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[WSG23] Daily Study Group: Introduction to Discrete Mathematics

POSTED BY: Marc Vicuna
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Tianyi Hu
Tianyi Hu
Posted 1 year ago

May I ask how to understand this result in Lesson 11 Binomial Identity? enter image description here
POSTED BY: Tianyi Hu

Hi Tianyi,

Honestly don't try to understand it, it seems to be a mistake. It took me a while to understand what was going on. I'm a mathematician in discrete mathematics, so I have limited knowledge of complex analysis. When I wrote that lesson, I was told this is the complex variant of the Vandermonde identity, related to the Chu-Vandermonde identity. After some digging, it seems this summation is wrong. I'll inform the Summation team to fix this.

Best, Marc Vicuna
POSTED BY: Marc Vicuna
Tianyi Hu
Tianyi Hu
Posted 1 year ago

In lesson 7, it says "Intersection is a higher priority operation than union."

Anyone can please explain why?
POSTED BY: Tianyi Hu
POSTED BY: Phil Earnhardt
POSTED BY: Marc Vicuna
POSTED BY: Roberto Catanuto
POSTED BY: Jamie Peterson
Soomi Cheong
Soomi Cheong
Posted 1 year ago

Question:

1) I watched all videos for the framework.

2) Then, I passed all the quizzes.

=> I could access my Course Completion Certificate.

3) I was not able to pass the final exam by 11:59 pm on November 10th, 2023 on Chicago time.

4) Even now I still work on the final exam. HOWEVER, sometime after 10 pm on November 10th, 2023 on Chicago time, "Grade My Exam" button was not enabled no matter what.

=>

HOWEVER,

on November 3rd, I received an e-mail from Wolfram U Team that included the below.

Daily Study Group: Introduction to Discrete Mathematics

Monday, October 16, 2023 · 11:00 a.m. · Central Time (US & Canada)

"The deadline to pass the six quizzes for your course completion certificate is Friday, November 10. "

=>

(Question to doublecheck my understanding):

The six quizzes were due on 11:59 pm, November 10th.

-> Only if we pass the six quizzes by then, we are eligible for the Coure Completion Certificate.

"You can take the exam anytime you feel ready; your Level 1 proficiency certification will be generated automatically from the course framework."

=>

(Very important Question (for me)):

No deadline for the final exam.

-> Thus, we should be able to take the final exam and make it graded even after the November 10th deadline of the six Quizzes.

Therefore,

anytime we pass the final exam, we will receive the Level 1 Certificate.

  • If misunderstood, would you enlighten me on it?

(Question)

How can we know about the answers to the final exam? I have asked the same question during gthe daily study group period. However, there is still no answer. Unless we receive 100%, we will never know about the correct answers.
POSTED BY: Soomi Cheong

A reminder to the Discrete Math Study Group participants that the deadline to pass the six quizzes for your course completion certificate is Friday, November 10. The exam can be taken anytime from the course framework. Refer to your Study Group emails for a link to the pre-release framework and to recording links from Study Group sessions. We heard a lot of positive feedback from Friday's review session. You might want to watch that recording, in particular.
POSTED BY: Jamie Peterson
POSTED BY: Marc Vicuna

Hi Marc,

I have a problem reproducing the hypergraph in Lesson 24 notebook, section "Final States". If I run

ResourceFunction[
  "WolframModel"][{{x, y}, {y, z}} -> {{x, y}, {z, y}, {y, w}, {w, 
    x}}, {{0, 0}, {0, 0}}, 11, "FinalStatePlot"]

The result is this hypergraph

enter image description here

Where I used the same rule as the example in the section before:

rule = {{x, y}, {y, z}} -> {{x, y}, {z, y}, {y, w}, {w, x}};

I suspect another rule was used when the notebook was created; probably similar to the one in the example of the ResourceFunction["WolframModel"] documentation: https://resources.wolframcloud.com/FunctionRepository/resources/WolframModel/

ResourceFunction[
  "WolframModel"][{{x, y}, {x, z}} -> {{x, z}, {x, w}, {y, w}, {z, 
    w}}, {{0, 0}, {0, 0}}, 11, "FinalStatePlot"]

Which gives the plot shown in the lesson notebook:

enter image description here
POSTED BY: Dave Middleton

Hello Dave,

The explanation actually even simpler! You're using the rule from slide 10, but the rule is actually found on slide 9. In other words, you could evaluate slide 10, then 9, then 11, and it would work. The rule is rule = {{x, y}, {x, z}} -> {{x, z}, {x, w}, {y, w}, {z, w}}; (slide 9)

and not rule = {{x, y}, {y, z}} -> {{x, y}, {z, y}, {y, w}, {w, x}}; (slide 10)

But this is fair, this order doesn't make much sense. I guess I'll just change the variable name of slide 10 to "rule2" or such. This will be corrected.

Thank you for noticing, Marc
POSTED BY: Marc Vicuna

Hello Study Group,

To confirm, the last question of lesson 22 lead to some confusion with reason, as the definition given for the vertex degree was wrong, or more precisely, only appliable to simple graphs. Therefore, the definition will soon be changed to "The number of incident edges to v is its degree.", since it's the number of edges that is important. This will be corrected.

Thank you for noticing and sorry for the confusion,

Marc
POSTED BY: Marc Vicuna

I'm a bit confused by what LinearRecurrence[] is doing. The one slide in Lesson 19 was a bit fast; I experimented with it a bit this morning and read the help file, and it now mostly makes sense.

One thing that still doesn't make sense is what LinearRecurrence does with the list of initial values. If I do

LinearRecurrence[{2}, {5, 4, Q, 2, 1, 6}, 10]

the response is

{5, 4, Q, 2, 1, 6, 12, 24, 48, 96}

I see in the documentation that only the last Length[ker] elements are used in the calculation -- the other elements are simply copied to the output. What is the physical (i.e., mathematical) significance of doing that copying operation on that subset of the input list? In other words, is there an example where someone would actually have a list of initial values that didn't matter? I have a hard time wrapping my brain around a list of inputs that are simply ignored.
POSTED BY: Phil Earnhardt
POSTED BY: Marc Vicuna
Tianyi Hu
Tianyi Hu
Posted 1 year ago
POSTED BY: Tianyi Hu

Hi Tianyi,

This rule has many different proofs, which may depend on the equivalences you have access to in this context. I would generally use a proof by contradiction for both sides, as seen in this proof, where the perpendicular lines represent a contradiction: enter image description here

This proof and other proofs are available here.

Best, Marc
POSTED BY: Marc Vicuna

Download files link in chat results in 404 error today. Old link previously saved works fine.
POSTED BY: Ray Chandler

I'm not seeing that, Ray. Today's (Monday, 10/23) link worked just fine for me. enter image description here
POSTED BY: Phil Earnhardt

Cassidy reported the link has been fixed.
POSTED BY: Ray Chandler
POSTED BY: Phil Earnhardt
POSTED BY: Marc Vicuna

Ray are you using Windows? Maybe the issue with the Lesson 1 notebook is happening because the filename has a question mark at the end. Most archivers have a problem with it as Windows does not allow filenames with a question mark.

7-Zip can handle files with invalid Windows filename characters and replace them with a "_" instead.

I assume Wolfram Research uses Macs where questions marks can be used in filenames.
POSTED BY: Dave Middleton

Dave, yes using Windows. When I open the zipfile using OS, the first file appears as ".nb" and presents Lesson 16 when I open it.
The new zip file today now has the Lesson 1 file but still contains the ".nb" file which is a second copy of Lesson 16.

POSTED BY: Ray Chandler

Hello Ray,

Yes I see that file also, I'll remove it. It will be corrected.

Thank you, Marc
POSTED BY: Marc Vicuna

Thanks.
POSTED BY: Ray Chandler

To answer a Q/A that appeared at the end of class today,

You can change the printing of any notebook using File->Print Settings->Print Setup or File->Print Settings->Print Setup->Printing Environment.

Personally, for my slides, I usually use a landscape print setup and an Elegant Printout printing environment, and then select the slide I want to print since there will be empty pages.

Feel free to experiment with the settings, and checking your result with File->Print Preview

Best, Marc
POSTED BY: Marc Vicuna

I'm curious why the community page for this study group has WSG23 in the name rather than WSG46.

POSTED BY: Ray Chandler
POSTED BY: Marc Vicuna

@ray chandler Why should the tag be WSG46? I thought the tags for the WSG were always WSGYY where YY are the last 2 digits of the year when the WSG was held. This pattern has been followed for dozens of WSGs over the last 5 years.

What is the significance of the tag WSG46, Mark? What does that stand for?
POSTED BY: Phil Earnhardt

@Phil Earnhardt, you're correct, we mixed up our tagging system for Wolfram Daily Study Groups. The community tag has usually referenced the year, but we also use WSG code numbers (mostly internally) to track our Study Groups in the order they are scheduled and organized by Wolfram U staff. The Introduction to Discrete Mathematics is our 46th Wolfram Study Group, so that's where that tag came from. Thanks for being an active participant in this initiative.
POSTED BY: Jamie Peterson

Download of zipped lesson files is missing Lesson 1. First file with no name is another copy of Lesson 16.

POSTED BY: Ray Chandler

Hello Ray,

It seems strange you don't have access to Lesson 1, I see it on the shared folder for the study group. In the mean time, here is lesson 1 is here in cloud and attached too.

Best, Marc

Attachments:
Lesson 1.nb
POSTED BY: Marc Vicuna

Sorry, I was able to download the individual Lesson 1 file so I had access. I just thought you might want to correct the zip file before you go production.

POSTED BY: Ray Chandler
POSTED BY: Phil Earnhardt
POSTED BY: Marc Vicuna
Updating Name
Updating Name
Posted 1 year ago

Looks like we start with Lesson 12 tomorrow. What about Lesson 11?
POSTED BY: Updating Name

Hello,

Indeed, the study group does not follow exactly the order of the lessons in the course, due to the restriction of 3 lessons per days. Instead, we will cover lesson 11 Monday, along with 2 other lessons about different types of proofs in discrete mathematics.

Best, Marc
POSTED BY: Marc Vicuna
POSTED BY: Jürgen Kanz
POSTED BY: Marc Vicuna

Hi Marc,

I am struggling with a statement in “Lesson 4 - Predicate Logic.nb”, Slide 6: enter image description here This is a special case of existence. -> I agree

It is unique and is denoted by ... -> Is it correct to say that Mathematica cannot print the right symbolic? Otherwise, the output of "Exists[x, x == -x]" is wrong.

Please clarify.
POSTED BY: Jürgen Kanz
POSTED BY: Marc Vicuna
José Dordá
José Dordá
Posted 1 year ago
POSTED BY: José Dordá

Hello.
POSTED BY: Richard Charette
POSTED BY: Marc Vicuna

Hello Marc!

I'm here to learn and to offer feedback.

Most of the lessons seemed fine in yesterday's recording. However, there was an issue with the photo of the woman chosen to portray "disorientation" and "confusion" at the 31:41 time stamp. The photo is misogynistic and inappropriate. Instead, try using a more generic image, such as a stick figure or a confused puppy with question marks all over it. This would be more appropriate and add a touch of humor to the presentation.

See you at 11AM.

Lori
POSTED BY: Lori Johnson
POSTED BY: Marc Vicuna

Thank you, very, very much for understanding!

POSTED BY: Lori Johnson
POSTED BY: Phil Earnhardt
POSTED BY: Dave Middleton
POSTED BY: Marc Vicuna

Thank you Marc,

I will explore the route to simplify and analyze set expressions in logical form and transfer them to sets later.
POSTED BY: Dave Middleton
POSTED BY: Dave Middleton
POSTED BY: Marc Vicuna

Hello Wolfram community!

This course will start in 15 minutes! If you're interested, join us now with the link above!

Happy learning to all!
POSTED BY: Marc Vicuna

Registered! The best Group Theory thing I ever figured out on my own: the late Skwish Toy inventor Tom Flemons pointed out to me that his manufacturing operation made the toy with a single elastic line that was segmented when the balls were glued to the end of the rods. That makes the lines of Skwish an Eulerian Cycle. In my University class, all of the groups used as examples for cycles, etc., were flat (and boring!) drawings on a page; I suggested to my prof to use the Skwish geometry on a problem set to mix things up a bit. The Manhattan Toy product is the best-selling tensegrity model on the planet, but most of the customers seem to just chew on it. :)

enter image description here
POSTED BY: Phil Earnhardt

Marc Vicuna has done a great job in developing this thoroughly up-to-date introduction to Discrete Mathematics.

I strongly recommend the Study Group to everyone!
POSTED BY: Devendra Kapadia

Hi Davendra!

I've enjoyed three of your courses. Nice to 'see' you again :-D
POSTED BY: Lori Johnson

Hello Lori,

Thank you very much for your active participation and support for these online courses!
POSTED BY: Devendra Kapadia

Well, Mathematica is addictive nerd candy and you Wolfram folk are pretty nice, online and in person. It's hard to stay away!
POSTED BY: Lori Johnson
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