if you have further issues or questions.

Best Wishes, Cassidy Hinkle

Regarding f[ ]: I like the consistent use of [ ] and not using ( ) for functions, or indiscriminately. I think one problem at least in elementary mathematics is our overuse of ( ) in different contexts, which confuses beginning students (and sometimes even seasoned mathematicians). So using [ ] for functions, { } for domains, and ( ) for only grouping actually makes the language of mathematics better.

My brain gets lost in bracket hell with deeply nested [[],[[],[[]]],[[]]] even when they are nicely indented. I find that using postfix operations makes these expressions much easier to understand. E.g.

Of the first 1000 primes which ones have a digit sum that is also prime?

Select[Map[Total, AssociationMap[IntegerDigits, Prime[Range[1000]]]], PrimeQ]

Range[1000] // Prime // AssociationMap[IntegerDigits/*Total] // Select[PrimeQ]

To understand the first one you have to work from inside to out. The second one maps naturally to the question in left-to-right, easy to read, and understand order.

Reverse Polish notation :) Reminds me of old HP calculators, and FORTH! So, all in all, pretty familiar to me. I actually prefer the prefix f@ argument, and using vectors for multivariate arguments, like f@{z, y, z}

Thanks for the hint regarding the HP41C clone! There are of course downloadable Apps that do (all or mostly) the same for less on your i-phone, but there is something magical about holding an HP41C calculator in your hand and not using your cell phone... I did a lot of solid RF Systems Engineering on my HP 41C before PCs and spreadsheets. I may just have to order one...

I am on travel and will miss a few workshop meetings. I reviewed the lesson on Asymptotics, and I have a few questions about the Singular Perturbation portion of the notebook.

1. The help file for AsymptoticDSolveValue lists options that may be set in the function, but I cannot find examples on how to set a value for the option when executing the AsymptoticDSolveValue command. Specifically, I want to compare the results using the "Quality" option to that obtained using "Speed". Hope that you can provide an example for each.

2. The example in the workbook shows how to find an asymptotic solution for the boundary-value problem, eqn = {[Epsilon] (y^[Prime][Prime])[x] + 2 Derivative[1][y][x] + y[x] == 0, y[0] == 0, y[1] == 1/2}; The solution presented seems to be implicitly a uniformly valid expansion for all x in the domain. [See plot in this section.] . What method was used to generate the asymptotic expansion solution presented in the workbook? That is, I typically use the method of matched asymptotic series for the inner and outer solution of the boundary-layer problem. The method of matched asymptotic solutions will generate a uniformly valide solution composite solution for all x. The boundary conditions will be satisfied exactly at both x=0 and x=1. The solution in the workbook, however, does not exactly satisfy the boundary condition y[1]=1/2. There is a small difference between the asymptotic soln value and the set value of 1/2. The difference is appreciable when epsilon is of O( 0.1) or larger. It appears that the method of matched asymptotics is not used in the Mathematica algorithm to generate the result in the workbook. What method does the code use?

Thanks

Hi everybody—today's "homework" question:

Part 1:

Use PrimePi and SparseArray's ability to specify elements via patterns to generate the following (10x10) matrix:

{{1, 2, 0, 0, 0, 0, 0, 0, 0, 0}, {2, 2, 3, 0, 0, 0, 0, 0, 0, 0}, {0, 
  3, 3, 4, 0, 0, 0, 0, 0, 0}, {0, 0, 4, 4, 4, 0, 0, 0, 0, 0}, {0, 0, 
  0, 4, 4, 5, 0, 0, 0, 0}, {0, 0, 0, 0, 5, 5, 6, 0, 0, 0}, {0, 0, 0, 
  0, 0, 6, 6, 6, 0, 0}, {0, 0, 0, 0, 0, 0, 6, 6, 7, 0}, {0, 0, 0, 0, 
  0, 0, 0, 7, 7, 8}, {0, 0, 0, 0, 0, 0, 0, 0, 8, 8}}

Part 2:

Modify the code above such that it produces a 30x30 matrix rather than a 10x10 one, then create a graph which has the result as its adjacency matrix. (Try using a circular embedding for the graph layout.)

Thanks Jose, this looks great! (and of course, I appreciate the Manipulate.)

There's a more compact way to write the pattern-matching for the initial SparseArray, if you're interested—recall that the Conditional statement can be any computation at all, not limited to checking equality, for example. I'm not sure if that's enough of a hint, but I'll post my version as a reply to this if you like, as I wouldn't want to spoil it before you've had a chance to think of it.

Terrible pun, Phil, I'm afraid you've gotta get out of here ;). I agree about local documentation; I really prefer it even though we don't bundle it by default anymore since it's gotten so large (though it's easy to download and install anyway). Our publishing guidelines are to link to webdocs, but I was thinking during today's lecture that I might ask to see if we can use local in some contexts, primarily for the reason you mention—click to copy is nice, but "edit and run" is a lot nicer!

Re: the homework problem, Band is a clever thought to have had. I must confirm that the fears you mentioned in chat have come to pass, though, as I generated the SparseArray as follows (and hopefully José sees this too, since it's a reply to the original comment):

sparse = 
 SparseArray[{i_, j_} /; Abs[i - j] <= 1 -> PrimePi[i + j], {10, 10}]

(Fortunately, I think you'll find this elegant enough to forgive me.)

Ha! But the question explicitly specifies the dimensions, so unless you're an incredibly fast typist, mine is still faster in the real world (and that's still true even in the case of your 11 million times larger array). I'll wag my finger and note that knowing when it's prudent to optimize is just as important as knowing how to optimize. (Contrarily: in a high-level language such as this, being able to think about sources of potential slowdown like you have is an invaluable skill!)

Thanks for letting us know, Dave—there's a strange issue with Community which sometimes occurs where the original username gets removed, and our "default" username in cases like those is Vitaliy's (ostensibly because he's the Director of Community Engagement).

Hi Carl—starting with a recent version of the language, fresh installs no longer come with the documentation by default. If I remember correctly, the user is asked during the installation process whether they would like to download and install local documentation. If not (or if they choose "no"), it's as simple as going to the menu and choosing something like "Download and Install Documentation". You don't—and as far as I know, never will—need a persistent internet connection to access documentation. It's just that the documentation is now on the order of a few gigabytes, so it was decided to leave it out by default and make it an optional installation.

Dear Arben,

I found a shorter code for the sparse array. If you have a different approach please share.

I also have a question in the attached document as I get some error messages and I can solve ir for the manipulate option.

Best regards

Attachments:

20230526 JD Spar...nb

I am curious about the automated proof system you mentioned on Tuesday. Can it detect statements that are unprovable in the current set of axioms (re: Goedel)? Or is that function not computable (Turing/Kleene) hence not doable by computer?

In Tuesday's presentation on Special Functions and Visualization, John McNally noted the use of Simplify or FullSimplify but cautioned that FullSimplify can take more time.

Is that really still the case? On modern processors, doesn't FullSimplify simply run fast enough? Do you have a real example where FullSimplify would make a noticeable difference?

The study group schedule notes that the Thursday June 1 session is about probability and differential geometry. I have a question about torsional forces. As noted in the wikipedia:

In the differential geometry of curves in three dimensions, the torsion of a curve measures how sharply it is twisting out of the osculating plane. Taken together, the curvature and the torsion of a space curve are analogous to the curvature of a plane curve.

I'd love to see a computation and visualization of the torsion of a 3D curve in the Wolfram Language. If this doesn't fit into the scheduled presentation, could you show an example (with WL Notebook) in the community discussion here? Thank you.