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[WSG23] Daily Study Group: Introduction to Finite Mathematics

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A Wolfram U Daily Study Group previewing the upcoming Introduction to Finite Mathematics course begins on Monday November 6, 2023.

Join me and your fellow learners for an introduction to various topics with important real-world application to economics, business, sociology, psychology, and other sciences. A curriculum concept to emerge from Dartmouth as an alternative to calculus-based courses of study, finite mathematics has become a common course offering at universities around the world.

After reviewing a few concepts from algebra, apply them to the study of linear optimization, matrices, annuities, probability, Markov chains, and two-player games.

The Introduction to Finite Mathematics course will soon be added to the Wolfram U catalog, so get a sneak peak of the lessons as part of this live study group. Participate in live Q&A, check your understanding with in-session polls, and more.

This Study Group runs weekdays Nov 6-17, with the exception of Nov 10.

REGISTER HERE

Please use this thread to collaborate and share ideas, materials and links to other resources with fellow learners.

Creating the full course has been a lot of fun, so I hope to see you all in the live study group! enter image description here

POSTED BY: John McNally
37 Replies

Hi all, you should start to see Exercises available in roughly half of the lessons for additional practice. The rest of the lessons will have exercises visible not too long after this post goes up. The exercises are ungraded, but provide you extra practice to build your confidence as you learn the material. Do let us know here if you have questions about newly visible exercises or anything else.

POSTED BY: John McNally
Posted 6 months ago

THANK YOU!

Noted already, actually :)

I will look forward to more exercises~

POSTED BY: Soomi Cheong

Hello John,

You did a good job teaching this class. Previously, I thought game theory would be boring, but I found the patterns intriguing. In particular, I enjoyed seeing graphs employed in Markov chains and would like to delve deeper into that. Thank you for sparking my interest! And thank you for the reasonable length of the final. REALLY, THANKS!

Also, your use of pauses in your videos made them extremely easy to listen to.

Take care, Lori

POSTED BY: Lori Johnson
Posted 6 months ago

The system is back up and working - Thanks!!!

POSTED BY: Randy Janke
Posted 6 months ago

John, I think that the system has been down... No progress checked. No Quiz Graded.. (lol)

Quiz and Final Exam are due on 12/1 (Fri), correct?

POSTED BY: Soomi Cheong

The issue has been noted and will be fixed soon.

POSTED BY: Anisha Basil
Posted 6 months ago

I was wondering if there might be a problem with Quiz 7 and maybe on Quiz 8. I completed Quiz 7 and clicked the "Get Results" and have no feedback. The system seems to hang. I restarted my Mac and even tried a different browser with no success. Any feedback is appreciated. Thanks, Randy

POSTED BY: Randy Janke

The issue has been noted and will be fixed soon.

POSTED BY: Anisha Basil
Posted 6 months ago

If I hit the exercises tab in any lesson in the beta framework, I am getting a 404 error. I cannot access any of the exercises. The lectures, quizzes, and ever-ubiquitous scratch notebook are working fine. Did I miss something? Do I somehow have a bum link to the framework? I am surprised to see nobody else mentioning this. I can make progress without looking at exercises, but it's rather strange.

I mentioned this in an e-mail to Wolfram-U a couple of days ago, but didn't get a response. Maybe they're shut down for the week.

POSTED BY: Phil Earnhardt

That's correct, the exercises are not yet up in the framework so that behavior is expected (for now).

POSTED BY: John McNally

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.

POSTED BY: John McNally
Posted 6 months ago

I'm having trouble crunching the Leontief Input-Output Model math; I finally figured what I think (hope) is a good question. Pretty clearly, there is a value in the LEOM matrix whose sum (??) must be less than or equal to one. What exactly is that "sanity" calculation?

Is the dot product and product of w matrixes the same thing?

TY.

--phil

POSTED BY: Phil Earnhardt

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.
POSTED BY: John McNally
Posted 6 months ago

I'm having inordinate difficulty reliably creating a matrix in the WL. I don't understand why the first statement creates a 3x3 matrix and the second does not:

POSTED BY: Phil Earnhardt

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} *)
POSTED BY: Daniel Lichtblau

As Dan was saying, generally you don't want to define things as their MatrixForm expressions. Define them purely in terms of lists of lists (or some equivalent way to do this programmatically). Then, if you want to see them as a matrix, use MatrixForm on the defined thing.

As a rule of thumb, if you use "=" and MatrixForm in the same line, it is highly likely to have intended (although counterintuitive) behavior. In other words define things one place, use MatrixForm to look at them someplace else.

POSTED BY: John McNally
Posted 6 months ago

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

POSTED BY: Phil Earnhardt

I am registered for the series but could not attend. Where can I find the associated notebooks to download? Thank you.

POSTED BY: George Wolfe
Posted 6 months ago

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.

POSTED BY: Phil Earnhardt
Posted 6 months ago

The main lecturer is pedagogically quite gifted as a presenter! Perhaps the best I have experienced -- certainly in mathematics.

POSTED BY: Renay Oshop

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.

POSTED BY: John McNally
Posted 7 months ago

I missed the first class. Then, I can't receive the course completion certificate? I will follow up the first class with the recording definitely. Still waiting for it..

As I thought, the audio was uploaded to the study group page. However, I did not receive it via e-mail. Is it because I missed the first class? Does this mean that I am not eligible for the course completion certificate no matter what? I never miss a class. Today was the first day I miss a class that I sign up for.

POSTED BY: Soomi Cheong

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.

POSTED BY: John McNally
Posted 7 months ago

what about the attendance certificate?

1) If we watch all the videos and pass quizzes of the framework (the study group will have its framework, right?), we will receive the attendance certificate?

2) If we pass the final exam, we will receive the level 1 certificate? These were my questions that I still have (lol).

  • I made a big mistake to miss the class. It was the first time for me to miss a class that I signed up for. I never miss a class under any circumstance unless I am hospitalized. Also, thanks to Wolfram, I have been able to study what I love - Wolfram Language, Mathematica, and Math.. what Wolfram teaches to the public is very fun. It's also mandatory for me to be qualified for Master's programs that I will apply for. Thus, it's a huge deal for me. I do hope that I can learn about the answers for my two questions above..

Thank you for your consideration.

POSTED BY: Soomi Cheong
Posted 7 months ago

@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.

POSTED BY: Phil Earnhardt
Posted 7 months ago

Hi John,

I have a conflicting work commitment today. What is the policy regarding a missed class or online discussion? (Obviously, I'm new to this.)

Roger

POSTED BY: Roger Rogers
Posted 7 months ago

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

POSTED BY: Phil Earnhardt
Posted 7 months ago

Thank you Phil

POSTED BY: Roger Rogers

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.

POSTED BY: John McNally
Posted 7 months ago

One request for John: I was recently listening to a discussion about the HeartMath "global consciousness project". My understanding is that this org has deployed a large number of computers worldwide that are performing nonstop coin-flipping. The project is noting long-running trends varying from a 50/50 distribution in the coin flips and is associating "global consciousness" events to those variations. I'm naturally skeptical, but I don't understand the mathematics of random coin-flippers to competently appreciate (or dismiss) this project. If this course could address means of understanding/analyzing the output of these flippers -- or perhaps provide pointers to lucid writeups -- I'd be grateful. Thank you.

POSTED BY: Phil Earnhardt

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

POSTED BY: Daniel Lichtblau
Posted 7 months ago

Thanks, Daniel. I can't accept a casual/pseudoskeptical dismissal of the Heartmath work. The details of Heartmath's random coin-flippers are well-documented; they are extremely sophisticated devices. If you examine those details and see some obvious reason they are inappropriate for the job, I (and others) would appreciate learning those details. But casually dismissing their devices with no specifics isn't advancing anyone's understanding.

POSTED BY: Phil Earnhardt

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.

POSTED BY: Daniel Lichtblau

Thanks for your course, when will this https://www.wolfram.com/wolfram-u/courses/mathematics/introduction-to-discrete-mathematics/ course begin ? Very interested to sign up

Have a great day or night

POSTED BY: Roberto Catanuto

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

POSTED BY: John McNally
Posted 7 months ago

John, the last 2 Daily Study Groups offered this fall (Discrete Math and Multivariable Calculus) commenced with an unreleased course framework. With Discrete Math, the framework Beta was released on Day 8 of the course; with MVC, I believe it was released in the third (final) week. I'm awfully fond of your work and presentation, but I'd strongly prefer to do courses where the framework was ready to rock on Day 0 of the course.

Will the Finite Mathematics course framework be ready to go on November 6? TIA.

@Wolfram U: if a DSG is commencing before its course framework is ready, could you please include a disclaimer noting that in the course announcements?

POSTED BY: Phil Earnhardt

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

POSTED BY: Marc Vicuna
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