We will reach out to you with your certificate.

Hi Conrad,

If "4" is assigned to p, and then you look at the head of p: Head[p], it will still be a string. The quotes just aren't shown but it p still acts like a string.

p = "\"4\""

This will show the quotes and p will still behave like a string.

Is that what you needed?

Lori

Conrad, I suppose you could dig into Global Preferences, but I personally wouldn't bother if your code is behaving as expected.

What exactly are you trying to do?

Understood! :D

@Rohit Namjoshi Thanks for the references and I'll definitely take a look at the links.

Replace[{3.1,Pi,\[Pi],E,10,21},{x_/;Element[x,Reals]->Framed[x]},{1}]

Unfortunately this also selects the Integers 10 and 21 which is the wrong requirement!

Pi is not a Real, but a Symbol

Replace[{3.1, \[Pi], Pi, \[Pi], 10, 3.14159, E}, { 
  x_ /; (MemberQ[{Real, Symbol}, Head[x]]) -> Framed[x]}, {1}]

creates frames for all but the Integer

I'm really not understanding what upvalues, downvalues, ownvalues, etc. are. Not how they're used, but what they are. I can find the documentation about them in the documentation center, but I never saw that it defines what they are. Can anyone help?

Quiz 3.3 question:

I am stuck on only one output detail with this question and it appeared as a very straightforward piece of code that just doesn't work! Where am I going wrong, what am I missing?

In[84]:= 
Element[\[Pi], #] & /@ {Complexes, Algebraics, Reals, Rationals, 
  Integers, Primes}

Out[84]= {True, False, True, False, False, False}

So Pi belongs to the domain of Reals!

However any of the input variants for Pi cannot be framed as expected with this Replace code:

Try inputting Pi in different ways ...\ [Pi], [FpormaPi], esc pi esc, ...

In[82]:= Replace[{3.1, \[Pi], Pi, \[Pi], 3.14159, E}, {x_Real -> Framed[x]}, {1}]

Out[82]= {
\!\(\*FrameBox[\!\(3.1`\),
StripOnInput->False]\), \[Pi], \[Pi], \[Pi], 
\!\(\*FrameBox[\!\(3.14159`\),
StripOnInput->False]\), E}

How do I frame the Pi symbol?

Syd

@Aristarque Monneron yes, each solution to the programming exercises in quiz 3 gets automatically graded and submitted when you click "Check Solution". We see your submissions for quiz 1 and 2 but not for quiz 3. Could you please email wolfram-u@wolfram.com and follow up with your notebook?

Hi Mitchell

I think Abrita's comment is quite clear on where ToString is not needed

Firstly {"a3bykmn","oka2bcka","bdkba1","4ckxyz"} is already a list of Strings so you do not need ToString for the input.

and where it is needed

You would need to use ToString to convert the digit back to String once you have isolated it and decremented it by 1

The code you posted earlier is close

StringReplace[{"a3bykmn","oka2bcka","bdkba1","4ckxyz"},p:DigitCharacter :>ToExpression[p-1]]

Just need to fix the ToExpression[p-1]]. p is a String, it needs to be converted to an Integer so 1 can be subtracted from it, the result needs to be converted to a String so StringReplace can do the replacement.

Hi;

Based on the definition and hints given by the problem, I think that everything is included in my solution, however I am not getting the desired output - see below. I am sure that it is something that I am doing incorrectly, but based on my knowledge at this point in time, I do not have a clue.

StringReplace[ToString[{"a3bykmn","oka2bcka","bdkba1","4ckxyz"}],p_DigitCharacter :>ToExpression[p-1]]

Hi Rohit;

The problem stated as hints that ToString[] and ToExpression[] would be needed in the solution of StringReplace[]. Abrita told me in a previous reply that I really didn't need to use ToString since the data was already in string format, so I remove it from my expression.

I need to read the digit characters from the data strings, for example pull the 3 from the first string a3bykmn, then subtract 1 from the value, write it back out as a 2, and then grab the next digit character from the next string oka2bcka which is a 2 subtract 1 giving 1 and so on.

Even after attending every lecture, I don't know how to do that.

Thanks,

Mitch Sandlin

Hi Abrita; Referring to 3.3 we are instructed to use Replace[] along with a set of rules to process even, odd and non integers. My solution only wants to process the first element of the string - see below.

Clear[x,y,z]
Replace[#,{x_/;EvenQ[x]->x*2,y_/;OddQ[y]->y*3,z_/;!IntegerQ[z]->Framed[z]}]&  [94,87,[Pi],49,46,"42",28,47,68,57,4,44,100,4.2,{23,1},57]

For example, if you run the function, it will return 188 (294). If you replace the first element of 94 with 87 and run the function, it will return 261 (387). If you replace the first element of 94 with Pi and run the function, it will return Pi with a box around it. Therefore, the logic seems to be working correctly, I just can't get the evaluation to move through the list, and I think I have tried everything that I can find in the documentation as well as the lecture notes. Do you have any suggestions.

Thanks, Mitch Sandlin

Hi Conrad;

I followed the example that you sent me a link to for SparceArray and again produced exactly the same output as the problem displayed, but still was not accepted as the correct answer. I do not know that to do at this point. Any suggestions.

Mitch Sandlin

Hi Doug;

Following your advice, I deleted my data from my SparseArray[] and moved it into a field named dta1= {{1,5}-> 1, etc.}}. Then loaded the data into the functions:

MatrixPlot[SparseArray[dta1,{20,20}]]

The new configuration gave me the exact same data as expected, as I have gotten for the last 5 days, with no error messages. However again, the grader didn't like it, gave me an X and told me to try again.

Thanks,

Mitch Sandlin

Hi, I was able to refactor Quiz 3 Problem 3.1 into a solution that appears to have been accepted by the backend. Also, I was definitely in the weeds for this problem. Anyway, could someone confirm that I have submitted all 3 quizzes for the study group?

ReplaceAll[x will only match a literal x e.g.

ReplaceAll[x :> y][{a, x, x^2}]
(* {a, y, y^2} *)

For this quiz question use Replace with a level specification (which is what the quiz asks for). Rather than nested If, consider using Which.

Hi Rohit;

Thanks for the reply directing me to use Which[] as opposed to using a nested If[]. However, I still do not understand why the nested If[] failed. I actually believe the Which[] is a much cleaner solution but unfortunately it doesn't seem to work either - see below. I actually tried both formats using RelpaceAll[] and // with no success.

As an aside, I even tried using x--EvenQ[x], x*2, with no success.

ReplaceAll[x,x:>Which[EvenQ[x],x*2,OddQ[x],x*3,!IntegerQ[x],Framed[x]]]{94,87,\[Pi]}

{94,87,\[Pi]}//.x_:>Which[EvenQ[x],x*2,OddQ[x],x*3,!IntegerQ[x],Framed[x]]

You are welcome, Abrita. I will post it as a separate post as well.

@Dave Middleton this is fantastic, especially in helping new users to find their way around the Entity framework. Can I request you to submit your notebook to the Notebook Archive and also create an independent post on community? You can add the groups like "Wolfram Language" or "Education" as well as "Data Science" when you post.

You're welcome Lori.

Even though the exercise to create a short tutorial made me wiser, I will still refer to it whenever I need entities :)

I'm working on Quiz 3 Problem 3.3. I have created a function, transform, that fulfills cases 1 - 3 and returns the correct value depending on the input. Now, I'm trying to integrate the function, transform, as a rule to the Replace function. Is there something that I'm missing within the current implementation?

@Rohit Namjoshi I was able to refactor into a better solution. Thanks for your assistance.

Yes Quiz 3 has only 5 questions.

Hi Doug,

Names ["Developer`*"] // 
  Partition[#, UpTo@3] & // 
  Grid[#, Alignment -> Left, Frame -> All] &

Conrad

If you press Get Results After a few seconds you should see your score below the button

Sometimes no score is given (I think the server may be too busy , or my connection is too slow ) and I just repeat the procedure until I get a score

Hi;

Working on problem 3.4, I have tried a number of techniques with absolutely no success. I can't seem to get the number recognized as a number since the If statement doesn't want to subtract 1 and I seem to be fighting constant errors. In the code below, I am outputting the whole If statement which highlights the problem. Any suggestions as to what I may be doing incorrectly?

StringReplace[ToString[a3bykmn],p_ :> If[DigitCharacter[p],p-1,p]]


If[DigitCharacter[a],a-1,a]~~If[DigitCharacter[3],3-1,3]~~If[DigitCharacter[b],b-1,b]~~If[DigitCharacter[y],y-1,y]~~If[DigitCharacter[k],k-1,k]~~If[DigitCharacter[m],m-1,m]~~If[DigitCharacter[n],n-1,n] 

When I move the RuleDelayed to the end of the statement, all I get is an error.

StringReplace[ToString[a3bykmn],{p_ , If[DigitCharacter[p],p-1,p]} :>P]

Hi;

What am I doing wrong here on the 1st problem - see below? I have included everything the problem indicates, but I am getting a syntax error regarding the position of my rule.

MatrixPlot[ SparseArray[data,{n,n} /;n>0]]

Thanks,

Mitch Sandlin

Sorry if the question is not clear. Referring to the third template for creating a SparseArray on http://reference.wolfram.com/language/ref/SparseArray.html SparseArray[data,{d1,d2, ...}], we woul dlike you to create your own 'data' with a rule (of the form pattern -> value). The example showing the construction of a tridiagonal matrix using patterns for indices on the documentation page linked above, may be a good starting point to solve this problem.

Thanks @Mitchell Sandlin. Please make sure you have emailed the notebook to wolfram-u@wolfram.com for manual grading.

For problem 3.5 we are asking you to explore how you can go about setting up the function definition so that answers to smaller problems (like f2], f[3], etc.) get stored for future use when the answer to a bigger problem (say f[10]) is requested. This can be done by the process of [memoization. You can incorporate memoization in this problem by getting the Wolfram Language to create downvalues automatically when it is trying to compute f[5]. In addition to the downvalues like

factorial[n_Integer/;n>=1]

and

factorial[0]

five other downvalues should be created automatically when f[5] is evaluated.

Hope this helps.

Just a reminder that we start early tomorrow at 1:30 AM CT for a series review. If you were unable to put in your request for a review topic, feel free to reply to this post and add it here.

You are very welcome.

When you click the "Check My Solution" button for each problem in Quiz 3, your graded submission (Correct or Incorrect) automatically gets recorded at our end. We are able to pull your total score for the quiz from those submissions.

Yes it should.

@Fabio Alcaro , Yes please email the notebook to wolfram-u@wolfram.com

Thanks

You can do a lot even without Regular Expressions. You will have to use dedicated functions to work with string patterns like StringReplace, StringMatchQ, StringContainsQ etc. You will find them listed here and you can use this tutorial to get started.

I suppose you want to clear ONLY a specific upvalue otherwise Unset or Clear would have been fine. You can use TagUnset.

In[1]:= sq /: area[sq] = s^2;
sq /: circ[sq] = 4 s;

In[2]:= sq /: circ[sq] =.

In[3]:= {area[sq], circ[sq]}

Out[3]= {s^2, circ[sq]}

I found another user try to do something similar here: https://community.wolfram.com/groups/-/m/t/1072731

@Jin Zhang I reached out to our instructor Dave Withoff for further help on this. Below I have posted Dave's suggestion:

This particular rule for x can be cleared using Clear[x,x] or Clear["x"].

For example:

In[1]:= x /: _[x] = 0
Out[1]= 0
In[2]:= Clear[x]
Out[2]= 0
In[3]:= Clear["x"]
In[4]:= Sin[x]
Out[4]= Sin[x]

Clear[x,x] would also work because that upvalue for x only applies to expressions with one argument x, and so that rule doesn't apply to Clear[x,x].

Clear["x"] clears any symbols with names that match the string pattern "x".

The basic problem, as you presumably noticed, is that the upvalue for x gets applied to anything of the form _[x], including Clear[x], and since upvalues get applied before downvalues, and since Clear[x] works using a downvalue for Clear, this makes it difficult to clear the rule for x.

Clear["x"] works because, although the string "x" gets converted to the symbol x within the Clear function, that conversion doesn't happen until after the downvalue for Clear is already being applied, and the Clear function clears the rule for x in a way that does not involve evaluating Clear[x].

More generally, this is an example of one of a small handful of inputs in the Wolfram Language that can be difficult to undo. These things almost never come up in practical applications, but they do sometimes come up by accident, or sometimes they come up when just trying things out to see what will happen.

For example, I do not recommend evaluating:

$Pre = Function[x, Pause[600]; x, HoldAll]

which will introduce a ten minute pause before every evaluation. The pause can be aborted, but it is difficult to remove that pause without waiting ten minutes for a subsequent evaluation to remove it.

It is unlikely that such a thing would be entered by accident, of course, but if a predicament arises where something that is difficult to undo has happened, a general solution is to quit the Wolfram Language session and start over.

In today's study group's "Exercises for Image Processing", Exercise 1. the code provided does not work on my Windows 10 21H2 machine with Mathematica version 13.0.1.0 i.e. the 2D slider t2 doesn't do anything.

img = Binarize[
   Graphics[{Disk[{0, 0}, 8], White, Disk[{0, 0}], Disk[{2, 2}]}, 
    ImageSize -> 200]];
Manipulate[
 ImageResize[ImageTrim[img, {t1, t2}], 
  400], {t1, {1, 1}, {177, 177}, {1, 1}, 
  Appearance -> "Labeled"}, {{t2, {400, 400}}, {271, 271}, {400, 
   400}, {1, 1}, Appearance -> "Labeled"}, ControlPlacement -> Left]

Is this an issue on my end or is this a bug? If the latter, is there a work-around?

Cheers,

Dave

Thanks Doug. The "Dynamic Updating Enabled" is on, or else the t1 2D slider wouldn't work either. Maybe my installation is corrupted somehow.

After spending some time problem solving, it's not an issue with the t2 slider after all. If I do:

img = Binarize[
   Graphics[{Disk[{0, 0}, 8], White, Disk[{0, 0}], Disk[{2, 2}]}, 
    ImageSize -> 200]];
ImageTrim[img, {{177, 177}, {271, 271}}]

The result is a white image of 24 x 24 pixels, not the picture in the Exercise solution. For some reason the code does not work with this image on my system, which I am not going to explore further.

If I replace the image by Dave's balloon image in the Lesson 27 notebook, all works fine.

At least, as an additional exercise I spent some time with sliders, Manipulate and even DynamicModule :)

Quiz 2, Problem 4, answer option A says "Displays a dialog box with the message 'Click OK', where evaluations can still be done without dismissing the dialog box", i.e. you can continue to evaluate further code in the notebook, without dismissing the dialog box.

Thanks Abrita

Inner[ Times, x, y,  BitXor ]

is the solution

I am not entirely clear about this behavior of Interval[ ]:

Thank you very much, Abrita and Dave!

I would never have thought of that...

I must confess that I am totally confused about the concept of precision in Mathematica / Wolfram Language. Let me share this confusion with you:

Thank you Lara for cheering me up. But I'm still ready to let gravity take its course ... :)

@Zbigniew Kabala, Here is Dave's response to your questions:

The problem of squaring an interval was left kind of open. Here is an explanation.

Thanks for your response to the Print issue I posted. The CellPrint code you provided works well. Based on that, I went back to the Print Help. My take on that is that Print generates something like CellPrint, though my attempt to use FullForm[HoldForm[Print[...]]] did not work. How does one find what the underlying Wolfram Language code of Print is or is Print just a function unto itself? That is, how do I find out whether Print is using CellPrint?

Since Print has no options, I tried Grid with Frame -> True, which shows that the width is set to that of the wider of the two lines of text. This suggests that at least part of the Print problem may have to do with cell width being set this way. To fix this, I added to Grid the option ItemSize. Here is the code, which works fine:

Grid[{{Style["Options for Plot and ListPlot", Bold, 16, 
Orange]}, {Style["Options in Common", Italic, 14, Blue]}}, 
Alignment -> Center, Frame -> True, ItemSize -> 50]

Attached file "GDorfman_GridToCenterText.nb" has the above code with and without ItemSize along with the corresponding output.

Attachments:

GDorfman_GridToC...nb

Doug,

To remove all docked cells

SetOptions[EvaluationNotebook[], DockedCells -> {}]

Try evaluating x by itself and I think you'll see where the Irishman comes from :). Run ClearAll[x] after that and NRoots will do its job as expected.

Try Ball instead of Sphere—despite colloquial usage, a sphere is a 2D object that embeds into 3D space.

I'm glad to hear it! I might be biased, but I do think it's pretty cool that you're able to achieve such a result. Also—while this may be a bit trivializing in some sense, we really do have a function for everything! Try out RegionMeasure, if you'd like, e.g.: Manipulate[ RegionMeasure /@ {Disk[{0, 0}, d], Sphere[{0, 0, 0}, d], Ball[{0, 0, 0}, d], Cuboid[{0, 0, 0}, d {1, 1, 1}]}, {d, 1, 5, 1}] This can be useful to provide some insight which is relevant to the dimensionality question we're discussing (somewhat paradoxically). On a related note, you might try something like Volume[Sphere[]] and get a (previously-)surprising result.

Or, you could make the variation continuous, then Plot to see the problem another way: Plot[Evaluate[ RegionMeasure /@ {Disk[{0, 0}, d], Sphere[{0, 0, 0}, d], Ball[{0, 0, 0}, d], Cuboid[{0, 0, 0}, d {1, 1, 1}]}], {d, 1, 5}, ScalingFunctions -> {"Log", "Log"}] (adding PlotLegends->"Expressions" would make it explicit, to wit.)

EDIT: I'd be loathe to forget RegionDimension!

Additional notes on this comment from above.

"If it sees n g[x] as a pattern, maybe it will see {point1,point2,n} * h[Ball[]] as an upvalue for h, and then construct n Balls from point1 to point2, but only if the symbol h is used."

I want to create a simple "extension" using tagged delayed assignments (up values) to allow n points to be enumerated over a line from point1 to point2. We try this naively and find that the implicit multiply operation is listable, so we get a list of the multiplied values.

In[150]:= ClearAll[g]
g /: n_List g[x_] := g2[g1[n], x]
{point1, point2, n} g[x]

Out[152]= {point1 g[x], point2 g[x], n g[x]}

This is not what we want. Instead of using the Times[] function, we will use h, which is not listable, in the above instead.

In[144]:= ClearAll[g]
g /: h[n_List, g[x_]] := g2[g1[n], x]
h[{point1, point2, n}, g[x]]

Out[146]= g2[g1[{point1, point2, n}], x]

g1 can be a function to generate the n points and then it is passed to g2 which does the volume rendering of x. Maybe there is an existing function for this, but this is a fun exercise anyway.

Basically, we are recognizing a certain context involving an outer scope of the function g, and then doing something special to it when we recognize it. This is an amazing ability! WOW!

I learned a lot in writing this stuff up. Tagged delayed assignments are really cool, and I had fun playing with the concepts which I had just recently learned.

I have added more cool examples on neat regions that can be generated using the GenerateLinearRegion UsingA methodology of a previous post. An exotic region is depicted below.

I also have added some things that alternatively work within the context of the + operator.

DrawLineOf[Ball] + From[{0, 0, 0}] + To[{5, 0, 0}]

This generates the same image as above. Because + is orderless, the items can appear in any order.

In fact we don't need the + above, and if we leave it blank it will use Times instread of Plus.

From[{0, 0, 0}] DrawLineOf[Ball] To[{5, 0, 0}]

This creates the same line of balls as above.

There is more discussion in the notebook.

Sorry for all the verbosity, but I am finding it hard not to work on this. In addition to finding the volume measure of these regions, it is even more amazing that in WL these regions can be integrated over (perhaps with a wave function as the integrand) or used as region constraint areas for numerical optimization problems.

Attachments:

volumesTaggedDel...nb

volumesTaggedDel...pdf

Expanding on your comments, Arben, we see indeed that integrating using Sphere vs. Ball clearly gives different answers.

In[6]:= Integrate[1, {x, y, z} \[Element] Sphere[]]

Out[6]= 4 \[Pi]

In[7]:= Integrate[1, {x, y, z} \[Element] Ball[]]

Out[7]= (4 \[Pi])/3

Using RegionMeasure allows the dimension of the integration to be specified.

In[8]:= RegionMeasure[Sphere[]]

Out[8]= 4 \[Pi]

Agreeing with your comment, Arben, Sphere[] is 2-dimsional, and its 3-D measure gives zero. WOW - that's a gocha.

In[10]:= RegionMeasure[Sphere[], 3]

Out[10]= 0

Note the correct answers using Ball[] below.

In[9]:= RegionMeasure[Ball[]]

Out[9]= (4 \[Pi])/3

In[11]:= RegionMeasure[Ball[], 3]

Out[11]= (4 \[Pi])/3

As a final note, we see and understand the next result.

In[12]:= RegionMeasure[Ball[], 4]

Out[12]= 0

Looking for a possible application for upvalues, I made the following definition:

f[x_ /; x < 1] := 1;

f[x_ /; x >= 1] := x x x;

Sqrt[f[x_] /; x >= -2 && x <= -1 ] ^:= 3;

If I now want to test the effectiveness of my definition by calculating a square root of f[-1.5], it does not seem to work at first glance:

Sqrt[ f[-1.5]] returns 1, and not the expected 3.

The same applies to a function plot:

Plot[Sqrt[ f[x]], {x, -5, 5} ]

On closer analysis, it turns out that the calculation first calculates the inner term, and the kernel then forgets that the inner value arose by evaluating f[x], and accordingly does not apply the upvalue.

If I forbid the evaluation of the inner term, we get the expected results:

Sqrt[ Unevaluated[ f[-1.5]]]

Plot[Sqrt[ Unevaluated[f[x]]], {x, -5, 5} ]

This shows me that upvalues do not allow the overloading of functions similar to OOP that I had hoped for. Always thinking about disallowing the evaluation of the inner term limits the usability in my eyes.

However, this begs the question. What is a real life use case for the upvalues?

The first two Print statements below center the text. The third Print statement, which just combines the first two, does not center the text. Attached file "GDorfman_PrintIssue.nb" shows the three Print statements and their output. Why does the third Print statement not center the text? How can it be modified so it does center the text?

Print[Style["Options for Plot and ListPlot",Bold,16,Orange,TextAlignment->Center]]

Print[Style["\nOptions in Common\n",Italic,14,Blue,TextAlignment->Center]]

Print[Style["Options for Plot and ListPlot",Bold,16,Orange,TextAlignment->Center],
Style["\nOptions in Common\n",Italic,14,Blue,TextAlignment->Center]]

Attachments:

GDorfman_PrintIssue.nb

[WSG22] Daily Study Group: A Guide to Programming and Mathematics with WL

The notebook for Friday's lesson (#19) appears to be missing. When will it be made available?

Is there a way to prevent Mathematica from inserting spaces into a URL I put in a notebook?

If I copy a URL into Mathematica, then copy it from there, it comes out like this:

https : // www . wolframalpha . com/input?i = Table %5 BExpand %5 B %28 Power %5 BGoldenRatio %2 Cn %5 D + -+Power \ %5 B %281 + -+GoldenRatio %29 %2 Cn %5 D %29 %2 FSqrt %5 B5 %5 D %5 D \ %2 C + %7 Bn %2 C + 0 %2 C + 18 %7 D %5 D

As @Lori Johnson mentions, if you paste a URL into a text cell it will be pasted correctly and even change into a hyperlink. You can create a text cell in a notebook as shown here: https://reference.wolfram.com/language/workflow/CreateATextCell.html

Thank you @Olga Pavlova

We are in the process of getting the quizzes ready for release. We hope to share a link to the first quiz by the end of the week. We will share it in the live session and also include it in reminder emails.

Q&A transcript from Day 5 of Week 1 has been added to the download folder. We'll add the digest from this week at the end of the week.

Something like this?

Plot[Evaluate[Abs[x /. sol]], {b, -5, 5},
 PlotRange -> All,
 PlotStyle -> ColorData[3, "ColorList"],
 PlotLegends -> "Expressions"]

Week 1 Review notebook added to download folder.

Thanks Richard.

It appears that f[x_] := f[x] =. .. is more efficient. Is there ever a case in which it should not be used?

Thanks for the response and explanation, @Richard Hewens

SetDelayed OR Set should serve well in defining a function.

Here is an example of where using Set and SetDelayed together is helpful and might explain why it would be not advisable to try and use them together ALL the time.

In the following example, when the need arises to store some constant values, immediate assignments are made. On the other hand, to store a more generic definition of the function, delayed assignment is used:

fib[0] = 0;
fib[1] = 1;
fib[n_] := fib[n] = fib[n - 1] + fib[n - 2]

The use of both Set and SetDelayed allows assignments to be made dynamically:

?fib

The Wolfram Language provides automatic recursion, coded into the delayed assignment definition of fib[n_]. Each time a new n is used, a new value for the function fib is defined and stored away. This avoids having to return all the way to the base case for every value that is used:

fib[3]

?fib

Trace[fib[4]]

Clear[fib]

When using the "f[x_] := f[x]=...", this is creating a more specific function with the same name (which will be called before the original f[x_] form). This is most useful when the function will be called multiple times with the same argument, is which case the computation will only need to be done once.

Hi Richard—I'm looking into this. For the time, I can note that it's not a property of Defer, since Hold and Unevaluated (at least) do the same thing. The current thought is that it's a formatting property of Times, and formatting is a bit of an arbitrary choice that language designers have to make. I do agree that it's strange that the additive identity does not format the same way for Plus, though.

Based on my previous experience ( about 6 classes taken at different times), I would recommend the following.
(1) Create a notebook, say "Class3_my practice and questions". Let's call it MNB (my notebook).
(2) Open the downloaded class notebook(s), typically one or two (CNBs).
(3) The goal is to reproduce in MNB the most of activities presented in CNBs. Also, consider some variations of the offered examples, mark the difficulties and formulate the questions.
(4) In doing so, make sure to create sections in MNB ( using Alt-1 - Alt-6 shortcuts, with textual inserts using Alt-7) reflecting the corresponding sections in CNBs (so that the general structure of MNB is similar to CNB, but it may include some additional sub(-sub)sections such as "My question to the forum", or "some additional examples", or "the definition of such and such function...").
(5) Watch the pieces of the class video addressing the questionable parts (in case you do not have time to watch the whole video).
(6) As a result, you should have a few unanswered questions. Never hesitate to post them on the forum. This is good for all the participants! So, consider it a public service :)
(7) In parallel, create the notebooks Quiz1, 2, etc for solving the quiz problems. Each lecture contains (hints to) the answers to some Quiz questions. Doing it continually makes the Quiz activities less stressful (make sure not to discuss directly the Quiz questions on the forum, but you can discuss any related general issues ).

Good luck.

This is really helpful - thank you!

Thank you. :-) Class is going a bit rapidly. Consequently, I like to work the notebooks and exercises after class in the evening to reinforce my learnings. I am very much enjoying the classes, but there are so many new ideas and insights every day that it takes some time and practice to internalize the use and application of all the tools we have been exposed to. What is the best way to get more practice?

Responding to multiple-choice Qs does not contribute to certification. It's for self-testing. Watching the lectures and passing the quizzes do.

I need to regroup for a trip that starts Monday. For that time I will switch to a cloud account and need to arrange file directories. (1) How to (up)load their files for the class? (2) How to order them based on the sessions' order number? . The ordering turned out to be especially ticky. Thank you