Why You Cannot Mix and Match Textbooks in College STEM Courses
This lesson explains why students in college STEM courses are expected to remain consistent with the assigned textbook and course curriculum rather than mixing together terminology, notation, and explanations from unrelated sources.
The lesson uses examples from standard university calculus textbooks to demonstrate how different authors often use different terminology, notation systems, explanations, and organizational structures even when discussing mathematically related concepts.
Different Textbooks Use Different Language
One of the main examples in the lesson compares terminology from Thomas’ Calculus and Stewart Calculus. In one textbook, a concept may be referred to as the “circulation density,” while another textbook may describe the same operation differently or omit the terminology entirely.
The lesson explains that if students begin inserting terminology from outside sources into homework or exams without understanding the assigned textbook’s language, instructors may interpret the work as copied or improperly sourced material.
The Assigned Textbook Defines the Course
A major theme throughout the lesson is that a college course is built around a specific textbook and curriculum. The assigned textbook determines:
- Notation
- Terminology
- Definitions
- Methods
- Proof structure
- Presentation style
- Expected communication standards
Students are encouraged to master one textbook at a time rather than attempting to piece together random explanations from multiple unrelated sources.
Textbook Learning vs Memorizing Internet Solutions
The lesson argues that memorizing isolated examples from internet videos, AI systems, or random tutoring sources does not teach students how to properly study mathematics.
Instead, the goal is to develop the ability to read and understand formal textbooks independently. Once students truly learn how to use textbooks, they can eventually study almost any advanced subject on their own.
Professional Communication Matters
The lesson explains that mathematics and physics are professional communication systems. Students are not only learning formulas. They are learning how to communicate technical information in a standardized academic format.
Using inconsistent notation or terminology from unrelated sources can create confusion and make it appear that students do not understand the assigned material.
Integrity and Academic Standards
The lesson strongly emphasizes academic integrity, intellectual honesty, and the importance of doing original work while properly learning from assigned educational resources.
Students are encouraged to avoid relying on shortcuts, copied internet material, or AI generated solutions in place of genuine textbook study and independent practice.
“If you understand how to use a textbook, then you can solve any problem.”
Final Message
The lesson concludes by encouraging students to focus deeply on the assigned textbook, remain consistent with course terminology, and develop real long term mathematical literacy rather than relying on fragmented outside material.
Learning how to properly read and use textbooks is presented as one of the most important long term skills for success in mathematics, physics, engineering, and other technical fields.
Transcript reference: :contentReference[oaicite:0]{index=0}
Original Transcript
All right, kids. This is just a real recap, quick recap on the previous two videos I just made. So, I just want to show you guys. So, here’s a here’s a standard syllabus from any regular university. This is UT Dallas Calculus integration. Any regular math, physics, engineering school. It says plagiarism from the web. Portions of papers from other courses from any source is unacceptable. You can use the textbook. In this case, calculus early transcendentials, James Stewart. So, I want to show you exactly why you cannot mix and match textbooks in school and you cannot use thirdparty garbage like Khan Academy or artificial intelligence. It will ruin your future. Okay. In the Thomas’s calculus book, they have something called circulation density. It is the K component of the curl. If you don’t know what that means, that’s okay. If I go here and I go to the Steuart calculus book, this is just one of many, many examples. Okay, this is what gets kids kicked out of class. So, here’s the circulation density in Thomas’s calculus, the K component of the curl. And if I go to the Steuart calculus book, there is no such thing as the circulation of density. All right? And you do have the exact same operation right here. We can rewrite the equation in Green’s theorem in vector form with the K component of the curl. Do you see how this is the K component of the curl which is the circulation density? So when you when we’re in here in Green’s theorem here, they don’t call it the K component of the curl or sorry they don’t call it the um well I don’t know if they call it the K component of the curl either, but they don’t call it circulation density. Those are different names. So, I’ve I’ve had kids for years and years and years, kids watch Khan Academy, they copy the stuff from Khan Academy, they copy whatever book Khan Academy used, they write down something like the circulation density. They turn in their homework. The professor goes, “What the hell is circulation density?” And you’re like, “Well, it’s the K component of the curl.” And they’re like, “No, it’s not. Where in the book does it say that?” And you’re like, “Uh, well, huh.” and and the professor is like, “You’ve plagiarized. We are going to fail you. It’s time for you to leave the class.” And you’re like freaking out because you’re like, “How did I how did I plagiarize? I only cheated. I don’t understand. I took somebody else’s work and passed it off as my own. That doesn’t make any sense.” So, if you go to Khan Academy or AI or some other cheating platform or a private tutor and they and they write down the circulation density is the K component of the curl to do the integral when you’re doing K’s uh Greens theorem. You’ll be asked to leave class for plagiarizing and then you’re like, I don’t understand how that is plagiarizing and it’s only because you’re there to study that textbook and only that textbook and you left the textbook and you took other people’s work and pass it off as your own. That’s plagiarizing. Define plagiarism. The act of presenting someone else’s work ideas or words in your as your own without proper acknowledgement or permission. Okay, you go to Khan Academy. First of all, they plagiarized this book without the permission of the author. I’m referencing the book here. I’m not taking it out of the book and claiming it to be mine like Khan Academy did. They copyright infringed the crap out of this. They don’t have the right to use these formulas and theorems without the author’s permission. There’s a gray area with education, but they’re not an educational platform. They’re a social media company. They don’t have the right to do that. I have the right to do this because this is an open source that I cited the source of where I’ve got the books in an open source and I’m showing you the actual book and I’m not claiming this is my work. Khan Academy stole this work and claims it’s their work. They are gigantic copyright plagiarizing company. They have no integrity and they steal money every day from unsuspecting donators that are duped by con artists. Ironic that it’s named Khan Academy because it’s a con artist company. You cannot use this stuff in college, okay? You shouldn’t be using it in high school. If you’re a high school teacher, you should be teaching your kids how to use textbooks, not cheat with Khan Academy and AI. If you don’t know how to use a textbook, you’re not doing math. So, if you’re in Thomas’s calculus and or Steuart’s calculus and you use the word circulation density, you’re plagiarizing. You’ll be asked to leave class. You’re not doing the math correctly. You’re in the wrong field. You cannot mix and match these things. Period. You got to get with the program. You either worship the textbook and stick with your curriculum or leave this field. you’re wasting your time. There’s no shame in that. Not everybody can do this. Even if you have a strong passion for it, it is not for everybody. There is no way I could do a business degree, okay? No way in hell I could finish a government history or business degree. Never in a million years could I do that. The only thing I could do is math. You know why? Because I’m not a liar. It’s easy for me to do math because I’m not a liar. And that’s the problem that most of you guys have. You’re all liars. You can’t do math if you lie and you’re in denial. So, but this is why you can’t mix and match textbooks,