Math for Computation
James B. Wilson
Professor of Mathematics
Vibe Coding
Start typing what you plan to do.
Let generative AI (ChatGPT, Copilot, Claude, Gemini, Grock...) fill in what is missing.
Leans on expert experience, fast, what everyone talks about.
What can the University even offer?
Common
Sense is
Inconsistant
\[\begin{array}{rl} A & \to B\\ A & \to C \\ \hline A& \to B \& C \end{array}\]
-
If you are an admin then you can add users.
-
If you are an admin then you can remove users.
If you are an admin then you can add AND remove users.
If Admin then Add
If Admin then Remove
If Admin then Add AND Remove
\[\begin{array}{rl} M & \to A\\ M & \to R \\ \hline M & \not\to A \& R \end{array}\]
-
If you have at least 12 core then you can stream in 1080p.
-
If you have at least 12 cores then you can host multiperson games.
But if you have 12 cores then YOU STILL MIGHT NOT HAVE ENOUGH TO STREAM AND HOST MULTIPERSON GAMES
Which seems right?
\[\begin{array}{rl} A & \to B\\ A & \to C \\ \hline A& \to B \& C \end{array}\]
\[\begin{array}{rl} A & \to B\\ A & \to C \\ \hline A& \not\to B \& C \end{array}\]
The vibe
What if both are wrong but both are clues to what is right?
\[\begin{array}{rl} A & \to B\\ A & \to C \\ \hline A& \to B \& C \end{array}\]
\[\begin{array}{rl} A & \to B\\ A & \to C \\ \hline A& \not\to B \& C \end{array}\]
\[\begin{array}{rl} A & \to B\\ A & \to C \\ \hline A\& A& \to B \& C \end{array}\]
If \(A\) is the type of claim where \(\frac{A \&A}{A}\).
Don't get carried away when \(A\& A\) is different from \(A\).
\(A\& A \vdash A\)
-
Unplugged & Unplugged is... unplugged
-
Admin privalages stay with you as many times as you need.
-
Your examples?
\(A\& A\not\vdash A\)
-
"Click mouse" And "Click mouse" is NOT the same as "Click mouse".
-
Cookies needs 1 cup of sugar and brownies need 1 cup of sugar... you need 2 cups of sugar!
-
Your examples?
Math for computaiton teaches you different logics.
Common
Sense needs
Context
Truth
- You came to class.
- \(2+3=5\)
- Puffer fish are poisones to humans
Truth is immutable, a fact, it doesn't change, and its different from Falsity.
Truth
-
You must be a subscriber to read articles.
-
You are a subscriber.
-
Therefore you can read files.
-
But you forgot your login password, so you are a subscriber but you can't prove it!
needs Evidence
Truth
- You arrive late to the airport and see a long line.
- Quickly you open you phone and reserve a spot in the express line.
- Confidently you walk over to the express line but you get stopped. Your name isn't on the list. You show the clerk you confirmation, but when they check they don't have you!
can also be Falsity
The real truth of Truth & Falsity
Classical Logic
Just True,False
Intuitionistic Logic
Truth comes from evidence
Paraconsistent Logic
True/False and some overlaps
Math for compution teaches you different facts about truth.
Common
Sense needs
Humans
Connection Manager
- You visit a webpage but get no page found error.
- You try again, and again.
- It is time to contact company to say their webpage is down.
- Wait, you never used the site before, maybe you should check that you have the right page!
Math for computaiton teaches you options for defaults and adaptations.
Math: made by humans to help humans.
Get you some.
Math for Computation
By James Wilson
Math for Computation
In the age of vibe coding what can reasoning offer to a modern programmer?
