Dear Dr. Lippolt,

All your solutions were accepted during manual grading of the exercises. We faced some issues with the auto-grader accepting alternate solutions to some of the problems. Our apologies for the inconvenience.

Hello,

I got my level 1 certificate today. Thank you very much for that. I still do not know what the problem was with the 6 results which have been marked as wrong, although my final result matched the expected result in 100%. Do I have to discard the way I used to solve them in the future, since I was on a completely wrong way, or was it just a glitch in the autograder?

It would be great if we could get a final notebook with the official right results so that we can see how we did in the exam, and where we could get better.

Best regards, Dr. Peter Lippolt, Hannover, Germany

I have a similar problem starting with first question. I used a shorthand notation of Part without "Part" that produced the requested elements from the question, but was marked wrong by auto-grader.

I'll keep working on the exercises.

This is an automatically generated Delivery Status Notification.

Delivery to the following recipients failed permanently:

• "wolfram-u@wolfram.com wolfram-u"@wolfram.com

Reason: Permanent Error

I was having trouble with auto grader on 7 problems. I was trying to submit a nb file with the solutions.

Good day, everyone.

I completed the exams notebook (not all of it, if we are to believe the results of the "Check" button). Earlier I was advised to submit the notebook via email. However, when I try to, I get the "Client host rejected: Your message was rejected due to spam filtering. Please see http://www.sophos.com/security/ip-lookup..." mail send error.

So, the questions I'd like you to assist me with are the following. Are there any other ways to submit the notebook? How do I know, if and when all the results (quizes and exams) are recieved and are ok (or not)? What does humanity exist for? The last question is optional.

My local installation of 2.17 works with my solution also without errors. However, in the cloud I get a completely different error message than Andreas. (@Andreas I put the entries in ChemicalData["name","property"] in different order, please see the reference.)

Maybe "my error message" is because I pasted the image directly into my solution? - But: How else?

Attachments:

errorMessage2-17.png

Hi Andreas and Larawag,

I have noticed the issues with both the questions using images. I have come to a similar conclusion as you both. Although your image processing code runs just fine on your local installations, the autograder seems to be running into an issue with the same code snippet in a cloud sandbox. We are looking into it. Hopefully we'll have a resolution soon. And as you have quoted, we do have the backup option of emailing the notebook. Thanks everyone for your patience as we work through these issues.

Best, Abrita

Hi Rajeev,

For the purposes of this particular study group I would encourage you to use Wolfram|One and the regular Wolfram notebook which offers some more flexibility in adding different types of content (text, code or images) to the notebook. You will have more freedom to write your own code in the Wolfram Language in this notebook. And to add images you can simply copy and paste them into your notebook.

The Wolfram Alpha Notebook Edition is intended for slightly different use--to enable users to provide free-form input to get instant answers to questions, create and customize graphs, and also add their own notes in text.

Please let us know or feel free to contact our support team if you have further questions about which product will best suit your needs and expectations. Thanks

Good day, everyone.

Being a russian, I'd like to point out, that we have 10 vowels in our alphabet: а, я, о, ё, ы, и, э, е, у, ю. I can solve exercise 2.11 of the exam the way you want me to, but that'd be wrong.

Hi Everyone, I understand you have been running into some issues with the autograder. If your solution is generating the same output as shown in the expected output and you are satisfied with all your code, please download a copy of the exercise notebook and email it to us wolfram-u@wolfram.com.

You will find the exercise notebook in the "Copied Files" directory among your cloud files. It should appear as "02_exercise.nb"

Are there more statements involved when you developed the answer, which perhaps are required to also be copied to the answer field?

Hi Everyone, I'm not having luck with the autograder input box. I've read Abrita's note above that a complete statement, or compound statement, including any definitions, is needed. For example exercise 2.3 I got the same statement in a practice notebook were the statement==answer yields true, copied the statement to the grader box where it says "try again". I think it was Abrida who said in this cases to log on to the Wolfram account - my files - copied files folder and email you a download. Is that the procedure ? Can you remind me, or post, the email addresses we can send to? Thank you John.

I get the same result , I think the auto-grader is not picking up the right solutions

Similarly 12.2 solution correct but rejected .

12.3 solution correct but get an error "ToExpression::sntxi : Incomplete expression; more input is needed"

Have you checked that your solution does not include unwanted "blanks"? I typically work with my local Mathematica, and copy paste finished solutions over into the examination notebook. For some solutions he shows me a "try again". If I remove all excess blanks directly in the examination notebook it sometimes works. Your "vowel" string appears to be a bit suspicious. (just an idea)

Hi Fedor, Please feel free to send your exercise notebook with all the solutions to wolfram-u@wolfram.com. Your solution looks fine.

I think there could be an error in question 2.5 of the exercises

"starting from n=0 to n=4"

should be "starting from n=0 to n=5 "

Please give that email address so we can query solutions to the auto-grader.

I used an expression in the form of

NestGraph[f , 0 , 5]

and produced the graph and was accepted by the autograder .

I just want to point out that when you send your solution to the autograder (by clicking on the "Check Solution" button) it does not have access to any definitions you may have created in the exercise notebook itself. So you will have to include that definition as part of your solution.

myList = {1,2,3,4};
Part[myList,2]

or

myList = {1,2,3,4};
myList[[2]]

Call me crazy, I work with Mathematica on a 60 inch Samsung monitor. I'd like some guidance on how to reset Mathematica defaults (window size, text size ) when opening new sessions and work books. Could all the adjustments be made in the Option inspector? Currently I use Cntrl- mouse scroll to adjust the text inside the notebook to a reasonable size, which has not effect on the Window Title and tool bar. Thanks in advance for any help or pointing me to further reading.

Great job Arben and Abrita, the course surprised me in how much I picked up, and by it's breadth. Exciting ride keeping up with the pace. John

I hate to bring this up, but in Quiz 2, problem 6 begins with the ungrammatical phrase "Which pure function takes a two inputs..." Clearly something is wrong here: I could delete the word "a" and get one answer, but if I imagine that the the question has missing words then I can easily find two words that would change my answer. I'm going with the choice of deleting the word "a", but thought you might want to fix the question at some point.

What is the email to query the exercises that are not marked correct by the auto grader? Can we just send the code for the specific question?

Commenting further on the post of larawag NN how can arbitrary precision 10 be better and more accurate than MachinePrecision which is almost 16 (15.9546) ?

Thank you Abrita for the detail and clear explanation.

However the code doesn't give the required result (two^four, three^four)

SequenceCases[{one, two, three, four}, {x_, y_, z_} :> y^z, Overlaps -> True]

However this works as expected:

{one, two, three, four} /. {first_, middle___, last_} :> {middle}^
  last

You could use Grid or Column as shown in this example at http://reference.wolfram.com/language/ref/Slider.html

Hey John,

Forgive me if this is a silly question, but have you imported some audio to be saved as "sufjanSong"? Unfortunately it's a copyrighted audio track, so I couldn't include it with the files, and you would have to add your own audio track in order for this Export to work properly.

If you don't feel like downloading/importing your own audio track, you could always use one of our ExampleData files:

Export["sineManipulate2.mp4", {"Animation" -> 
   Manipulate[
    Plot[Sin[k x], {x, 0, 2 \[Pi]}, 
     PlotRange -> {-1, 1}], {{k, .1, "Wavenumber"}, .1, 5}], 
  "Audio" -> Audio["ExampleData/car.mp3"]}, "Rules"]

Video functionality is still fairly nascent in the Wolfram Language, and as a result you might not find it as well-exposed in the documentation as some of our more longstanding functionality. I found this Export functionality documented in this guide . Lastly, I'm not sure about the specifics of your error message there, but let me know if it persists after trying the above suggestion.

Arben

Import["hoffmann_ohno.mp4", "FrameCount"]

626

vid = Video["hoffmann_ohno.mp4"]; vidFrames = VideoExtractFrames[vid, All];

Length[vidFrames]

627

Are there 626 frames or 627 frames?

Hi Ron, The use of alternatives in Element seems like a very function specific implementation where

Element[x1 | x2 | ... | xn, domain]

asserts that all the xi are elements of dom, i.e. for a domain dom,

In fact you will see the following

In[4]:= Element[{x1, x2, x3, x4}, Reals]

evaluates to:

Out[4]= (x1 | x2 | x3 | x4) \[Element] Reals

Which is the same as

In[4]:= Element[#, Reals] &[{x1, x2, x3, x4}]

Out[4]= (x1 | x2 | x3 | x4) \[Element] Reals

You are right about SubsetQ -- it has been implemented to work for two lists, similar to other functions for operations on sets. (In the Wolfram Language, sets are represented by sorted lists.)

This is a very low priority post concerning the behavior of Element and of SubsetQ.

First, there have been times when I wanted a function that checks that each element in a list is a real number. In the past I've resorted to variations of

realVectorQ1[vec_?VectorQ]:=Apply[And, Map[Chop[Im[#]]==0. &, vec]]

which can be improved, perhaps, using Element:

realVectorQ2[vec_?VectorQ] := Apply[And, Map[Element[#, Reals] &, vec]]

However, I just learned of the alternate usage for Element which allows it to apply to a list of alternatives, which means we could write the function as:

realVectorQ3[vec_?VectorQ]:=Element[Alternatives@@vec, Reals]

This is nice and short, but I find it confusing: why is Alternatives, which I think of as related to the logical operator Or, involved in an operation that seems to involve an And statement? Probably I'm just worrying too much.

My second question: why does SubsetQ not apply to domains as well as lists? It would be really nice to just use SubsetQ[vec, Reals], but both arguments need to be lists as far as I can tell.

Again, really low priority here. Ron

Thank you for reporting the error. Not sure why RotateLeft crept in there. It should simply be:

BarChart[data2[[All, 2]], ChartLabels -> Placed[data2[[All, 1]], Below, Rotate[#, Pi/2] &]]

The idea was to rotate the labels by 90 degrees to avoid crowding at the bottom of the chart.

Getting there .... :-)

someText = {"State A", "State A1", "State A2", "State B", "Random Test"};

stringToAction[string_] :=
 Which[
  StringMatchQ[string, "State A*"],
  "actionA",
  StringMatchQ[string, "State B*"],
  "actionB",
  True,
  "State Unrecognized: " <> string]

stringToAction /@ someText
(* {"actionA", "actionA", "actionA", "actionB", "State Unrecognized: Random Test"} *)

stringToAction2[string_] :=
 Switch[
  StringCases[string, "State " ~~ x_ ~~ ___ :> x],
  {"A"}, "actionA",
  {"B"}, "actionB",
  _, "State Unrecognized: " <> string]

stringToAction2 /@ someText
(* {"actionA", "actionA", "actionA", "actionB", "State Unrecognized: Random Test"} *)

If you have to deal with more than a handful of states and actions, rather than generating a long Switch or Which manually, considering using a list of rules and maybe Dispatch.

Rohit, you didn't answer my question. Perhaps I didn't state it clearly. I'd like a single Switch/Which clause to capture all the strings, "State A1" … "State A3" I can't figure out how to do that. By my reading of the documentation, I assumed a "form" of StringMatchQ[#,"State A*"] would work. It did not. What should I do differently to make that work?

Rohit, you again misunderstood the issue. The issue is to put this into the switch statement. Here I take your answer, and put it into the switch statement. It fails. (In my original test on my notebook, I had the &, I just missed it when I typed it in here. This time I copied/pasted.) The first three entries in the output list should be "actionA" but they are all unrecognized by the switch statement.

someText = {"State A", "State A1", "State A2", "State B", "Random Test"};
stringToAction[x_] := Switch[x
   , StringMatchQ[#, "State A*"] &, actionA
   , "State B", actionB
   , _, "State Unrecognized" <> x
   ];
Map[stringToAction, someText]

{"State UnrecognizedState A", "State UnrecognizedState A1", "State UnrecognizedState A2", actionB, "State UnrecognizedRandom Test"}

I got Switch to work with StringCases rather than StringMatchQ:

f[myInput_] :=
 Switch[
  First@StringCases[myInput, 
    "State" ~~ Whitespace ~~ s_ ~~ ___ :> s],
  "A",
  Print["action for A"],
  "B",
  Print["action for B"],
  _,
  Print["None of the above"]
  ]

This is doing a very simple pattern test. You'll need to work on the string pattern a little more to make it more robust. The way I arrived at the solution is by going to the documentation for Switch, and then after looking at the examples (neither of which had string matching examples) I wandered over to the linked tutorial (from the links at the top right). The tutorial on Conditionals demonstrated using If, Which and Switch. The example

r[x_] := Switch[Mod[x, 3], 0, a, 1, b, 2, c]

seemed closest to my need. Although, still not an example with Strings, I concluded if I could place my string pattern test as the first argument and pull out the matching part of the string, then each possible match (and the default _ ) could be one of my alternative "forms" of my switch statement, based on which I could return different outputs.

Hope this helps.

Hi John, It may be helpful to view a list (or really any expression in the Wolfram Language) as a tree. You can even visualize it using the function TreeForm. For example here is a nested list with Dimensions {4, 3, 2} and its TreeForm representation:

words = {{{"anisotropy", "mugful"}, {"organist", 
     "socialization"}, {"worsening", "feeder"}}, {{"mawkishness", 
     "polity"}, {"technique", "cathartic"}, {"sore", 
     "zenith"}}, {{"aniline", "linguine"}, {"brutality", 
     "boutonniere"}, {"nonintervention", "venation"}}, {{"zirconium", 
     "compartmentalization"}, {"pentathlon", 
     "servitor"}, {"immovability", "blah"}}};

Dimensions[words]
{4, 3, 2}

TreeForm[words]

This tree/expression/list has 3 levels. Levels provide a general way of specifying collections of parts in Wolfram Language expressions. Since it has 3 levels, you can use a maximum of 3 indices to extract parts of this list using the Part function. The following will get a word from the last level:

words[[3,2,2]]

But attempting to get words[[3,2,2,1]] gives the error "Part::partd: Part specification <<1>> is longer than depth of object."

At Level 0 we have the entire expression. At Level[expr,{-1}] we have a list of all "atomic" objects in the expression, in this case each individual word.

Your interpretation "level spec is the depth of these indices" therefore makes sense.

"levelspec" allows you to specify at which level a particular function should work on an expression. If we want to StringJoin the elements of words at level 2, we should Apply at level {2}.

In[40]:= Apply[StringJoin, words, {2}]

Out[40]= {{"anisotropymugful", "organistsocialization", 
  "worseningfeeder"}, {"mawkishnesspolity", "techniquecathartic", 
  "sorezenith"}, {"anilinelinguine", "brutalityboutonniere", 
  "noninterventionvenation"}, {"zirconiumcompartmentalization", 
  "pentathlonservitor", "immovabilityblah"}}

If we want to StringJoin at level 2, we need to Apply at level {2}:

In[41]:= Apply[StringJoin, words, {1}]

Out[41]= {"anisotropymugfulorganistsocializationworseningfeeder",  "mawkishnesspolitytechniquecatharticsorezenith", "anilinelinguinebrutalityboutonnierenoninterventionvenation", "zirconiumcompartmentalizationpentathlonservitorimmovabilityblah"}

Hope this helps.

Hello everyone! I was doing the exercises of the seventh session but I can't find the file "weather.dat". Could you please share it? Thanks in advance.

Thanks!!!!

Thank you. Sorry about that - we'll get these edited.

Hi John,

Thanks for the notebook. My suspicion is that Accumulate is packing the array automatically—if it is packable—and that Accumulate was updated some time between the creation date of this original notebook and the present. See the linked notebook, where I change a 0 to a 0. to preclude the possibility of packing, and get (suspiciously...) a 10x slowdown. I can't be sure that that's because the array is no longer "packable", but that's my best guess.

I've asked through an internal channel for some clarification on this, and will update you if I learn anything!

https://www.wolframcloud.com/obj/arbenk/Published/05%20Numerics%20PackArray%20Timing%20(test).nb

Exercise 7.7 states "...load your package to introduce the rules for the function fib..."

How exactly do i load the package fib as generated by exercise 7.7?

Needs["..."] or Get["..."] are not working properly.

Executing the packed array timing example I didn't get the order of magnitude faster execution. Attached file shows the timing I got. Anyone have an idea why the timing stayed the same? Thanks in advance.

Attachments:

05 Numerics Pack...nb

Reminding our Study Group participants that the New in Version 12.2 webinar starts in less than 1 hour, at noon CST. Today's topics include the latest enhancements in visualization, the new area of bio-sequence computation, and new functionality for Wolfram Notebooks and working with code.

Sign up for the webinar here: https://wolfr.am/TyPQmtDD

Yesterday's Study Group recording is now available: https://wolfr.am/TyQ6Qt0q

sol = NDSolve[{f''[x] + f'[x] + 8 f[x] == 0, f[0] == 0, f'[0] == 1}, 
f, {x, 0, 10}] ;

Plot[Evaluate[f[x] /. sol], {x, 0, 10}, PlotRange -> All]

Expressions like Plot[Evaluate[f[x] /. sol] are given in the Help-examples of NDSolve

In the solution for Exercise 5.8 Plotting a result from NDSolve the following expression is given

Plot[f[x] /. sol, {x, 0, 10}, PlotRange -> All]

Both expressions give the same diagram.

In which cases i have to use Plot[Evaluate[f[x] /. sol] and in which cases i have to use Plot[f[x] /. sol] ?

From time to time I consider equations like "f(x) = some right-hand side". To investigate this kind of equations, I want to transform them by a rule like \xi = x/some factor, say \xi = x/a. (Typically, x and a have the same dimension and thus \xi is dimensionless.) Therefore, I want Mathematica to find and collect all quotients of x/a and replace them with \xi.

Replacing "(1 + x)^6 /. x -> 3 - a" is quite simple and standard. But the reverse way doesn't seem to work, does it? Unfortunately I didn't find any hints in the reference.

So, how do you deal with this symbolic issue?

Thank you very much for your quick reply, Arben!

You hit my point exactly, but "of course" I have more difficult examples in mind:

Example 1:

In[1]:= (-((4 s^2)/(-1 + s^2)^2) + (2 s)/(-1 + s^2))/(
  2 (1 + (4 s^2)/(-1 + s^2)^2)^(3/2)) + 
  Sin[(2 s)/(-1 + s^2)] /. (2 s)/(-1 + s^2) -> \[Xi]

Out[1]= (-((4 s^2)/(-1 + s^2)^2) + \[Xi])/(
 2 (1 + (4 s^2)/(-1 + s^2)^2)^(3/2)) + Sin[\[Xi]]

My expected output looks like this

(-\[Xi]^2 + \[Xi])/(2 (1 + \[Xi]^2)^(3/2)) + Sin[\[Xi]]

Example 2: In the example above I have already helped Mathematica, of course it would be nice if the task could also be solved when one is one step further away - i.e. if this equation had to be substituted:

-((2 s^2)/((-1 + s^2)^2 (1 + (4 s^2)/(-1 + s^2)^2)^(
   3/2))) + s/((-1 + s^2) (1 + (4 s^2)/(-1 + s^2)^2)^(3/2)) + 
 Sin[(2 s)/(-1 + s^2)] /. (2 s)/(-1 + s^2) -> \[Xi]

So you could summarize that I would like to have a) an automatism (or a workaround or a strategy) that collects the terms as desired (see Example 2) and b) also considers powers of the variable (see Example 1).

Thank you Arben for bringing this link to my attention (and of course for the quick and on-target reply...).

Thanks Arben, The german term Ersetzung attacted me as I read German. That's a useful function. John.

Plot has attribute HoldAll and tries to evaluate the function Normal[Series[...]] only after assigning specific numerical values to x. As you have shown in the resolution, in this case we need to force the symbolic evaluation of Series[Sin[x],{x,0,someInteger}] to obtain the power series expansion for Sin[x] before trying to substitute numeric values for x. This is why the following is unable to plot:

Plot[Normal[Series[Sin[x], {x, 0, 10}]], {x, -2 Pi, 2 Pi}]

But using Evaluate resolves the issue:

Plot[Evaluate[Normal[Series[Sin[x], {x, 0, 10}]]], {x, -2 Pi, 2 Pi}]

That was what I did, among other variations, but nothing worked in Chrome. I switched to a different browser and had no trouble. I'm guessing there is a way of telling Chrome it's OK to download DAT files, but I couldn't find it on a first pass through the settings.

Hi Ron, Selecting the two .dat files and clicking on Download from the "... Actions" menu should allow you to download a zip containing the two data files.

Hi Roger, The link to the quiz that was shared in the study group session today, will alsol be included in the next reminder email for the webinar.

Hi Michael, We're re-sending the link to you via email.

In slide 31 of the notebook for the second day, it looks like there is a small error in coding for the function FixMatrix. The code works fine for square matrices (as in the examples given), but not for general matrices, because the mapping over the column numbers is taken over the row numbers instead. It can be fixed by replacing

Range[Length[mat]] (*the list of row numbers*) 

by either

Range[Length[Transpose[mat]]] 

or

Range[Last[Dimensions[mat]]] (*the list of column numbers*)

Ron Goetz

Hi Fedor, The syntax coloring is giving us a hint that the "?" is not working on the local symbol x but on the global symbol (since x appears black, not green). So it is correctly informing us of the status of the global "x". Perhaps you could try replacing "?x" with Information[x] which would ensure the right "x" was being used for information.

We ran into some issues with a couple of examples during today's session. Here are possible resolutions to those issues:

• First 500 digits of Pi: ResourceFunction["NthDigit"][\[Pi], #] & /@ Range[500]
• Example of using lists in the same way (domain of input values) in two different Wolfram Language functions: Table[Sin[x],{x,1,10}] and Plot[Sin[x],{x,1,10}]

Here is the example of processing the DNA sequence from the BRCA 1 gene (with the nucleotides as chemical entities instead of just string characters):

Counts[Characters[Entity["Gene", {"BRCA1",  {"Species" -> "HomoSapiens"}}]["ReferenceSequence"]] /. 
     {"A" -> Entity["Chemical", "Adenine"], 
      "T" ->  Entity["Chemical", "Thymine"], 
      "G" ->  Entity["Chemical", "Guanine"], 
      "C" -> Entity["Chemical", "Cytosine"]}]

For all the new folks who attended Study Group today: Feel free to try Wolfram One (https://www.wolfram.com/wolfram-one/) to open up the notebook we shared with you.

Unfortunately it appears that the free basic plan does not allow file upload or the option to download and install the Wolfram Desktop. You would have to subscribe to a paid plan for those options.

You could download and install a trial version of Mathematica to open the shared notebooks https://www.wolfram.com/mathematica/trial/

The "Wolfram Language basics" study group begins today. See you there!