I might expand on this later, but primarily I just don't think it's reasonably possible to implicitly know. You can chain and combine pure functions in any number of ways, and because the "variable(s)" for all of them are all just # (or #n), it's important to be able to explicitly delineate where one operation ends and another begins.

Hi everybody! As it turns out, the "Working with Data" example that I thought was broken in today's review actually does work—it's just that due to the somewhat strange nature of the import/generation of the data, the kernel didn't change the color of the associated symbols. So: after clicking "Create Sample Data", you'll be able to use numericData and housePriceDataRaw without issue despite their being blue. Once you start interacting with them, they should change to black :).

Added it to the Sample Data folder.

Hi everybody—I've uploaded a filled-in Q&A transcript to the Course Materials folder (in the QnA subfolder). Here, I've gone through and added some notes/expanded upon some of the given answers—as well as filled in the very small number of questions which had not yet already been answered—for days 1-7 of this study group

This is a great way to review the material and prepare for quizzes, and also just has some generally "good to know" information, in my estimation. Please do check it out!

Hi Jonathan—it is correct on my end, yes. We did have a key issue with an earlier version, but you shouldn't be experiencing that. I can't discuss quiz answers here, but please see the documentation for Apply. If that doesn't clear things up (which I expect it doesn't, or you probably wouldn't be asking), feel free to email me at my first name, last initial @wolfram.com and we can discuss specifics.

Hi Arben,

Thanks a lot for the explanations! Let me explain where my confusion arose, as it could be useful feedback for future courses.

First, "High-precision Numbers" is simply the wrong technical term. Numbers with a precision higher than $MachinePrecision are called "arbitrary-precision numbers" according to earlier parts of the notebook and the documentation page you've linked. This is a bit nitpicky, but it honestly confused me.

Second, I asked the wrong question. I should have asked "Why does N[Exp[100000000000000000]] yield Overflow if numbers larger than MaxMachineNumber are represented by arbitrary-precision numbers"? To which you would have answered that even for these numbers there's an upper limit, $MaxNumber.

For this reason I think it would be helpful to change the notebook slightly: just delete two zeros, and you arrive at a number that is still pretty big but can be handled by Mathematica.

In[55]:= N[Exp[1 000 000 000 000 000]]
Out[55]= 7.*10^434294481903251

Of course, there's no denying that it is impressive that Mathematica is able to do the calculations you've shown even with the larger number.

Cheers, Jörn

P.S. New question: how do I enter a dollar sign here without screwing up the output?

Hi Arben;

When I try to attach the OneNote file for Windows 10 (.one suffix I believe), I receive a message that the file type is not supported and the "Add a file ..." operation is terminated. Can I send the file to an email, or is there a workaround to the message?

Thanks,

Mitch Sandlin

Ha! I'm not sure it's necessary—we have people from so many backgrounds who teach Wolfram Language super well—but it helps with the broader types of questions we can get, for sure.

After our work with Point[] yesterday, it would certainly be educational to have an animated point moving around the path (and indicating the changes in velocity). This would be similar to graphically showing the orbits of planets in the solar system on their respective ellipses with a higher velocity as they get closer to the sun located at one foci. That would probably be a better problem to look at first. Do I just need Animate[] to be moving that point along a curve?

Yes, just Manipulate or Animate will suffice if you have a functional representation of the position of the body over time. For an elliptical orbit, it can get a little complicated—but I think with some assumptions you should be able to write something down. However, if you wanted to be a bit cutesy about it, you could use our NBodySimulation function... let's try it with three bodies, using the entity framework's knowledge about the masses of celestial bodies. This example is lightly modified from the documentation:

Maybe try to modify this to look at just two bodies of your choosing!

Perhaps more to the point of your question... consider this:

Two comments about the RMT Ropes "dragon roll": I'm fairly certain that our bones, muscles, and CNS never ever encountered any movement like this before. While awkward at first, our CNS does figure it out, and then it figures out how to polish the movement to be graceful and efficient. We don't have to know a peep about the physics or its computation; we just do it. When I was moving with the rope this AM, I noticed that it's certainly possible to move through the pattern without touching the ground (i.e., getting any lifting force from that bounce). However, the required forces to get the rope over your head are far smaller if you let the bounce happen. That's the general theme of impedance and gait in the human body: reactance doesn't usually make the movement possible; it makes the movement significantly more efficient. Again, it's astonishing that the CNS just notices that bounce, rolls with it, and figures out how to #!$$ use it. The CNS-controlled biomechanics of the human body are dazzling and humbling.

It is indeed pretty incredible—I've done a lot of powerlifting in my life and trained up many new people, and in all cases it's amazing to watch how people adapt in a way that clearly isn't just due to increased strength, but increased proprioception.

Thanks phil!

where can I find data2D.dat?

Thank you, very helpful links.

A few, but I wouldn't sweat it :) Those are the ones I use frequently (in addition to @@@), but I provided a few links showing ~all of the shortcuts in last week's review notebook. Those resources were:

A cheat sheet of the sometimes mysterious-looking abbreviations would be helpful. I think so far we have seen the following:
@
/@
@@
/.
/;
//
~
Did I miss any?

When would one choose to use FindRoot rather than NSolve? At first glance, NSolve seems better since it promises to seek all roots. But, in what sort of situations is NSolve likely to fail and FindRoot succeed?

Tremendous commentary Arben! I'd been wondering why we needed a PhD to be leading this course; I'm wondering no more. I'll almost certainly defer diving into this for the next two weeks, but will definitely pick it back up.

After our work with Point[] yesterday, it would certainly be educational to have an animated point moving around the path (and indicating the changes in velocity). This would be similar to graphically showing the orbits of planets in the solar system on their respective ellipses with a higher velocity as they get closer to the sun located at one foci. That would probably be a better problem to look at first. Do I just need Animate[] to be moving that point along a curve?

Two comments about the RMT Ropes "dragon roll": I'm fairly certain that our bones, muscles, and CNS never ever encountered any movement like this before. While awkward at first, our CNS does figure it out, and then it figures out how to polish the movement to be graceful and efficient. We don't have to know a peep about the physics or its computation; we just do it. When I was moving with the rope this AM, I noticed that it's certainly possible to move through the pattern without touching the ground (i.e., getting any lifting force from that bounce). However, the required forces to get the rope over your head are far smaller if you let the bounce happen. That's the general theme of impedance and gait in the human body: reactance doesn't usually make the movement possible; it makes the movement significantly more efficient. Again, it's astonishing that the CNS just notices that bounce, rolls with it, and figures out how to #!$$ use it. The CNS-controlled biomechanics of the human body are dazzling and humbling.

How would I don this using Map? Thank you. Visualize {1,4,3,5,2} with a piechart,numberline,lineplot and barchart.Place these in a 2×2 grid.

Hi Mitch—I think I'd need the actual OneNote file to try anything here, as I don't use many Office products and don't have any experience with this.

You could try this.

Please see the background information in the attached "Impedance Background" Notebook (including a link to the RMT Ropes "dragon roll" video). Questions: 1. How can I make a simple animation that approximates the path of the centerline of the RMT rope motion? Is there an example of this helical path somewhere? 2. I'd like to compute a path based on the approximate forces on the rope, and show the resistance/reactance forces in a separate panel. I'd like to show the phase relationship between resistance/reactance, but not freak out people unfamiliar with the complex number representation of impedance. Suggestions? 3. Does Mathematica provide a way to visually capture the 3D path of [a marked] centerline of the rope? I may need to stitch the inputs from multiple cameras together? I was thinking of producing a 3DP of this captured path.

One unrelated request: can you capture an audio sample from your cat and show us a Fourier transform of it for the study group? Do we look at Fourier transforms? Maybe your cat just wants to contribute to the presentation. Meeeeeow.

Attachments:

Impedance Background.nb

Glad it's useful! For completeness, you could cleverly turn a rule into a definition, in any case, with: Set@@(x->a) which is equivalent to: Apply[Set,x->a]

Could you remind us how to let x equal (say) the first solution of Solve[x^2 + a x + b == 0, x] ? The Solve command outputs replacement rules, and my question is about how to turn that rule into an assignment to the variable x.

Ah, of course—the list itself is not a number... in that case, we should explicitly specify a level rather than replacing all of the expressions which match: Replace[col,s_/;!NumericQ@s->42,1]

Hi!

Hoping this hasn't been asked already: we've seen on day 2 that Map[f, g[a,b,c]] yields g[f[a],f[b],f[c]]. This no longer works if g is a function:

Cheers, Jörn

Hi Mitch—yes, I remember this. Attached is my best shot, if I've read what you've said here correctly.

1. For the last plot, I've changed from the default (axis) display to a frame display, choosing to only display the frame on the bottom and left edges (the left frame edge replaces the y axis). I've used this to place not Ticks, but FrameTicks at the very bottom. I set the frame opacity to 0, and then set the frame ticks opacity to 1. This is necessary because without manual specification of the frame ticks style, they inherit the style of their associated frame. I updated the previous two plots to only have left frames; they keep their axes, removed the gridline at x=0, and slightly modified their plot range paddings so that the frames appear more like axes.

2. To put it technically, this can often be a bit of a PITA. In this case, however, because of the way that Epilog works, you can just outright write the color inside the list of graphics options which specifies epilog. I've done that and changed the point sizes to all be equivalent, assuming that you want only the color to be the distinguishing factor. (Easy enough to change back if not, of course.)

Here's what I get for a final result:

I don't love that the points on the edges are cut off... it's due to the PlotRangePadding option. You can change that from {0,.1} to just .1 and it'll fix it, but it adds a liiiiittle space between the plot itself and the frame-edge that's serving as our y axis. If you do that, you probably want to modify the ticks such that the 0 is not included, because it looks cluttered... not sure how to avoid this presently, so pick your poison!

Attachments:

Plot_DerivativeD...nb

Hi Arben;

Many, many moons ago, you helped me with a column plot, which I have been refining ever since. There are two final refinements than I have been working on but have not been able to figure out as of yet and was wondering if you could help me - see attached.

1. Move the Ticks of the 3rd plot all the way to the bottom. Currently, they seem congested at the origin position. I have not found anything in the documentation that allows me to move the Ticks.

2. I would like to implement your earlier suggestion and key the colors of the Ticks to the legend (say red, Blue and black). Changing the legend is not a problem, but changing the Ticks are. I have unsuccessfully tried several things which did not work and thought I would ask.

Thanks,

Mitch Sandlin

Attachments:

Plot_DerivativeDisplay.nb

It’s the same situation in the iPad/iOS flavor of the app.

I think I had to upload notebooks from the desktop version during my previous testing. :-(

The web interface has a button which will allow you to upload notebooks…

Drawing Tools palette: where can I find it in Mathematica 13.2 on a Mac? I do not see it in the Graphics menu or the Palettes menu.

A few questions from a beginner:

1. All Functions: the basic syntax of functions, how to interpret and resolve error messages, how to use help pages, how to find the best function(s) to use in a given situation
2. Shortcuts/Cheatsheets: Keyboard, shortcut keys, and other cheatsheets pages to help navigate the syntax, system, etc.
3. Best practices/tips and tricks: writing code, debugging, making it intelligible to others, most useful general functions, etc.
4. Entities/Datasets: list of available items, how to best pull data, identify data elements available within in, the best way to utilize, etc.
5. Specific functions: MAP and related functions - step x step and primary ways it's used. How to find the longest word in WordList[] Thanks.

Hello, i, j, and k are still legitimate names wherever the user of a language has a choice at all.

You completely misunderstood. I wasn't talking about the semantics and interpretation of any programming language. I was talking about the meaning of those variables that has been burned into the brains of generations of programming students. I did think it was kinda neat that some version of [iteration variables] have been around for ~65 years -- the traditional age of retirement -- and perhaps it's time to give [iteration variables] a metaphorical retirement.

Hello all, please see notebook.

Attachments:

29144207.nb

I am having troubles importing the exercises into Wolfram Cloud application. I am working on android tablet and I extracted the exercises into Download folder. There is no import option. Please help.

Attachments:

Screenshot_20230...jpg

It's a totally relevant and reasonable question to ask. They are indeed very similar, and I don't believe Animate does anything that Manipulate can't: it's basically a stripped down version of the full Manipulate interface which has fewer possible options and which automatically begins animating upon evaluation, that's all!

Hi everybody—I've added today's data files to the Course Materials folder, so you can now use them while trying out today's notebook yourself.

In data visualization, I am trying to visualize the relationship as to how the surface area of a sphere and its volume changes as the radius increases using the two formulas below:

Surface area of a Sphere - 4 [Pi] r^2 Volume of a Sphere = 4/3 [Pi] r^3

I am using Manipulate[] function to increase the radius - see attached. However, visualization of the output is difficult since the output of the surface area is in square meters and the output of the volume is in cubic meters - two different units of measure. Please give me some direction as to what visualization function to use.

Thanks,

Mitchell Sandlin

Attachments:

AreaVsVolume.nb

Of course! I've received confirmation that this is the right way to think of this, and suggested a way of looking at the expression that might make this clearer still: ExpressionTree[u, "Subexpressions"]

Thanks for clarifying these issues, Arben!

Friday is fine. Thanks!

Hi again Phil—the first part should be doable without issue with just the regular Graphics3D interface (e.g. what you see when you use Plot3D or anything like that). The second part is also doable, but in a few different ways... I think the best way would be to use Animate or Manipulate (along with some of the camera positioning/perspective options). This way, you could set up the visualization to animate however you like (w.r.t. the flythrough and all), and the user could pause it at any point to rotate it and so on because in the end, it's still a Graphics3D object like discussed above.

This could be a bit tricky to set up, as flythroughs are much easier to explain than they are to code, but it can absolutely be done. Exporting a video would also be completely trivial!

Aha. I found the Q&A button in the BigMarker software while replaying today's session. I'll look for that icon tomorrow during the live session. Are the questions of other participants viewable, or can I only view my own questions and answers? TY.

From comments in the presentation today, I believe there is some other place that [many] questions are being asked/answered. I don't see that area or any way to get to it. What am I missing? Help!

Arben,

One area I’ve struggled with concerns Levels of expressions. So in preparation for my question(s) concerning MapAt, and MapThread, I figured I’d study “the book” (https://reference.wolfram.com/language/tutorial/Expressions.html#24855). I do alright until almost the very end where negative Levels are introduced…

Level[u, {-1}] results in {a, a, a, a, f} because these are the bottom leaves on the TreeForm, as near as I understand it. Where things start going sideways is when Depth[] is introduced. The next example shows, Depth[g[a]] which returns 2. Why is it two? Is it because Depth counts the expression head, “g” as well as the argument “a” as a level?

The final example also doesn’t behave as I expect. It says, Level[u, {-2}] results in {g[a], h[a]}, but if we’re starting at the bottom of the TreeForm and proceeding up two levels, why aren’t {f[a], f[a], f[f]} also included? They all have two levels up from the bottom of the TreeForm…

Mitch,

Per the documentation for these functions, the arguments are assumed to be in radians. You can use the function Degree to convert between degrees and radians.

Hope this helps.

J.

Great content thus far....

I wanted to ask about wolfram being leveraged as part of a larger code base. How would that work?

Arben, do you have a sampledata.xls file that we can download into our local computers? Alternatively, do you have the URL for a sampledata.xls? You may have identified teh URL in your presentation, but I didn't write it down. TY.

Hi.

As someone with previous Mathematica experience (over 20 years ago!), I’m looking forward to this review. Since I work from an iPad, I’m interested in learning the differences between the desktop and on-line versions of the program. So far, the distinction between commands like CloudExport, and Export are lost on me. Hope we can (briefly) address these topics.

Look forward to getting started. Thanks.

J.