Why STEM Students Cannot Mix Textbooks, AI, and Internet Sources
This lesson continues the discussion about why STEM students are expected to follow the assigned textbook, notation system, and syllabus structure within their university courses.
The lesson explains that even when two textbooks appear mathematically similar, their notation systems, theorem statements, terminology, assumptions, and structural definitions can differ significantly.
Why Different Textbooks Create Problems
The lesson compares several calculus and algebra textbooks and demonstrates that the same mathematical concepts are often presented differently depending on the author.
Examples discussed include:
- Absolute value function notation
- Piecewise function definitions
- Fundamental Theorem of Calculus notation
- Green’s Theorem notation
- Curl notation and circulation density terminology
Even when the mathematics is ultimately equivalent, the presentation and terminology may differ enough that instructors recognize immediately when students are copying notation from outside sources rather than following the assigned course material.
The Assigned Textbook Defines the Language of the Course
A central theme of the lesson is that mathematics is a professional communication system. The assigned textbook defines:
- Definitions
- Notation
- Theorems
- Conditions
- Terminology
- Structure of proofs
- Communication standards
When students bring notation from unrelated internet sources, artificial intelligence systems, or external textbooks into the classroom, they may create confusion because the notation no longer matches the assigned curriculum.
The “Circulation Density” Example
One major example discussed in the lesson involves the phrase “circulation density” used in one calculus textbook while another textbook refers only to the K component of the curl without using the same terminology.
The lesson explains that if students copy terminology from unrelated sources without understanding the assigned textbook’s presentation, instructors may interpret the work as improperly sourced or copied material.
The broader point is not simply about memorizing terminology. The point is that every textbook develops its own internal communication structure and students are expected to remain consistent with the language of that course.
Textbook Literacy Is the Real Skill
The lesson repeatedly emphasizes that college mathematics is not about memorizing isolated worked examples from videos or artificial intelligence systems.
The real long term skill is learning how to:
- Read textbooks carefully
- Follow formal notation systems
- Interpret theorem conditions
- Understand definitions precisely
- Communicate mathematics professionally
- Work independently through difficult material
Students who learn how to use textbooks correctly eventually gain the ability to study advanced mathematics, physics, engineering, and scientific subjects independently.
Why AI and Internet Sources Can Become Dangerous
The lesson warns students that internet platforms, AI systems, random videos, and copied solutions often mix terminology and notation from many unrelated textbooks without clearly identifying the source material.
This creates major problems because students may unknowingly combine incompatible notation systems while believing the material is identical.
The lesson argues that this weakens genuine understanding and encourages students to memorize patterns rather than develop real mathematical literacy.
“If you can’t get through your thick skull that you are in that class to study the textbook they slam on the table in front of you, you’re in the wrong field.”
Final Message
The lesson concludes by encouraging students to commit fully to the assigned textbook, the course syllabus, and the professional communication standards of the class rather than relying on fragmented internet material.
The long term goal is not simply solving homework problems. The goal is developing the ability to think, communicate, and study like a professional scientist, mathematician, engineer, or technical expert.
Transcript reference: :contentReference[oaicite:0]{index=0}
Original Transcript
All right, kids. I’m just going to show you why you’re uh you’re ruining your education here when you’re using AI and Khan Academy and things like that. So, in the previous video, I showed you this. It’s just a standard syllabus from UT Dallas standard calculus syllabus. They tell you plagiarism, especially from the web, from portions of the paper of other courses and any other sources is unacceptable and will be dealt with the university’s policy on plagiarism. They say plagiarism to snuff out argument. They’re saying, “Kid, I’m not going to argue with you. If you do this, we’re going to ask you to leave.” Okay? You’re paying us a lot of money to guide you through the textbook. You either let us guide you through the textbook or get the hell out of our class because you’re not welcome here. Uh we’re not going to let somebody who lies and cheats and steal be in a environment that requires people’s the the work that you’re going to do as a scientist. People’s lives depend on your ability to be trustworthy. We are not going to let lying cheats pass through the system into that world easily. [laughter] You might be able to slip on through, but then you got to deal with the next level. That’s the people who interview you. People like me, lie detectors. If you’re a lying, cheating, pirating felon, you are not going to get very far in this world, no matter how good you can balance equations, cheating with AI. Okay, so let me show you this this book here, Calculus Early Transcendentials, ETH edition. All right, this is the textbook that they want you to use. So, I have this book in my collection of books here and I have my citations for it for where I found them because I am not a criminal stealing these things. I’m getting them from open sources illegally and if I can’t find them, I buy them. And these this book here, James Stewart Calculus, this is the seventh edition of the book. I found it here at this website. And uh this is not illegal for me to look at this book at this website. It is illegal for you to download this through pirating software or and torrenting software. Torrrenting software may not be illegal yet, but pirating software is. So this book here is essentially it’s open source. Whoever has it hosted either has the right to have it hosted or will be asked to cease and desist or whatever the website at some point. As a consumer, it’s not your responsibility to make sure an open source has legal content on it. So uh anyways, just just to point that out. But the reason why you know these the reason why artificial intelligence artificial intelligence and Khan Academy they will destroy your STEM education. You you’re in the wrong field if you can’t abandon that stuff. When you’re in these textbooks at the very beginning of the book there is a preface chapter and there is introductory information. In the preface chapter here uh or at least in chapter one let me let me go to chapter one. This book it’s called chapter one is sometime or well they got a preview here diagnostics whatever all the stuff that comes leading up to chapter 1 is usually the rules and conditions that you can use within the book depending on how they structure the book. But here it looks like we’re just starting at chapter one. So in chapter one here what they’re doing is they’re introducing you to the rules, properties, theorems that are allowed to be used. Okay. So I I want I want you to guys to look at this here. Does anybody know what this is? Is essentially it’s talking about this right here. Right? The absolute value of xgx x if x is greater than equal to zero. This is this is the absolute value. That’s a function. Okay. Now I want you to look here. If I go to another book, I go to say an algebra book. I go to Sullivan algebra
and here if I go to the absolute value function
their definition for the absolute value function hate when that happens is almost the same if not the same let me see here they got for here they got x is greater than equal to zero when x so if you got the absolute value of a is a x is greater than equal to zero absolutely is greater than equal to zero and so these are essentially the same definitions in these two books I mean that is the same they’re both the same but if I go to another algebra book
I believe in this one the definition is nearly the same but it’s written upside down I believe the way they did yeah they so they they wrote the same exact exact thing here.
So they they wrote the exact same thing for the definition of the absolute value except for they have negativex on top and x on the bottom. Here here they don’t have it as a peiewise function here. They just have them together like this. And here they have them together and as a peace-wise function. Notice how he’s got negativex on the bottom with x less than zero and x less than zero with negative x on the top here. Those are two different definitions. I know it seems like they’re exactly the same because they essentially are, but because the author flipped the negative x on top and this one has it on the bottom, they’re two different they’re two different definitions. And if you c I know this unlikely that you would lose points this way, but if you copy the definition from here and you’re in this book and you use this definition, technically it’s wrong. And it may seem at this level to you it’s like that’s ridiculous like that it seems so so silly such a small thing and I I understand that but when you get really deep into math the notation you use and the structure of the definitions at the beginning of the book they affect the calculations at the end of the material that tiny little alteration can have a huge impact on the uh re the calculations that you have later on. And it’s um [snorts] it’s important to understand that the definitions in these books are often written differently. They have different definitions. This is like fundamental theorem in calculus. In this book, they give you the definition for the fundamental theorem of calculus part one as g of x from a to x here. But there is another definition that is important. And I let’s take a look at the Thomas’s calculus and see what they um what they wrote in the Thomas’ calculus book.
if they write the exact same thing. So this is fundamental theorem of calculus.
So I got the mean value fundamental theorem part one. So in this book they are giving it the definition frime of x is the derivative da da da is lowercase f. Get these books out of here. And in this book they are giving it to you. They’re they’re telling you the exact same thing. F of t g ofx is equal to this. If you take the derivative of this g prime then it’s f ofx. x x is between a and b. And here they it’s it’s essentially the exact same thing in this case. It’s just written a bit differently. My point is that if you’re in this book and you write if you write it like this and you’re in the Steuart book, if you use this definition, which you might see on a YouTube video, because they don’t site, nobody cites any sources on YouTube, it’s all gibberish. Anything you watch on YouTube is nothing. It’s gibberish. If you continue watching people on YouTube that scribble on coloring boards without citing or referencing the books they’re in and verifying everything under the conditions of those books, you are a fool. You need to leave STEM immediately. It’s not helping you. Uh but uh for the most part [snorts] for the most part these definitions are essentially the same but the notation and the structures can change and the definitions themselves can definitely change. In some in some books you are going to see certain theorems that have like eight conditions and other books will have like 10 conditions and it just changes. But it’s it’s the the point is is that when you’re when you guys are in when you are in these books, okay, the purpose the purpose of the course is to have a professional guide you through learning how to use the textbook assigned. If you guys use anything from the internet, other courses, other s sources, you’ve got people here that wrote this syllabus for you. We’ve been doing this stuff for decades and decades and decades to snuff out argument. We tell you, look, if you don’t want to follow the syllabus, you should leave this degree. It’s not for you. And you’re like, uh-uh, I can just memorize songs and I can play songs and people will hire me to read and write sheet music after I learned how to listen to songs on the radio. That doesn’t make any sense. Listening to music is learning how to play a musical instrument. That’s how you guys sound when you watch Khan Academy and use artificial intelligence to help you cheat with your homework. You’re like, you’re like listening to the radio. That’s how you learn how to play guitar, dude. Like, duh. Like, cuz that’s all you’re doing. You can memorize the melody of that song. You’ll never be able to play it on a musical instrument. You can memorize the solution to fake problems. These are all fake problems. They’re not real problems. The solutions to these questions are not real. This is theory. You are working in theory, non-dimensional language. It’s not real world questions. So when you copy fake solutions to fake problems from fake sources, you’re getting a fake education. Let’s take a look at the substitution rule. Okay, it’s not you substitution. It doesn’t say you substitution. It says the substitution rule. You guys all have a real problem with that. The substitution rule here. So here is uh f of g ofx g prime of x. And there here they got f of g ofx g prime of x. They have the same one. They have the same exact theorem in both of these books for this one. And so those theorems are identical. These two books are essentially identical. I mean, they really are identical. And it it’s you will get to the same destination with each which is with each of these books. But the problem is is that the notation changes and the flow and the structure changes. So, if you start using notation and stuff from this book when you’re not allowed to, then uh you’re going to be in trouble for plagiarizing because you’re using the incorrect notations. I know that you guys think that seems silly, but you just don’t understand yet. And people like me who’ve been doing this for longer than you’ve been breathing are like, “Kid, you’re doing it wrong.” And you’re like, “I don’t understand. I’m getting the same answer.” No, you’re not getting the same answer. It’s just coincidental. How do you know that’s the right answer? You don’t. Because in the real world, in the real world, man, the how do you know this is theory? These questions are not real. They’re not it’s not going to apply in the real world. Everything is going to change when you take this out of context, when you take it out and put it into the real world. Uh but anyways, let let’s take a look here in the um Greens theorem notation. Let’s take a look at their notation here. So they here here’s a here’s a sample of something um the scalar expression of circulation density of a vector field. Circulation density. I don’t know if I’ve ever read that word in the Steuart book that. So there’s a perfect example. The expression is also called the K component of the curl denoted by curl of f. K of the vector field. So this is something that you will not find in the Steuart calculus book is the circulation density of a vector field. That’s not in there. But the curl’s in there. And do they talk about that component of the curl in this book ever? Let’s go here to
curl and divergence. So they don’t they don’t talk about that in this book.
And this is where you guys are going to run into big problems when you are using internet to cheat. You’re going to run into big problems because you’re going to have so so look at this curl of f. K. Curl of f.k. Pay attention to this. So this is the greens theorem in the vector form can be rewritten as curl of f.k. The tangential component. In this book, they did not label it as circulation density. So if you use that term circulation density, that is not in this book. But here is that exact same formula right here. Okay? That’s exactly what they’re telling you right here. The curl of f. K is equal to this right here. if you have M and N and uh however, you know, it’s um there’s some discrepancies with what they’re talking about here because the curl is some whatever that’s a different story. But my my point is kids, my point is to you that this book is not the same book. It ultimately will get you to the same destination, but the definitions and the theorems are different. If you use this definition, circulation density, and you are in Stuart calculus book, the professor is going to say, “What the hell is circulation density?” And you’re going to say, “Uh, well, it’s the K component of the curl.” And the professor is like, “No, it’s not. The K component of the curl is the K component of the curl. What is circulation density?” And you’re like, “Uh, well, uh, I didn’t cheat. Well, where did you get this from? We’re in Stuart calculus. Where did you get this circulation density from?” and you’re like, “Uh, well, I what?” Uh, and and you’re getting kicked out of class for cheating and plagiarizing. And the professor keeps asking you, “Where did you get if you didn’t cheat or plagiarize? Where the hell did you learn circulation density?” And you’re like, “Well, I I use Khan Academy.” And that’s what they called it. And the professor is like, “Did you read the syllabus, kid? Says you cannot use Khan Academy right here.” And nothing from the internet, nothing from other courses, period. No artificial intelligence. You can use the book. And now you’re taking you’re taking definitions from other books and you’re passing it off for this book. You’re you’re not doing math. You’re just randomly writing things down. So be very careful, okay? Because these books are not the same. You can’t leave the book. And if you can’t get that through your thick freaking skull that you are in that class to study that textbook that they slam on the table in front of you, you’re in the wrong field. All right? trying to help you, okay? Don’t take it personally. There’s no shame in switching your major. It’s better to switch your major in calculus one before you get too deep. If you if you cheat through calculus one, two, three, linear algebra, differential equations with Khan Academy and AI, you’re going to get way too deep into this degree. It’s going to be over for you. Have a nice day.