The exercises for some lessons should now be visible in the course framework, stay tuned for updates on the rest that will also be appearing shortly.

Let me answer these two questions separately.

1. In the Leontief Input-Output models, there are two things that must be the case for it to actually be possible to meet consumer demand. First, the matrix I-A (where A is the input-output matrix) must be invertible. Second, it is possible for such a matrix to be invertible but the product Inverse[I-A].d to give negative values for some entries of X (the total output). Mathematically, this is perfectly sensible, but in terms of a physical model of an economy, we need the total output in each sector to be positive.
2. In Wolfram Language, Dot[A,B] (or just A.B) computes the tensor you get by contracting the last index of A with the first index of B. So Dot is actually more general than matrix multiplication. However, if A and B happen to be matrices, then yes. A.B is the usual matrix product of A and B.

It's a long-standing gotcha which amounts to MatrixForm being (arguably) badly designed. If one uses e.g. InputForm or FullForm then the formatting is applied and the wrapper disappears. The MatrixForm wrapper alas does not disappear. So instead of a rectangular list of lists, the structure is MatrixForm[list-of-lists].

Maybe this rewriting of your example will help to clarify. (For display purposes I converted the Out[1] cell to InputForm so it would avoid showing a mess of linear syntax.)

In[1]:= e1 = MatrixForm[{{0.2, 0.1, 0.1}, {0.1, 0.2, 0.2}, {0.1, 0.1, 0.3}}]

(* Out[1]//MatrixForm= MatrixForm[{{0.2, 0.1, 0.1}, {0.1, 0.2, 0.2}, {0.1, 0.1, 0.3}}] *)

In[2]:= MatrixQ[e1]

(* Out[2]= False *)

In[4]:= {Head[e1], MatrixQ[e1[[1]]]}

(* Out[4]= {MatrixForm, True} *)

Thank you both. My only self criticism was failing to look in the Wolfram system documentation first, which clearly noted the issue.

George, to get the links, the simplest thing is to send an e-mail to wolfram-u@wolfram.com. The URL of the beta framework was included in reminder e-mails for the class sessions for the later sessions (8-10). It wasn't released until then. I don't think students are supposed to share the links here.

You should have links to the lecture archives in the "Recording available" annoncements you got from Wolfram U daily.

I appreciate it Renay! I'll chalk this up to input from my instructors in the UIUC college of education and to my colleagues at various schools. Hooray for teachers.

Hi, I'm not sure why you may not have gotten an email about the recording being up; however, there is no requirement to attend the live sessions. Live sessions are obviously nice, but life happens and you can definitely catch up on the recorded versions.

@Soomi Cheong, I'm also in the class. The recording notification for Session 1 (audio + video) was sent out at 6:05PM Eastern Standard Time (US) today -- about 1 hour ago. The Wolfram-U team has to do some processing to turn around the archive. Sometimes, it's published within an hour; sometimes, it takes several hours.

If you didn't receive the notification, you should send an e-mail to wolfram-u@wolfram.com and they will be able to help you.

Roger, I'm a fellow student, but I've gone through several Wolfram-U Daily Study Groups. There's no problem missing a session. A few hours after each session, the Wolfram-U team will e-mail everybody in the course a message containing a link to an archive video of today's session. You can play back (and pause and replay sections) at your leisure.

If you ever have customer service questions, an e-mail to wolfram-u@wolfram.com will get you a personal response.

--phil

Yes, thanks Phil for answering this! And like Phil said, don't worry about missing a day. The text materials and the video links can both be accessed outside of the "live" time. The live time is obviously nice for being able to ask questions immediately and easily, but the design of all the courses is such that people can learn asynchronously too.

Phil, when random cyber coin flips start to correlate with world events, it’s a good time to change the random number generator.

My response skeptical, not pseudoskeptical.

Nor is it casual. I’ve worked with RNG’s and with RNG test suites. The idea behind most (or perhaps all) such tests is to probe for statistically significant correlations. This is especially the case for testing of iid uniform random bit streams. Ergo if their RNG’s are showing such correlations then they are not doing a good job generating random bits.

I looked at the site by the way. I was not able to find details about their bit generators, other than that they are apparently considerably scaled up in volume this past year.

Hi Roberto, the study group for Discrete Mathematics (which is different from Finite Mathematics) began on Oct 16, and the full versions of courses will go live not too far after their study groups conclude

Hi Roberto,

This is Marc, the instructor of the course for Discrete Math. The study group just finished today, the course framework will be available in a few days.

Happy learning! Marc